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# Calculate The Value Of The Equilibrium Constant For The Reaction Yahoo

The equilibrium constant for a reaction is 10. The first stage is to fill in the missing values in the table. 50 x 10-5 moles O 2, and 2. (1) (v) Write an expression for the equilibrium constant, K c, for the reaction. Now we're gonna use the So the reaction goes to completion, all right, with a huge value for the equilibrium constant like that, you pretty much don't have anything for your reverse reaction. Calculating The Equilibrium Constant Keq. (Use the reaction free energy given below. If one removes original substances from a reaction in this state, one increases the formation or the exploit. 0 kJ/mol thanks!!!. Because saponification values are listed in KOH (potassium hydroxide) the value must be converted from potassium to sodium to make bar soap; potassium soaps make a paste, gel or liquid soap. Describe the changes that occur after each stress is applied to the equilibrium. What is the significance of the value of Kc in this case? I have the answers for all but the Kc value. It depends on the ionic strength and temperature and is independent of the concentrations of reactants and products in a solution. forward and reverse reactions are elementary), so at equilibrium: Rate 1 = Rate-1 → k 1[N2O4] = k-1[NO2]2 [N O] [NO ] 2 4 2 2 1 ⇒ 1 = = − K k k →K is a constant which depends on T (K = 0. the answer is 1. Chemical Equilibrium Consider a reversible reaction taking place at constant temperature: aA + bB cC + dD The reactantsA and B combine to form productsC and D. Recognize the characteristics of chemical equilibrium. at equilibrium:. Solution: Calculate the value of the equilibrium constant for the reaction:D in equilibrium with A + 2 B, A + 2 B in equilibrium with 2 C, K c = 2. Using the chemical reaction given above, we can rewrite the Equilibrium constant expression to reflect concentration. 9 x 10-3 H+ + PO43- HPO42- 2. Answer to: Calculate the value of the equilibrium constant K for the reaction 2D ? A + 2B from the following information A + 2B ? C K_c = 3. In contrast, recall that according to Hess’s Law, Δ H for the sum of two or more reactions is the sum of the Δ H values for the individual reactions. Since the equilibrium constant is decreasing as heat is added, this means the amounts of products are decreasing and the amount of reactants are increasing. Recognize the characteristics of chemical equilibrium. (1) (v) Write an expression for the equilibrium constant, K c, for the reaction. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 6 x 108 calculate the numerical value of the equilibrium constant for the following reaction at the same temperature. The cause for these incorrect readings was most likely human error, such as incorrect measurement. If the volume of the container is reduced to one-half of its original volume, the value of the equilibrium constant will be [JIPMER 2001]. The concept of site availability (σ s) is introduced, whereby it has the capability to reduce the reaction rate. 0μ10-14 Now, we have seen that the equilibrium constant of a sum of two reactions is the product of the equilibrium constants of the summed reactions. You can calculate the effect of changing temperature on Thus, if you know the #ΔH^°# and the equilibrium constant at one temperature, you can calculate the equilibrium constant at some other temperature. Equilibrium Constant Kc and How to Calculate It. Melhor resposta: We can't figure it out unless you give us Ka or Kb and the initial concentrations of the weak acid/base. Use the concentrations of tetraborate ions and sodium ions to calculate the equilibrium constant. However, the value of K will not depend on the initial concentrations of reactants and products. Equilibrium Constant Determination INTRODUCTION Every chemical reaction has a characteristic condition of equilibrium at a given temperature. The equilibrium expression will be as shown below Therefore, it is important when the value of an equilibrium constant is quoted that the equation is also specified. 4 mole of iodine and 2. An equilibrium experssion can be formulated based on the chemical reaction rates for the forward and reverse reactions. A large value of K implies that there are more products than reactants and that the equilibrium lies to the right. 8 x 10-4 for HCN and HNO2 respectively, calculate the equilibrium constant for the following reaction: HCN + NO2. Equilibrium constants can be used to calculate the equilibrium concentrations of reactants and products by using the quantities or concentrations of the reactants, the stoichiometry of the balanced chemical equation for the reaction, and a tabular format to obtain the final concentrations of all species at equilibrium. (2) PhysicsAndMathsTutor. Equilibrium Constant Kc and How to Calculate It. If the equilibrium constant is involved, make sure that the concentrations you use are the concentrations at equilibrium , and not the concentrations. The equilibrium constant for the reaction: 2F 2 (g) + O 2 (g) ⇆ 2OF 2 (g) at a particular temperature, a 2. If one removes original substances from a reaction in this state, one increases the formation or the exploit. So, the reaction is in equilibrium. What is the value of the equilibrium constant for the reaction, 2. The reaction for the formation of HF (g) from H 2 (g) and F 2 (g) has an equilibrium constant of 1. If we measure concentration of a product, it reaches a constant value short of that predicted by the theoretical yield calculation. The equilibrium constant for the reaction is determined the standard free energy change: ΔG° = RT ln K p; The sign of the temperature dependence of the equilibrium constant is governed by the sign of ΔH°. The quantitative aspects of equilibrium are explored thoroughly through discussions of the law of mass action as well as the relationship between equilibrium Now using this information we can actually calculate the K_p value for this reaction. Unit 2 Notes - Equilibrium. Context for Use. K in the conversion and convert temperature to. Partial pressures are used for calculating the pressure constant. And then the rather trickier ones. Because saponification values are listed in KOH (potassium hydroxide) the value must be converted from potassium to sodium to make bar soap; potassium soaps make a paste, gel or liquid soap. It should be consistent because this constant is dened to. 9 to a high of 421. The cause for these incorrect readings was most likely human error, such as incorrect measurement. If Kc is greater than Q, then the reaction proceeds in the Write the reaction quotient formula. 45x 10^ -a. 314 J/mol•K a. The thermodynamic equilibrium constant $$K$$ is the proper quotient of the activities of species in reaction equilibrium. 520 M and [C] = 0. Magnitude and direction of the Chemical Equation and K. The equilibrium constant built in aspen has the following equation: ln (Keq) = A + B / T + C*ln (T) + D*T. This preview has intentionally blurred sections. calculate the equilibrium concentrations of the reactants and products. Calculate the equilibrium constant, Kc, for the reaction. 50 x 10 ^-5 mol/L 2) [H2]= 3. (e) State the effect, if any, of an increase in temperature on the value of Kp for this reaction. Jif the initial amount of AgI is 0. The equilibrium shifts to oppose the change, returning the system to having equal rates on both. 001, implies that the reaction has not proceeded to a significant extent. You will then add the forces analytically by adding their components and graphically by drawing the vectors and determining if they add to zero using the rules for the addition of force vectors listed above. The equilibrium constant is related to the concentration (partial pressures) of the products divided by the reactants. Equilibrium constants (Keq) are a way of the quotient of a reaction which has reached equilibrium. 0 degrees C is 1. 00-L flask is filled with 0. The equilibrium constant is a ratio of the concentration of the products raised to the appropriate powers to the concentration of the reactants raised to the appropriate powers. and is a mathematical number, a bit like pi. If we measure concentration of a product, it reaches a constant value short of that predicted by the theoretical yield calculation. ii) Predict the direction in which the reaction will proceed at 700. 0183 regardless of what we might try to do with the concentrations. write the equilibrium-constant expression and calculate the value of the equilibrium constant for each of the following reactions at 298 K. (Use the reaction free energy given below. Demonstrate that reaction mixtures with differing concentrations of reactant. 10 x 10^2 grams of solid NaHCO3 had been placed in the 5. It depends on the ionic strength and temperature and is independent of the concentrations of reactants and products in a solution. Equilibrium Constant Kc and How to Calculate It. at equilibrium:. For the same reaction, calculate the molar concentration of reactants and products at equilibrium if initially 1. (Use the reaction free energy given below. 00 mol of H 2 and 6. Use the data to calculate the. Therefore, in our experiment Fe3+ ions and SCN- ions used to calculate the equilibrium constant Kc of formation of FeSCN2+ solution. How would the calculated value of the equilibrium constant be affected for this sample? With the increased volume of the solution, the. 0μ10-14 Now, we have seen that the equilibrium constant of a sum of two reactions is the product of the equilibrium constants of the summed reactions. What is the significance of the value of Kc in this case? I have the answers for all but the Kc value. 2 kilo joule per mole at what temperature will the reaction become spontaneous during dialysis and their lives to be constant over the temperature range is 10. integrated form, it looks like so, and this relates equilibrium constant K2 at temperature T2, equilibrium constant K1, temperature T1, heat of reaction, the gas constant, so with just two data point we could calculate delta H if we want to be more accurate and use the three data points we could use the form that this equation was derived from. Practice Problems. However, the value of K will not depend on the initial concentrations of reactants and products. The quantitative study and measurement of heat and enthalpy changes is known as thermochemistry. So the reaction is shifting from right to left. Notice that the ratio is always written with the products over the reactants. A catalyst speeds up both forward and backward reactions by equal amounts, hence it has no effect on the position of the equilibrium and just speeds up the rate at which. Calculate the equilibrium partial pressure (atm) of ammonia, assuming that some solid NH4HS remains. equilibrium constant. 2 educator answers. 314 J/mol•K a. (a) NaHCO3(s) NaOH(s) + CO2(g) Answer: Keq = PCO2 (b)Value of the Equilibrium Constant:. Calculate Kc for the reaction below. 42% of the molecules are in the chair form. Kc =[A2B] / [A2][B] = 0. 105; Kp = 2. The rate constant for the reaction H 2 (g) + I 2 (g) ---> 2HI(g) is 5. All the equilibrium constants tell the relative amounts of products and reactants at equilibrium. Consider the Reaction between Hydrogen and Iodine. 50M CH4 ad 0. 0 If [A] were not equal to 3. 00 M, and [C] = 0. Demonstrate that reaction mixtures with differing concentrations of reactant. When equilibrium is attained, the pressure of IBr is 0. Many organic reactions are reversible and will reach equilibrium in time. N2(g) + 3 H2(g) 2 NH3(g) PNH3 = 3. What are the pressures of I 2 and Br 2 at this point?. The equilibrium constant at 427 o C for the reaction: N 2 (g) + 3H 2 (g) 2NH 3 (g) is K p = 9. I can state what is equal at. 00mol of NOCl was placed in a1. In other words (K 2b) 1/2 = K 3b or (0. Context for Use. The relationship between the products and the reactants in an equilibrium reaction is expressed with the help of the equilibrium constant (denoted by K). Homework Help: Calculate the equilibrium constant Kc for the reaction at this temperature. The thermodynamic equilibrium constant $$K$$ is the proper quotient of the activities of species in reaction equilibrium. 1 10-3 atm Calculate the value for the equilibrium constant Kp at this temperature. Similar Questions. The change in each quantity must be in agreement with the reaction stoichiometry. 0 If [A] were not equal to 3. By comparing the value of Q to the equilibrium constant, K eq, for the reaction, we can determine whether the forward reaction or reverse reaction will be favored. The equilibrium constant from 3b is the square root of the equilibrium constant from 2b. 0 kJ/mol Enter a numeric answer only. 600 M, [B] = 1. Calculate the value of the equilibrium constant, Keq , for the following reaction at 298 Kelvin. Importantly, K is temperature-dependent. Introduction: In order to calculate the equilibrium constant for a reaction, one must first be familiar with the notion of dynamic equilibrium. Economic equilibrium is a situation of the balance of economic forces and in this article, we'll talk about the equilibrium Price and Quantity. Suppose the following information reflects the closed economy of Casolari Land. Why reactions come to equilibrium. This chemistry video tutorial provides a basic introduction into how to solve chemical equilibrium problems. Calculate the value of the equilibrium constant please help me solve this. a thermodynamic equilibrium constant, denoted by ⊖, is defined to be the value of the reaction quotient Q t when forward and reverse reactions occur at the same rate. Calculate the value of the equilibrium constant for reaction 3-di-t-butylcyclohexane exists in two forms that are known as the "chair" and "boat" conformations. Once you know its heat capacity, you can use a calorimeter to calculate the specific heat of an unknown substance. I have lab values for the reaction, however, this was a stand alone post lab question and did not direct me to use the lab values. The thermodynamic equilibrium constant $$K$$ is the proper quotient of the activities of species in reaction equilibrium. At chemical equilibrium , the chemical composition of the mixture does not change with time and the Gibbs free energy change Δ G {\displaystyle \Delta G} for the reaction is zero. The equilibrium constant for a reaction that is the sum of two or more reactions is equal to the product of the equilibrium constants for the individual reactions. The maximum frictional force (when a body is sliding or is in limiting equilibrium) is equal to the coefficient of friction × the normal reaction force. (iv) Calculate the number of moles of ethyl ethanoate formed at equilibrium in the first test tube. But the forward and reverse reactions are in balance at equilibrium, so there is no net change in the concentrations of the reactants or products, and the reaction appears to stop on the macroscopic scale. The equilibrium constant Kc for the following reaction is equal to 0. And then the rather trickier ones. The rate constant for the reaction H 2 (g) + I 2 (g) ---> 2HI(g) is 5. Our techniques for working diprotic acid or diprotic base equilibrium problems can be applied to triprotic acids and bases as well. Answer to: Calculate the value of the equilibrium constant K for the reaction 2D ? A + 2B from the following information A + 2B ? C K_c = 3. An equilibrium mixture in a 2. The equilibrium constant for the ionization of an acid is called the acid ionization constant (Ka). Assume only one hydrolysis reaction occurs. The equilibrium constant of the reaction : AgI (s) <=> Ag+ (aq) + I-(aq) is 10-16. For a specific reaction, which of the following statements can be made about K, the equilibrium constant?. Use the data to calculate the. asked by @students3479 • almost 2 years ago • Chemistry. Consider the Reaction between Hydrogen and Iodine. Calculating Equilibrium Constants. Economic equilibrium is a situation of the balance of economic forces and in this article, we'll talk about the equilibrium Price and Quantity. 700 M [B]= 1. Calculate the equilibrium constant for the reaction. SO reacts with O2 to produce SO2. Yahoo Products. Describe the changes that occur after each stress is applied to the equilibrium. If explains how to calculate the equilibrium constant k for a new reaction by changing another reaction. Choose an expert and meet online. But the forward and reverse reactions are in balance at equilibrium, so there is no net change in the concentrations of the reactants or products, and the reaction appears to stop on the macroscopic scale. The concentration at equilibrium of one of the reaction products will be measured by titration and this value used to calculate the equilibrium concentrations of the remaining species. If a body is moving, friction will be taking its limiting value. Use Reaction (5) in the Introduction to relate the concentration of tetraborate ions to the concentration of sodium ions. The reaction mechanism involves an adsorption element, where the model is an extension of the Langmuir adsorption model. 4 x 10-2M Total solution volume: 100mL Calculate the equilibrium concentration of Ag+ (uncomplexed). K = equilibrium constant. The equilibrium constant ( K eq) for the reaction aA + bB -> pP + qQ is defined as the following: K eq = [P] p [Q] q / [A] a [B] b. Use equilibrium quantities in calculations involving the equilibrium constant, K. The following equilibrium pressures were observed at a certain temperature for the reaction given below. (iv) Calculate the number of moles of ethyl ethanoate formed at equilibrium in the first test tube. Write the rate law for the reaction. where the value K is the equilibrium constant. 4 mole of iodine and 2. The concept of site availability (σ s) is introduced, whereby it has the capability to reduce the reaction rate. Once the equilibrium concentrations of all the reaction species are known the equilibrium constant will be calculated. So it is not much changed during the reaction and the reaction will be. Calculate a value for K p at this temperature and give its units. 00×10 -3 mol oxalic acid 2 mol H + 1 mol oxalic acid 1 mol OH 1 mol H + 1000. 32 × 10 -24 161. integrated form, it looks like so, and this relates equilibrium constant K2 at temperature T2, equilibrium constant K1, temperature T1, heat of reaction, the gas constant, so with just two data point we could calculate delta H if we want to be more accurate and use the three data points we could use the form that this equation was derived from. 0183 regardless of what we might try to do with the concentrations. If a body is moving, friction will be taking its limiting value. The constant, Keq, defines for equilibrium of the chemical reaction. Activation Energy The activation energy can be calculated by taking the difference of the transition state enthalpy and the reactant enthalpy. The value of the equilibrium constant is not affected by either changes in concentration, pressure or addition of a catalyst. An equilibrium system for the reaction between hydrogen and iodine to give hydrogen iodide at 670 K in a % litre flask contains 0. Now we have to calculate the value of. Calculate the equilibrium constant (Kc) for the reaction at this temperature. Since the reaction is shown going to completion, the rightmost box will most accurately depict the equilibrium concentrations. Calculate the ionization constant of an acid or base from the pH of an aqueous solution of known concentration. All the equilibrium constants tell the relative amounts of products and reactants at equilibrium. This example problem demonstrates how to calculate the equilibrium concentrations from initial conditions and the reaction's equilibrium constant. The point at which a reaction occurs at the same rate in both directions is known as equilibrium. A catalyst speeds up both forward and backward reactions by equal amounts, hence it has no effect on the position of the equilibrium and just speeds up the rate at which. For any reversible reaction, there can be constructed an equilibrium constant to describe the equilibrium conditions for that reaction. At equilibrium,. If two reactants are mixed, they will tend to react to form products until a state is. When calculations involving the equilibrium constant are done, the following tips may help: Always read the question carefully to be sure that you understand what you have been asked to calculate. The equilibrium constant for the ionization of an acid is called the acid ionization constant (Ka). So, your formula looks like this If you would like to try a version of the formula that allows you to have a different periodic payment interval to the compounding frequency, please see the ' periodic. Chemical Equilibrium Hill, Petrucci, McCreary & Perry 4th Ed. a thermodynamic equilibrium constant, denoted by ⊖, is defined to be the value of the reaction quotient Q t when forward and reverse reactions occur at the same rate. 00 mol of F 2 were combined in a 1. The following equilibrium pressures were observed at a certain temperature for the reaction given below. In this experiment we will study the equilibrium properties of the reaction between iron (III) ion, Fe3+,. The equilibrium constant Kc for the following reaction is equal to 0. ) 2NO + O2 = 2NO2 in the gaseous state. Calculate the value for the equilibrium constant for each of the following aqueous reactions? Calculate the value for the equilibrium constant for each of the following aqueous reactions. What are the different. An equilibrium experssion can be formulated based on the chemical reaction rates for the forward and reverse reactions. 50 L reaction vessel at 400ºC. Dynamic equilibrium occurs when the rate at which a chemical substance reacts is equal to the rate at which it is formed. The constant doesn't depend on initial concentrations of the reactants and products, as the same ratio will always be reached after a certain period of time. 2 educator answers. 0 x 10^-14 at 25C and 2. Worksheet #9 Equilibrium Calculations Solve each problem and show all of your work. 5: Calculating Equilibrium Constants - Chemistry LibreTexts. The equilibrium constant,Kc, is calculated from the equilibrium concentration values using the equation:Kc = [FeSCN2+][Fe3+][SCN-]The purpose of the experiment is to calculate Kc of reaction (1) for several reaction mixtures with initiallydifferent concentrations of the reactants, in order to show. Acid/Base Reactions. I can calculate the value of Keq given the concentrations of the reactants and products at equilibrium. I'm not sure which equation is supposed to be reversed. 2 x 10-8 calculate the equilibrium constant for the following reaction. Calculate Kp and Kc for the reaction 4) At 1280C the equilibrium constant for the reaction is 1. Calculate the value of the reaction quotient, Q, for the galvanic cell expressed using shorthand notation below. You don't need to worry exactly what it means, although if you have to do calculations with the Arrhenius equation, you may have to find it on your calculator. (Use the reaction free energy given below. The reaction mechanism involves an adsorption element, where the model is an extension of the Langmuir adsorption model. Describe the changes that occur after each stress is applied to the equilibrium. At equilibrium the pressure exerted by the water molecules at a given temperature remains constant and is Fig 7. Imagine that you are trying to push a book along a table with your finger. Take the following generic equation:. We need to know two things in order to calculate the numeric value of the equilibrium constant: the balanced equation for the reaction system, including the physical states of each species. If a body is moving, friction will be taking its limiting value. 0 degrees C is 1. Equilibrium calculations, Equilibrium constants, reaction quotients, and the state of equilibrium and disturbing equilibrium- Le Chatelier's principle. •Many Reactions seem to STOP before all the reactants are used up. 4 where a = initial number of moles of Fe3+, b = initial number of moles of HSCN, c = number of moles of FeSCN2+ at equilibrium and V = total volume of equilibrium solution. The Chemical Equilibrium Calculator helps researchers in chemical equilibrium constants related calculations. Calculating Equilibrium Constants. For an endothermic reaction (#ΔH# is positive), #K# increases with an increase temperature. When the reaction is at equilibrium, the Kc for the reaction in terms of the molar concentration of the. Calculate the equilibrium constant $K_\mathrm c$ for the following reaction at that temperature With that in hand, we can determine what the equilibrium constant of $(3'')$ would look like and how that can be traced back to the other equilibrium constants. The equilibrium constant Kc for the following reaction is equal to 0. The change in each quantity must be in agreement with the reaction stoichiometry. Calculate the value of the Equilibrium Constant for this reaction at 200°C. Acid/Base Reactions. If the container volume is decreased while the temperature is kept constant, pressure will increase. •The Concentrations of Reactants and Products reach constant values. * Calculations involving pressure assume ideal gas behavior. Calculate the value of the equilibrium constant, Keq , for the following reaction at 298 Kelvin. the value of Kc = 4. The moisture content of wood in an environment held at the constant conditions of temperature and relative humidity will come to an equilibrium with its An Excel spreadsheet (titled "EMC Calculate") is available that will calculate an estimate of the EMC based on the dry-bulb temperature and one of. Solving for the natural log of the equilibrium constant gives the following equation:. 0 g of SO were initially placed in a reaction vessel containing excess oxygen gas, calculate the number of moles of SO that was left if equilibrium was reached when 96. 45x 10^ -1 mol/L 3) [ NH3]= 2 x 10 ^4 mol/L. Furthermore, the specific mathematical form of the equilibrium constant must correspond to the correct chemical equation for the reaction. Summary of the Volume-Change-Shifts in Equilibrium Predicted by Le Chatelier’s Principle. A dynamic equilibrium occurs in a reaction when product and reactant concentrations cease to change and both are being produced/consumed at an equal rate. Calculate the equilibrium concentrations of N2 and H2, and find Kc for the reaction below. (Use the reaction free energy given below. When gases react at equilibrium, it's possible to calculate their pressures using a number known as the equilibrium constant, which is different for each reaction. K has a unique value for a given reaction at a fixed temperature and pressure. A The first step in any such problem is to balance the chemical equation for the reaction (if it is not already balanced) and use it to derive the equilibrium constant expression. The equilibrium constant is a quantity which characterizes an equilibrium in a reaction and is based on the nal concentrations of involved compounds. Calculate the value of the equilibrium constant, Keq , for the following reaction at 298 Kelvin. Calculate Kc for the reaction below. 05175 mol/L, [F(g)] = 0. Practice Problems. Use initial quantities when calculating the reaction quotient, Q, to determine the direction the reaction shifts to establish equilibrium. 81 % decomposed at 873. Yahoo Products. Unless you're asking for equilibrium constant. A model has been derived for the magnesium hydrogenation reaction at conditions close to equilibrium. What will be the value of ${{\Delta }_{0}}$G° ?. It is Q = concentration of products/concentration of reactants, where the concentration is raised to the power of the coefficient. F2(g) = 2F(g) Unit Conversions K = C + 273 Answer: 0. 4 x 10-4 M-1 s-1 at 326 o C. Equilibrium constant. equilibrium by forming more products. This video tutorial helps explain the basics of Calculating the Equilibrium Constant. Each quiz questions has two parts. It depends on the ionic strength and temperature and is independent of the concentrations of reactants and products in a solution. equilibrium was reached at a given temperature, the mixture contained 26. 20 at 250°C. Calculate the value of #K_p# for the reaction #"H"_2(g) + "Cl"_2(g) rightleftharpoons 2"HCl"(g)#, given the following reactions and their #K_p#?. Calculating the value of the equilibrium constant for a reaction is helpful when determining the amount of each substance formed at equilibrium as a ratio of each other. The quantitative study and measurement of heat and enthalpy changes is known as thermochemistry. A large value of K implies that there are more products than reactants and that the equilibrium lies to the right. •Many Reactions seem to STOP before all the reactants are used up. There is a special relation between the standard potential of a redox reaction and the equilibrium constant = , where n is the number of moles of electrons transferred. a thermodynamic equilibrium constant, denoted by ⊖, is defined to be the value of the reaction quotient Q t when forward and reverse reactions occur at the same rate. After equilibrium was established, it was found that 28% of the NOCl had dissociated according to the equation 2NOCl(g) = 2NO(g) + Cl2(g). The equilibrium constant for the reaction is 10 calculate the value of deltaGtheta; Given R=8JK^-1mol^-1;T=300K - Chemistry - Thermodynamics. equilibrium by forming more products. This chemistry video tutorial provides a basic introduction into how to solve chemical equilibrium problems. com The equilibrium constant is the value of the reaction quotient that is calculated from the expression for chemical equilibrium. Calculating The Equilibrium Constant Keq. Also, make sure that no liquids or solids are included in the equilibrium constant. Kc =[A2B] / [A2][B] = 0. 0 1 or 2 g calculate the rate constant k from a rate equation h explain from CHEMISTRY 12 at Cambridge. (iv) Calculate the number of moles of ethyl ethanoate formed at equilibrium in the first test tube. (d) Calculate the value of the equilibrium constant at 25°C for the reaction represented by the equation in part (b). NH3(g) 1 2 N2(g) + 3 2 H2(g). At 410 o C the rate constant was found to be 2. This is what to write: Now, all you have to do is substitute numbers into the problem. For a specific reaction, which of the following statements can be made about K, the equilibrium constant?. A reaction mixture is made containing an initial [SO2Cl2] of 2. Equilibrium Constant Kc and How to Calculate It. If explains how to calculate the equilibrium constant k for a new reaction by changing another reaction. 0 liters and allowed to reach equilibrium at 205 C. Finally, it discusses how to calculate the equilibrium constant k using ice tables. 4 Depiction of equilibrium for the reaction. Then, you're introduced to the single most important expression used to solve equilibrium problems: the equilibrium constant. At equilibrium there is no net electron transfer which is Ecell =0 and Q=K. PCl 3(g) Calculate a value for the equilibrium constant, K p,. How do I calculate the equilibrium constant of a reaction from two related reactions' constants? How to calculate the equilibrium constant for an esterification? 1. K is the equilibrium constant. My values for the equilibrium constant varied greatly in some of ten trials, ranging from a low of 28. What change, if any, would occur in the value of ΔG° for this reaction as the temperature is increased? Explain your reasoning using thermodynamic principles. 19) The equilibrium constant (Kp) at 721 K for the reaction 2HI(g) (( H2(g) + I2(g) is 0. If the equilibrium constant is much less than one, we say the reactants are favored and the. The relation between E^0 and the equilibrium constant K is given by. 50 mol NOCl was placed in a 2. For an endothermic reaction (#ΔH# is positive), #K# increases with an increase temperature. In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the (equilibrium) values of economic variables will not change.


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# Installation

## Installation of pre-compiled binaries

After registration at the Mrcc homepage, pre-built binaries are available in the download area. These binaries were compiled with the Intel compiler (and Intel MKL) version 19.0.3 and should utilize optimal instruction sets (e.g., AVX-512) of modern CPUs. If your CPU is still not correctly identified, the MKL_ENABLE_INSTRUCTIONS environment variable enables you to use an architecture-specific code path of your choice in Intel MKL routines. To install these executables, Linux operating system and the 2.23 or later version of the GNU C Library (glibc) is required. To use the MPI-parallel executables, Intel MPI 2019 also has to be installed. The precompiled binaries are linked against the Intel MPI 2019 Update 3 library, and it is highly recommended to use this particular Intel MPI version with the precompiled binaries. It is also strongly suggested to install the newest stable version of Libfabric (1.9.0 or later) from the https://github.com/ofiwg/libfabric repository as some of the previous versions provided via the Intel MPI package could cause irregular runtime behavior. The binaries are provided in a gzipped tar file, mrcc.YYYY-MM-DD.binary.tar.gz, where YYYY-MM-DD is the release date of the program. Note that you will find several program versions on the homepage. Unless there are overriding reasons not to do so, please always download the last version. To unpack the file type

tar xvzf mrcc*.binary.tar.gz

Please do not forget to add the name of the directory where the executables are placed to your PATH environment variable.

## Installation from source code

To install Mrcc from source code some version of the Unix operating system, Fortran 90 and C compilers as well as BLAS (basic linear algebra subprograms) and LAPACK (linear algebra package) libraries are required. Optionally, Mrcc can also be linked with the Libxc library of density functionals [79, 53] and the PCMSolver library for continuum solvation [17, 1]. For an MPI-parallel build, a working MPI installation is also required. Please be sure that the directories where the compilers are located are included in your PATH environment variable. Please also check your LD_LIBRARY_PATH environment variable, which must include the directories containing the BLAS and LAPACK and, if linked against, the Libxc, PCMSolver, and MPI libraries.

After registration at the Mrcc homepage the program can be downloaded as a gzipped tar file, mrcc.YYYY-MM-DD.tar.gz, where YYYY-MM-DD is the release date of the program. Note that you will find several program versions on the homepage. Unless there are overriding reasons not to do so, please always download the last version. To unpack the file type

tar xvzf mrcc*.tar.gz

To install Mrcc add the current working directory to PATH (e.g., export PATH=.:\$PATH on bash) and run the build.mrcc script as

build.mrcc [$<$compiler$>$] [-i$<$option1$>$] [-p$<$option2$>$] [-g] [-d] [-s] [-f$<$folder$>$] [-l$<$library$>$]

$<$compiler$>$ specifies the compiler to be used. Currently the supported compiler systems are:

Intel Intel compiler GNU GNU compiler (g77 or gfortran) PGF Portland Group Fortran compiler G95 G95 Fortran 95 compiler PATH Pathscale compiler HP HP Fortran Compiler DEC Compaq Fortran Compiler (DEC machines) XLF XL Fortran Compiler (IBM machines) Solaris10 Sun Solaris10 and Studio10 Fortran Compiler (AMD64)

If the build.mrcc script is invoked without specifying the $<$compiler$>$ variable, a help message is displayed.

Optional arguments:

-i

specifies if 32- or 64-bit integer variables are used. Accordingly, $<$option1$>$ can take the value of 32 or 64. The 32-bit integer version is not supported any more.
Default: 64 for 64-bit machines, 32 otherwise.

-p

generates parallel code using message passing interface (MPI) or open multi-processing (OpenMP) technologies. Accordingly, $<$option2$>$ can take the MPI[=$<$MPI implementation$>$] or OMP values. OpenMP and MPI parallelizations have been tested with the Intel compiler and the Intel MPI and Open MPI implementations. If -pMPI is specified, the library given by $<$MPI implementation$>$ will be linked to Mrcc. The default value of $<$MPI implementation$>$ is IntelMPI with the Intel compiler and OpenMPI for other compilers. Please note that currently the two parallelization schemes can only be combined for the scf, mrcc, and ccsd programs, other executables will be compiled with only OpenMP parallelization even if -pOMP and -pMPI are both set.
Default: no parallelization.

-g

source codes are compiled with debugging option (use this for development purposes)
Default: no debugging option.

-d

source codes are compiled for development, no optimization is performed (use this for development purposes)
Default: codes are compiled with highest level optimization.

-f

specifies the installation folder. Executables, basis set libraries, and test jobs will be copied to directory $<$folder$>$. If this flag is not used, you will find the executables, etc. in the directory where you perform the installation.

-l

Mrcc is linked with an external library. Currently the options for $<$library$>$ are libxc and pcm, which require the installation of the Libxc and the PCMSolver libraries, respectively. See notes below.

-s

Mrcc is linked statically. Non-MPI-parallel executables are linked entirely statically, while MPI-parallel executables link Intel-provided libraries statically.

Notes:

1. 1.

After the installation please do not forget to add the directory where the Mrcc executables are located to your PATH environment variable. This is the $<$folder$>$ directory if you used the -f flag at the installation, otherwise the directory where you executed the build.mrcc script.

2. 2.

The build.mrcc script has been tested on several platforms with several versions of the supported compilers and libraries. Nevertheless you may need to customize the compiler flags, names of libraries, etc. These data can be found in the build.mrcc.config file, please edit this file if necessary. Please do not change build.mrcc.

3. 3.

To ensure the best performance of the software, the use of Intel compiler is recommended.

4. 4.

If you use Mrcc together with Molpro, you can also use the Molpro installer to install Mrcc, please follow the instructions in the Molpro manual (www.molpro.net).

5. 5.

If Mrcc is linked with the Libxc library, Libxc must be installed before starting the installation of Mrcc. Note that you must compile Libxc with the same Fortran compiler as used for the installation of Mrcc. At the installation of Libxc, it is recommended to set the installation path of Libxc (--prefix=<install dir> option of configure) to the directory where the installation of Mrcc is carried out, otherwise please set the LIBS_LIBXC environment variable to the installation path of Libxc (i.e. export LIBS_LIBXC=<install dir> in bash, where <install dir> contains lib/libxcf03.a and lib/libxc.a) before running build.mrcc. See the manual for the Libxc project for details [53], as well as the examples below. The current release of Mrcc has been tested with the 4.3.4 version of Libxc.

6. 6.

If Mrcc is linked with the PCMSolver library, PCMSolver must be installed before starting the installation of Mrcc. At the installation of PCMSolver, it is recommended to set the installation path of PCMSolver (--prefix=<install dir> option of setup.py) to the directory where the installation of Mrcc is carried out, otherwise please set the LIBS_PCM environment variable to the installation path of PCMSolver (i.e., export LIBS_PCM=<install dir> in bash, where <install dir> contains lib/libpcm.so, or lib/libpcm.a in the case of static linking) before running build.mrcc. See the manual for the PCMSolver project for details [1], as well as the examples below. The current release of Mrcc has been tested with the 1.1.3 version of PCMSolver.

7. 7.

If the program is compiled for multi-node parallel execution, MPI-parallel executables (*_mpi) are generated. The compilation is performed by mpiifort when $<$MPI implementation$>$=IntelMPI is set, otherwise the mpifort compiler wrapper is used.

8. 8.

For the compilation of MPI-parallel executables, a working MPI installation is necessary. Currently Open MPI version 4 and Intel MPI (2017 or later) implementations are supported. Open MPI has to be patched with commits 07830d0 and 51acbf7 from https://github.com/open-mpi/ompi. Please, consult Sect. 9.3 for additional MPI settings required at runtime.

Examples:

1. 1.

Compile Mrcc for OpenMP parallel execution with the Intel compiler (recommended):
build.mrcc Intel -pOMP

2. 2.

Compile Mrcc for OpenMP parallel execution with the Intel compiler and install it to the /prog/mrcc directory (recommended):
build.mrcc Intel -pOMP -f/prog/mrcc

3. 3.

Compile Mrcc for OpenMP and combined OpenMP-MPI parallel execution with the Intel compiler and Intel MPI, and link with the Libxc and the PCMSolver libraries supposing that Mrcc is compiled in the /prog/mrcc directory. This will enable all features of Mrcc and is highly recommended.

1. (a)

Installation of the Libxc library:
Download the Libxc library (libxc*.tar.gz) from the homepage of the Libxc project [53].
tar xvzf libxc*.tar.gz
cd libxc*
./configure --prefix=/prog/mrcc/ FC=ifort
make
make check
make install
cd /prog/mrcc

2. (b)

Installation of the PCMSolver library:
curl -L https://github.com/PCMSolver/pcmsolver/archive/v1.1.3.tar.gz | tar -xz
cd pcmsolver-1.1.3
./setup.py --cxx=icpc --cc=icc --fc=ifort --int64 --omp --prefix=/prog/mrcc/
cd build
make
make install
export LD_LIBRARY_PATH=\$LD_LIBRARY_PATH:/prog/mrcc/lib
cd /prog/mrcc
cp pcmsolver-1.1.3/api/pcmsolver.F90 pcmsolver.f90

3. (c)

build.mrcc Intel -pOMP -pMPI=IntelMPI -llibxc -lpcm

4. 4.

Compile Mrcc for serial execution with the Intel compiler:
build.mrcc Intel

5. 5.

Compile Mrcc for parallel execution using MPI environment with the Intel compiler for 32-bit machines:
build.mrcc Intel -i32 -pMPI

6. 6.

Compile Mrcc with the Intel compiler for parallel execution using OpenMP and MPI parallelization through the Open MPI library (recommended):
build.mrcc Intel -pOMP -pMPI=OpenMPI

## Installation under Windows

Under the Windows operating system the pre-built binaries cannot be directly executed, and the direct compilation of the source code has not been attempted so far. For Windows users we recommend the use of virtualization software packages, such as VirtualBox, which allow Linux as a guest operating system. In that environment Mrcc can be installed in the normal way as described in the previous subsections.

format: plain


text:
# nLab sigma-continuous valuation

Contents

### Context

#### Measure and probability theory

measure theory

probability theory

# Contents

## Definition

### In set theory

In measure theory, a $\sigma$-continuous valuation on a $\sigma$-complete lattice $(L, \leq, \bot, \vee, \top, \wedge, \Vee)$ is a valuation $\mu:L \to [0, \infty]$ such that the $\sigma$-continuity condition is satisfied: for all sequences $s:\mathbb{N} \to L$, if $s(n) \leq s(n + 1)$ for all natural numbers $n \in\mathbb{N}$, then

$\mu(\Vee_{n:\mathbb{N}} s(n)) \leq \sup_{n:\mathbb{N}} \mu(s(n))$


text:
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# Arc length intro

AP.CALC:
CHA‑6 (EU)
,
CHA‑6.A (LO)
,
CHA‑6.A.1 (EK)

## Video transcript

- [Voiceover] We've used the definite integral to find areas. What I want to do now is to see if we can use the definitive role to find an arc length. What do I mean by that? Well, if I start at this point on the graph of a function, and if I were to go at this point right over here, not a straight line, we know already how to find the distance in the straight line but instead we want to find the distance along the curve. If we lay a string along the curve, what would be the distance right over here? That's what I'm talking about by arc length. What we could think about it is okay, that's going to be from x equals a to x equals b along this curve. So how can we do it? Well, the one thing that integration, integral calculus is teaching us is that when we see something that's changing like this, what we could do is we can break it up into infinitely small parts. Infinitely small parts that we can approximately with things like lines and rectangles, and then we could take the infinite sum of those infinitely small parts. So let me break up my arc length. Let me break it up into infinitely small sections of arc length. Let me call each of those infinitely small sections of my arc length a, I guess I could say a length to differential, an arc length to differential, I call it ds. I'll draw it a much bigger that when I at least I conceptualize what a differential is, just so that we could see it. What do I mean by breaking it up into these ds's? Well, if that's the ds, and then let me do the others in other colors, that's another infinitely small change in my arc length. Another infinitely small change in my arc length. If I summed all of these ds's together, I'm going to get the arc length. The arc length, if I take is going to be the integral of all of these ds's sum together over this integral so we can denote it like this. But this doesn't help me right now. This is in terms of this arc length that's differential. We do know how to do things in terms of dx's and dy's. Let's see if we can re-express this in terms of dx's and dy's. If we go on a really, really small scale, once again, we can approximate. This is going to be a line. We just the way that we approximated area with rectangles at first. But if we have an infinite number of infinite small rectangles, we're actually approximating a non-rectangular region. The area on a non-rectangular region. Similarly, we're approximating with lines with the infinitely small and there's infinite number of them, you are actually finding the length of the curve. Well, just focusing on this is a line for now. This distance right over here, I'm just going to try express in terms of dx's and dy's. So this distance right over here, that's dx. You can do this as infinitely small change in x, and this distance right over here, this is a dy. Once again, I'm being loosey-goosey with differentials. Really giving you conceptual understanding, not a reader's proof, but it'll give you a sense of where the formula for arc length is actually coming from. Based on this, you can see the ds could be expressed based on the Pythagorean Theorem as equal to dx squared plus dy squared, or you could rewrite this as square root of dx squared plus dy squared. So we could rewrite this. We could say this is the same thing as the integral of, instead of writing ds, I'm going to write it as the square root of dx squared plus dy squared. Once again, this is straight out of the Pythagorean Theorem. Now this is starting to get interesting. I've written in terms of dx's and dy's but they're getting squared. They're under radical sign. What can I do to simplify this? Or at least write it in a way that I know how to integrate. Well, I could factor out a dx squared, so let me just rewrite it. This is going to be the same thing as the integral of the square root. I'm going to factor out the dx squared, dx squared times one plus dy over dx squared. Notice this, and this is exact same quantity. If I distribute this dx squared, I'm going to get this right up here. Now I can take the dx squared out of the radical. So this is going to be the integral of, let me write that in the white color, the integral of one plus dy, dx squared. This is interesting because we know what dy, dx is. This is the derivative of our function, dy, dx squared. If you take the dx squared out of the radical, the square root of dx squared is just going to be dx. This is just going to be dx. This is just going to be dx. Now this is really interesting because we know how to find this between two bounds. We can now take the definitive role from a to b. This is now we are integrating a bunch of dx's or we're integrating with respect to x. We could say, "Okay, x equals a to x equals b." Let's take the sum of the product of this expression and dx, and this is essential. This is the formula for arc length. The formula for arc length. This looks complicated. In the next video, we'll see there's actually fairly straight forward to apply although sometimes in math gets airy. If you wanted to write this in slightly different notation, you could write this as equal to the integral from a to b, x equals a to x equals b of the square root of one plus. Instead of dy, dx, I could write it as f prime of x squared, dx. So if you know the function, if you know what f of x is, take the derivative of it with respect to x squared added to one, take the square root, and then multiply, and then take the definite integral of that with respect to x from a to b. We'll do that in the next video.
AP® is a registered trademark of the College Board, which has not reviewed this resource.


text:
Home > Standard Error > Standard Error Quantile

# Standard Error Quantile

## Contents

P-P plot— similar to the Q-Q plot, but used much less frequently. If yes can you point me to some reasoning?Thanks for all answers.RegardsPetrPS.I found mcmcse package which shall compute the standard error but whichI could not make to work probably because I The distribution of the variable X restricted to an interval [a, b] is called the truncated normal distribution. (X − μ)−2 has a Lévy distribution with location 0 and scale σ−2. I expect that if you looked at different sample sizes you'd findthat variance eventually decreases slower than 1/n, perhaps n^(-2/3) orsomethingFor p=0.51, the asymptotics probably aren't going to work until n http://activews.com/standard-error/standard-deviation-versus-standard-error-of-measurement.html

The central limit theorem implies that those statistical parameters will have asymptotically normal distributions. When is it a good idea to make Constitution the dump stat? Just curious ...... Rectified Gaussian distribution a rectified version of normal distribution with all the negative elements reset to 0 Complex normal distribution deals with the complex normal vectors.

## Quantile Estimation Error

It can be seen that for n=200 the formula and the simulations are close. When p = 0, use x1. Bootstrap is preferable because it makes no assumption about the distribution of response (p. 47, Quantile regressions, Hao and Naiman, 2007). Search on that.

1. Is there anything that one can do in instances wheref(Q.p) = 0?
2. If X has a normal distribution, these moments exist and are finite for any p whose real part is greater than −1.
3. If also required, the zeroth quartile is 3 and the fourth quartile is 20.
4. Whether these approximations are sufficiently accurate depends on the purpose for which they are needed, and the rate of convergence to the normal distribution.
5. Thus, s2 is not an efficient estimator for σ2, and moreover, since s2 is UMVU, we can conclude that the finite-sample efficient estimator for σ2 does not exist.
6. Not an R question. 2.
7. But, in general, the median and the mean can differ.
8. Quartile Calculation Result Zeroth quartile Although not universally accepted, one can also speak of the zeroth quartile.

Rolf Turner-3 Threaded Open this post in threaded view ♦ ♦ | Report Content as Inappropriate ♦ ♦ Re: standard error for quantile In reply to this post by ted.harding-3 Also the reciprocal of the standard deviation τ ′ = 1 / σ {\displaystyle \tau ^{\prime }=1/\sigma } might be defined as the precision and the expression of the normal distribution For a population, of discrete values or for a continuous population density, the k-th q-quantile is the data value where the cumulative distribution function crosses k/q. Kurtosis Most useful knowledge from the 30's to understand current state of computers & networking?

I know that >>> >>> x<-rlnorm(100000, log(200), log(2)) >>> quantile(x, c(.10,.5,.99)) >>> >>> computes quantiles but I would like to know if there is any function to >>> find standard error The system returned: (22) Invalid argument The remote host or network may be down. doi:10.2307/2685212. The var(X.p) then depends on ratio to parent > distribution at this p probability.

A function with two Lagrange multipliers is defined: L = ∫ − ∞ ∞ f ( x ) ln  ( f ( x ) ) d x − λ 0 Normal Distribution You want the distribution of order statistics. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the Did I manage to understand?

## Quantiles

Description: The qth quantile of a data set is defined as that value where a q fraction of the data is below that value and (1-q) fraction of the data is In the mean time I have got several other answers which helped me to understand the topic. Quantile Estimation Error kurtosis 0 Entropy 1 2 ln  ( 2 σ 2 π e ) {\displaystyle {\tfrac μ 3 μ 2}\ln(2\sigma ^ μ 1\pi \,e\,)} MGF exp  { μ t + Maritz-jarrett Method Eating Skittles Like a Normal Person Why are terminal consoles still used?

Otherwise a rounding or interpolation scheme is used to compute the quantile estimate from h, x⌊h⌋, and x⌈h⌉. (For notation, see floor and ceiling functions). check over here Usually we are interested only in moments with integer order p. Under the Nearest Rank definition of quantile, the rank of the fourth quartile is the rank of the biggest number, so the rank of the fourth quartile would be 10. 20 These values are used in hypothesis testing, construction of confidence intervals and Q-Q plots. Standard Error Of Order Statistic

Confidence intervals See also: Studentization By Cochran's theorem, for normal distributions the sample mean μ ^ {\displaystyle \scriptstyle {\hat {\mu }}} and the sample variance s2 are independent, which means there More precisely, the probability that a normal deviate lies in the range μ − nσ and μ + nσ is given by F ( μ + n σ ) − F Introduction to robust estimation and hypothesis testing. his comment is here Its CDF is then the Heaviside step function translated by the mean μ, namely F ( x ) = { 0 if  x < μ 1 if  x ≥ μ {\displaystyle

Vector form A similar formula can be written for the sum of two vector quadratics: If x, y, z are vectors of length k, and A and B are symmetric, invertible Median A = m - 1 B = n - m Wi = BETCDF(i/n,A,B) - BETCDF((i-1)/n,A,B) where BETCDF is the beta cumulative distribution function with shape parameters A and B. \( C_k When p ≥ (N - 1/3) / (N + 1/3), use xN.

## If, instead of using integers k and q, the “p-quantile” is based on a real number p with 0 < p < 1 then p replaces k/q in the above formulae.

The examples of such extensions are: Pearson distribution— a four-parametric family of probability distributions that extend the normal law to include different skewness and kurtosis values. Your cache administrator is webmaster. However, many numerical approximations are known; see below. Confidence Interval Typically the null hypothesis H0 is that the observations are distributed normally with unspecified mean μ and variance σ2, versus the alternative Ha that the distribution is arbitrary.

Not the answer you're looking for? I did a wee experiment with f(x) = 15*x^2*(1-x^2)/4 for -1 <= x <= 1, which makes f(Q.50) = f(0) = 0. Better still, it's a polynomial, so you could evaluate theintegral exactly.-thomas--Thomas LumleyProfessor of BiostatisticsUniversity of Auckland reply | permalink Related Discussions [R] the standard error of the quantile [R] Retrieve regression weblink This is the maximum value of the set, so the fourth quartile in this example would be 20.

Therefore, 6 is the rank in the population (from least to greatest values) at which approximately 2/4 of the values are less than the value of the second quartile (or median). When p = 1, use xN.


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# An Illustrated Guide to TMLE, Part II: The Algorithm

The second post of a three-part series to help beginners and/or visual learners understand Targeted Maximum Likelihood Estimation (TMLE). This section walks through the TMLE algorithm for the mean difference in outcomes for a binary treatment and binary outcome.

This post is an expansion of a printable “visual guide” available on my Github. I hope it helps analysts who feel out-of-practice reading mathematical notation follow along with the TMLE algorithm. A web-based key without explanations is also available here.

# Why the Visual Guide? 🎨

TMLE was developed in 2007 by Mark van der Laan and colleagues at UC Berkeley, and it is slowly but surely starting to see more widespread use. Since learning about TMLE, I’ve believed many more analysts with a skill set similar to mine could be using TMLE, but perhaps find even the most introductory resources to be a bit daunting.

I am a very applied thinker, and I’ve tried to write this tutorial in the way I would have found most useful and accessible when I began learning about TMLE. Each step is accompanied by:

1. a non-rigorous explanation
2. an equation using the simplest notation possible
3. in-line R code
4. a small graphic representing the computation on a data frame or vector

This last piece is super important for me, because I remember best when I associate an image with what I’ve learned. If the graphics are also useful to you, it may be helpful to open this corresponding key in another browser or print the visual guide for reference.

This tutorial is not meant to replace the resources I used to learn TMLE, but rather to supplement them. I use the same mathematical notation as the TMLE literature to make it easier to move back and forth. I hope you find the way I think about the algorithm useful, but if not, consider checking out the references I’ve listed in Part III. TMLE is a very powerful method and will undoubtedly only grow in popularity in statistics and data science.

# TMLE, Step-by-Step 🚶🏽

Let’s look at the algorithm step-by-step. As you’re reading, keep in mind that there are R packages that will do this for you as easily as running a glm() or coxph() function. This tutorial is to help understand what’s going on behind-the-scenes.

One final note before we dive into the algorithm:

### Superlearning

I use the ensemble learning method superlearning (also known as “stacking”) to demonstrate TMLE. This is because superlearning is theoretically and empirically proven to yield the best results in TMLE.

If you’re new to superlearning/stacking, the necessary knowledge for this post is that it allows you to combine many machine learning algorithms for prediction. When I use SuperLearner() in the following example code, I could have used glm(), randomForest(), or any other parametric or non-parametric supervised learning algorithm.

Note that the choice of base learners for superlearning is not the point of this post. In practice we simply want to add flexible machine learning models which we think may reflect the underlying data distribution. For a tutorial on superlearning, you can check out one of my previous blog posts.

### Initial set up

Let’s first load the necessary libraries and set a seed.

library(tidyverse) # for data manipulation
library(kableExtra) # for table printing
library(SuperLearner) # for ensemble learning

set.seed(7) # for reproducible results

Next, let’s simulate a data set for demonstration of the algorithm. This data will have a very simple structure: a binary treatment, $$A$$; binary outcome, $$Y$$; and four confounders: $$W_1$$, $$W_2$$, $$W_3$$, and $$W_4$$.

generate_data <- function(n){
W1 <- rbinom(n, size=1, prob=0.2) # binary confounder
W2 <- rbinom(n, size=1, prob=0.5) # binary confounder
W3 <- round(runif(n, min=2, max=7)) # continuous confounder
W4 <- round(runif(n, min=0, max=4)) # continuous confounder
A  <- rbinom(n, size=1, prob= plogis(-0.2 + 0.2*W2 + log(0.1*W3) + 0.3*W4 + 0.2*W1*W4)) # binary treatment depends on confounders
Y <- rbinom(n, size=1, prob= plogis(-1 + A - 0.1*W1 + 0.2*W2 + 0.3*W3 - 0.1*W4 + sin(0.1*W2*W4))) # binary outcome depends on confounders
return(tibble(Y, W1, W2, W3, W4, A))
}

n <- 1000
dat_obs <- generate_data(n) # generate a data set with n observations

kable(head(dat_obs), digits=2, caption = "Simulated data set.")
Table 1: Simulated data set.
Y W1 W2 W3 W4 A
1 1 0 6 1 1
1 0 1 6 3 0
0 0 0 3 2 0
1 0 1 5 1 1
1 0 0 5 2 0
1 0 1 6 1 1

As mentioned earlier, TMLE can estimate many different statistical estimands of interest. In this example, our statistical estimand is the mean difference in outcomes between those who received the treatment and those who did not, adjusting for confounders.

Under causal assumptions, this could be identifiable as the Average Treatment Effect (ATE). I won’t go through the identification process here (see Part III, References), but since TMLE is often used for causal inference, let’s pretend for this example that we previously met causal assumptions and call our statistical estimand, $$\Psi$$, the ATE.

$ATE = \Psi = E_W[\mathrm{E}[Y|A=1,\mathbf{W}] - \mathrm{E}[Y|A=0,\mathbf{W}]]$ The ATE, once we estimate it, will be interpretable as the mean difference in outcomes in a hypothetical world where everyone received the treatment compared to a hypothetical world where no one received the treatment.

At this point in set-up, we should also pick our base machine learning algorithms to combine via superlearning to estimate the expected outcome and probability of treatment. Let’s use LASSO (glmnet), random forests (ranger), Multivariate Adaptive Regression Splines (MARS) (earth), and a generalized linear model (glm) for demonstration.

sl_libs <- c('SL.glmnet', 'SL.ranger', 'SL.earth', 'SL.glm') # a library of machine learning algorithms (penalized regression, random forests, and multivariate adaptive regression splines)

## Step 1: Estimate the Outcome

The very first step of TMLE is to estimate the expected value of the outcome using treatment and confounders as predictors.

This is what that looks like in mathematical notation. There is some function $$Q$$ which takes $$A$$ and $$\mathbf{W}$$ as inputs and yields the conditional expectation of $$Y$$:

$Q(A,\mathbf{W}) = \mathrm{E}[Y|A,\mathbf{W}]$ We can use any regression to estimate this conditional expectation, but it is best to use flexible machine learning models so that we don’t have unnecessary assumptions on the underlying distribution of the data.

We can think about the above equation as some generic regression function in R called fit() with inputs in formula form: outcome ~ predictors:

In real R code, we’ll use the SuperLearner() function to fit a weighted combination of multiple machine learning models (defined earlier in sl_libs). This function takes the outcome Y as a vector and a data frame X as predictors.

Y <- dat_obs$Y W_A <- dat_obs %>% select(-Y) # remove the outcome to make a matrix of predictors (A, W1, W2, W3, W4) for SuperLearner Q <- SuperLearner(Y = Y, # Y is the outcome vector X = W_A, # W_A is the matrix of W1, W2, W3, W4, and A family=binomial(), # specify we have a binary outcome SL.library = sl_libs) # specify our superlearner library of LASSO, RF, and MARS ## Loading required namespace: glmnet ## Loading required namespace: earth ## Loading required namespace: ranger Then, we should estimate the outcome for every observation under three different scenarios: 1. If every observation received the treatment they actually received. We can get this expected outcome estimate by simply calling predict() on the model fit without specifying any new data. $\hat{Q}(A,\mathbf{W}) = \mathrm{\hat{E}}[Y|A,\mathbf{W}]$ We will save that vector of estimates as a new object in R. Q_A <- as.vector(predict(Q)$pred) # obtain predictions for everyone using the treatment they actually received

2. If every observation received the treatment.

To do this, we’ll first need to create a data set where every observation received the treatment of interest, whether they actually did or not. Then we can call the predict() function on that data set.

$\hat{Q}(1,\mathbf{W}) = \mathrm{\hat{E}}[Y|A=1,\mathbf{W}]$

W_A1 <- W_A %>% mutate(A = 1)  # data set where everyone received treatment
Q_1 <- as.vector(predict(Q, newdata = W_A1)$pred) # predict on that everyone-exposed data set 3. If every observation received the control. Similarly, we create a data set where every observation did not receive the treatment of interest, whether they actually did or not, and call the predict() function again. $\hat{Q}(0,\mathbf{W}) = \mathrm{\hat{E}}[Y|A=0,\mathbf{W}]$ W_A0 <- W_A %>% mutate(A = 0) # data set where no one received treatment Q_0 <- as.vector(predict(Q, newdata = W_A0)$pred)

Next, let’s create a new data frame, dat_tmle, to hold the three vectors we’ve created so far, along with the treatment status $$A$$ and observed outcome $$Y$$. Notice that when $$A=1$$, the expected outcome $$\mathrm{\hat{E}}[Y|A,\mathbf{W}]$$ equals the expected outcome under treatment $$\mathrm{\hat{E}}[Y|A=1,\mathbf{W}]$$. When $$A=0$$, the expected outcome $$\mathrm{\hat{E}}[Y|A,\mathbf{W}]$$ equals the expected outcome under no treatment $$\mathrm{\hat{E}}[Y|A=0,\mathbf{W}]$$.

dat_tmle <- tibble(Y = dat_obs$Y, A = dat_obs$A, Q_A, Q_0, Q_1)
kable(head(dat_tmle), digits=2, caption = "TMLE Algorithm after Step 1")
Table 2: TMLE Algorithm after Step 1
Y A Q_A Q_0 Q_1
1 1 0.83 0.65 0.83
1 0 0.72 0.72 0.87
0 0 0.48 0.48 0.70
1 1 0.83 0.65 0.83
1 0 0.62 0.62 0.81
1 1 0.87 0.72 0.87

We could stop here and get our estimate of the ATE by computing the average difference between $$\mathrm{\hat{E}}[Y|A=1,\mathbf{W}]$$ and $$\mathrm{\hat{E}}[Y|A=0,\mathbf{W}]$$, which would be the mean difference in the expected outcomes, conditional on confounders. This estimation method is often called standardization, simple substitution estimation, g-formula estimation, or G-computation.

$\hat{ATE}_{G-comp}= \hat{\Psi}_{G-comp} = \frac{1}{N}\sum_{i=1}^{N}(\mathrm{\hat{E}}[Y|A=1,\mathbf{W}]-\mathrm{\hat{E}}[Y|A=0,\mathbf{W}])$

ate_gcomp <- mean(dat_tmle$Q_1 - dat_tmle$Q_0)
ate_gcomp
## [1] 0.1938238

However, this G-computation ATE estimate does not have the appropriate bias-variance tradeoff for the ATE because it was built to have the best bias-variance tradeoff for estimating the outcome, conditional on confounders, rather than the ATE. We also cannot compute the standard error of the estimator because we don’t know the sampling distribution of the machine learning estimates.

## Step 2: Estimate the Probability of Treatment

The next step is to estimate the probability of treatment, given confounders. This quantity is often called the propensity score, as in it gives the probability or propensity that an observation will receive a treatment of interest.

$g(\mathbf{W}) = \mathrm{Pr}(A=1|\mathbf{W})$

We will estimate $$\mathrm{Pr}(A=1|\mathbf{W})$$ in the same way as we estimated $$\mathrm{E}[Y|A,\mathbf{W}]$$: using the superlearner algorithm.

A <- dat_obs$A W <- dat_obs %>% select(-Y, -A) # matrix of predictors that only contains the confounders W1, W2, W3, and W4 g <- SuperLearner(Y = A, # outcome is the A (treatment) vector X = W, # W is a matrix of predictors family=binomial(), # treatment is a binomial outcome SL.library=sl_libs) # using same candidate learners; could use different learners Then we need to compute three different quantities from this model fit: 1. The inverse probability of receiving treatment. $H(1,\mathbf{W}) = \frac{1}{g(\mathbf{W})} = \frac{1}{\mathrm{Pr}(A=1|\mathbf{W})}$ We can estimate the probability of receiving treatment for every observation by using the predict() funcion without specifying any new data, and then take the inverse of that. g_w <- as.vector(predict(g)$pred) # Pr(A=1|W)
H_1 <- 1/g_w

2. The negative inverse probability of not receiving treatment.

$H(0,\mathbf{W}) = -\frac{1}{1-g(\mathbf{W})}= -\frac{1}{\mathrm{Pr}(A=0|\mathbf{W})}$ The probability of not receiving treatment for a binary treatment is simply 1 minus the probability of treatment.

H_0 <- -1/(1-g_w) # Pr(A=0|W) is 1-Pr(A=1|W)

3. If the observation was treated, the inverse probability of receiving treatment, and if they were not treated, the negative inverse probability of not receiving treatment. I’ll discuss why later, but in the TMLE literature this is called the clever covariate.

$H(A,\mathbf{W}) = \frac{\mathrm{I}(A=1)}{\mathrm{Pr}(A=1|\mathbf{W})}-\frac{\mathrm{I}(A=0)}{\mathrm{Pr}(A=0|\mathbf{W})}$

To calculate the clever covariate, we’ll first add the $$H(1,\mathbf{W})$$ and $$H(0,\mathbf{W})$$ vectors to our dat_tmle data frame, and then we can use $$A$$ to assign $$H(A,\mathbf{W})$$.

dat_tmle <- # add clever covariate data to dat_tmle
dat_tmle %>%
bind_cols(
H_1 = H_1,
H_0 = H_0) %>%
mutate(H_A = case_when(A == 1 ~ H_1, # if A is 1 (treated), assign H_1
A == 0 ~ H_0))  # if A is 0 (not treated), assign H_0

We now have our initial estimates of the outcome, and the estimates of the probability of treatment:

kable(head(dat_tmle), digits=2, caption="TMLE Algorithm after Step 2")
Table 3: TMLE Algorithm after Step 2
Y A Q_A Q_0 Q_1 H_1 H_0 H_A
1 1 0.83 0.65 0.83 2.18 -1.85 2.18
1 0 0.72 0.72 0.87 1.61 -2.65 -2.65
0 0 0.48 0.48 0.70 3.40 -1.42 -1.42
1 1 0.83 0.65 0.83 2.39 -1.72 2.39
1 0 0.62 0.62 0.81 2.30 -1.77 -1.77
1 1 0.87 0.72 0.87 2.13 -1.88 2.13

## Step 3: Estimate the Fluctuation Parameter

To reiterate, in Step 1 we estimated the expected outcome, conditional on treatment and confounders. We know those machine learning fits have an optimal bias-variance trade-off for estimating the outcome (conditional on treatment and confounders), rather than the ATE. We will now use information about the treatment mechanism (from Step 2) to optimize the bias-variance trade-off for the ATE so we can obtain valid inference.

🚨 Warning: this step is easy to code, but difficult to understand unless you have a background in semiparametric theory. Let’s first look at what we’re doing, and then I’ll discuss at a very high-level why we’re doing that in a later section.

The point of this step is to solve an estimating equation for the efficient influence function (EIF) of our estimand of interest. Without diving into what an EIF or an estimating equation is, let’s accept for a moment that they will help us:

1. Update our initial outcome estimates so that our estimate of the ATE is asymptotically unbiased (under certain conditions, see Part III, Statistical Properties).

2. Calculate the variance, and thus the standard error, confidence interval, and p-value for our estimate of the ATE for hypothesis testing.

Next, let’s take a look at a model that will help us solve an EIF estimating equation and then update our estimates:

$logit(\mathrm{E}[Y|A,\mathbf{W}]) = logit(\mathrm{\hat{E}}[Y|A,\mathbf{W}]) + \epsilon H(A,\mathbf{W})$

To reiterate, I haven’t explained at all why this step works; we’re just focusing on implementing it for now.

If we look at the left side, we can see this equation contains the true outcome $$Y$$, just $$logit$$ transformed. Luckily for us, there’s a well-known model that $$logit$$ transforms the left side of an equation: logistic regression. Our estimating equation looks a lot like a simple logistic regression, actually: $$logit(\mathrm{E}[Y|X]) = \beta_0 + \beta_1 X$$.

Do you see how our equation also has a vector on the right-hand side, $$H(A,\mathbf{W})$$, with a corresponding coefficient, $$\epsilon$$? The only difference is that the “intercept” in our equation, $$logit(\mathrm{\hat{E}}[Y|A,\mathbf{W}])$$ is not a constant value like $$\beta_0$$; it is a vector of values. We can see it as an offset or a fixed intercept in a logistic regression, rather than a constant-value intercept.

Therefore, to accomplish our goal of solving an estimating equation for the EIF we can leverage standard statistical software and fit a logistic regression with one covariate, $$H(A,\mathbf{W})$$, and the initial outcome estimate, $$logit(\mathrm{\hat{E}}[Y|A,\mathbf{W}])$$, as a fixed intercept. The outcome of the logistic regression is the observed outcome, $$Y$$.

Two technical points for application: we use qlogis to transform the probabilities $$\mathrm{\hat{E}}[Y|A,\mathbf{W}]$$ to the $$logit$$ scale. Also, the R code for a fixed intercept is -1 + offset(fixed_intercept).

glm_fit <- glm(Y ~ -1 + offset(qlogis(Q_A)) + H_A, data=dat_tmle, family=binomial)

Note that we are only using a logistic regression because it happens to have the correct form for solving the estimating equation for the EIF for the ATE estimand. It has nothing to do with having a binary outcome, and it isn’t putting any parametric restraints on our data.

Next we need to save the coefficient from that logistic regression, which we will call $$\hat{\epsilon}$$:

eps <- coef(glm_fit)

In the TMLE literature, $$\epsilon$$ is called the fluctuation parameter, because it provides information about how much to change, or fluctuate, our initial outcome estimates. Similarly, $$H(A,\mathbf{W})$$ is called the clever covariate because it “cleverly” helps us solve for the EIF and then update our estimates.

We will use both the fluctuation parameter and clever covariate in the next step to update our initial estimates of the expected outcome, conditional on confounders and treatment.

## Step 4: Update the Initial Estimates of the Expected Outcome

Almost done! Let’s recap:

• In Step 1, we obtained initial estimates of the expected outcome using machine learning (ML). These ML estimates are optimized to estimate $$E[Y|A,W]$$, not the ATE.

• We need to update those initial expected outcome estimates using information about the treatment mechanism, so we computed the expected probability of treatment, conditional on confounders, in Step 2.

• Then, in Step 3, we used quantities from Step 1 and Step 2 to solve an estimating equation for the EIF. We didn’t talk about why this works; we simply accepted for now that this is how we can target our estimand of interest (the ATE).

• Now, we will update our initial outcome estimates from Step 1 using information from Step 2 and 3 to obtain the correct bias-variance tradeoff for the ATE.

To update our expected outcome estimates, we first need to put the initial expected outcome estimates on the $$logit$$ scale using qlogis() because that’s the scale we used to solve our estimating equation for the EIF in Step 3. Then we can calculate how much we need to fluctuate our initial estimates using the product of the clever covariate and fluctuation parameter: $$H(A,\mathbf{W}) \times \hat{\epsilon}$$. These are our outputs of Step 2 and 3, respectively. We will add that quantity to the initial outcome estimates to create updated outcome estimates. Finally, we can put the updated estimates back on the true outcome scale using plogis().

Note we can use $$expit$$ to show the inverse of the $$logit$$ function, and we will denote updates to the outcome regressions as $$\hat{\mathrm{E}}^*$$ instead of $$\hat{\mathrm{E}}$$.

1. Update the expected outcomes of all observations, given the treatment they actually received and their baseline confounders.

$\hat{\mathrm{E}}^*[Y|A,\mathbf{W}] = expit(logit(\mathrm{\hat{E}}[Y|A,\mathbf{W}]) + \hat{\epsilon}H(A,\mathbf{W}))$

H_A <- dat_tmle$H_A # for cleaner code in Q_A_update Q_A_update <- plogis(qlogis(Q_A) + eps*H_A) 2. Update the expected outcomes, conditional on baseline confounders and everyone receiving the treatment. $\hat{\mathrm{E}}^*[Y|A=1,\mathbf{W}] = expit(logit(\mathrm{\hat{E}}[Y|A=1,\mathbf{W}]) + \hat{\epsilon}H(A,1))$ Q_1_update <- plogis(qlogis(Q_1) + eps*H_1) 3. Update the expected outcomes, conditional on baseline confounders and no one receiving the treatment. $\hat{\mathrm{E}}^*[Y|A=0,\mathbf{W}] = expit(logit(\mathrm{\hat{E}}[Y|A=0,\mathbf{W}]) + \hat{\epsilon}H(A,0))$ Q_0_update <- plogis(qlogis(Q_0) + eps*H_0) ## Step 5: Compute the Statistical Estimand of Interest We now have updated expected outcomes estimates, so we can compute the ATE as the mean difference in the updated outcome estimates under treatment and no treatment: $\hat{ATE}_{TMLE} = \hat{\Psi}_{TMLE} = \frac{1}{N}\sum_{i=1}^{N}[\hat{E^*}[Y|A=1,\mathbf{W}] - \hat{E^*}[Y|A=0,\mathbf{W}]]$ tmle_ate <- mean(Q_1_update - Q_0_update) tmle_ate ## [1] 0.1920762 We can then say, “the average treatment effect was estimated to be 19.2%.” If causal assumptions were not met, we would say, “the proportion of observations who experienced the outcome, after adjusting for baseline confounders, was estimated to be 19.2% higher for those who received treatment compared to those who did not.” ## Step 6: Calculate the Standard Errors for Confidence Intervals and P-values This point estimate is great, but we usually need an estimate of variance so that we can compute confidence intervals, test statistics, p-values, etc. This is another step that contains quite a lot of theory, so I’ll give another birds-eye view for now. If you’re curious, you can read more about this in Part III. To obtain the standard errors, we first need to compute the Influence Function (IF), which is the empirical version of what we used our estimating equation to figure out in Step 3. The IF tells us how much each observation influences the final estimate. The equation for the IF looks like this: $\hat{IF} = (Y-\hat{E^*}[Y|A,\mathbf{W}])H(A,\mathbf{W}) + \hat{E^*}[Y|A=1,\mathbf{W}] - \hat{E^*}[Y|A=0,\mathbf{W}] - \hat{ATE}$ infl_fn <- (Y - Q_A_update) * H_A + Q_1_update - Q_0_update - tmle_ate Once we have the IF, we can take the square-root of its variance divided by the number of observations to get the standard error of our estimate. $\hat{SE} = \sqrt{\frac{var(\hat{IF})}{N}}$ tmle_se <- sqrt(var(infl_fn)/nrow(dat_obs)) Once we have that standard error, we can easily get the 95% confidence interval and p-value of our estimate. conf_low <- tmle_ate - 1.96*tmle_se conf_high <- tmle_ate + 1.96*tmle_se pval <- 2 * (1 - pnorm(abs(tmle_ate / tmle_se))) kable(tibble(tmle_ate, conf_low, conf_high), digits=3, caption = "TMLE Estimate of the ATE") Table 4: TMLE Estimate of the ATE tmle_ate conf_low conf_high 0.192 0.134 0.25 Then we can successfully report our ATE as 0.192 (95% CI: 0.134, 0.25). Note that a TMLE estimator is asymptotically normally distributed, so we could bootstrap the entire algorithm to get our standard errors instead. # Using the tmle package 📦 Luckily there are R packages so that you don’t have to hand code TMLE yourself. R packages to implement the TMLE algorithm include tmle, tmle3, ltmle, and lmtp. The code using the original tmle package’s tmle() function is: tmle_fit <- tmle::tmle(Y = Y, # outcome vector A = A, # treatment vector W = W, # matrix of confounders W1, W2, W3, W4 Q.SL.library = sl_libs, # superlearning libraries from earlier for outcome regression Q(A,W) g.SL.library = sl_libs) # superlearning libraries from earlier for treatment regression g(W) tmle_fit ## Additive Effect ## Parameter Estimate: 0.19111 ## Estimated Variance: 0.00088683 ## p-value: 1.3847e-10 ## 95% Conf Interval: (0.13275, 0.24948) ## ## Additive Effect among the Treated ## Parameter Estimate: 0.18898 ## Estimated Variance: 0.00092392 ## p-value: 5.0597e-10 ## 95% Conf Interval: (0.1294, 0.24856) ## ## Additive Effect among the Controls ## Parameter Estimate: 0.19297 ## Estimated Variance: 0.0010143 ## p-value: 1.3687e-09 ## 95% Conf Interval: (0.13055, 0.2554) We can get the same result (variation due to randomness in the machine learning models) in just a few lines of code: the estimate using the original tmle package is 0.191 (95% CI: 0.133, 0.249). To learn more about the statistical properties of TMLE and the underlying theory, continue on to Part III. Alternatively, return to the motivation in Part I, or see the full tutorial code below. # Full tutorial code library(tidyverse) # for data manipulation library(kableExtra) # for table printing library(SuperLearner) # for ensemble learning set.seed(7) # for reproducible results sl_libs <- c('SL.glmnet', 'SL.ranger', 'SL.earth') # a library of machine learning algorithms (penalized regression, random forests, and multivariate adaptive regression splines) generate_data <- function(n){ W1 <- rbinom(n, size=1, prob=0.2) # binary confounder W2 <- rbinom(n, size=1, prob=0.5) # binary confounder W3 <- round(runif(n, min=2, max=7)) # continuous confounder W4 <- round(runif(n, min=0, max=4)) # continuous confounder A <- rbinom(n, size=1, prob= plogis(-0.2 + 0.2*W2 + log(0.1*W3) + 0.3*W4 + 0.2*W1*W4)) # binary treatment depends on confounders Y <- rbinom(n, size=1, prob= plogis(-1 + A - 0.1*W1 + 0.2*W2 + 0.3*W3 - 0.1*W4 + sin(0.1*W2*W4))) # binary outcome depends on confounders return(tibble(Y, W1, W2, W3, W4, A)) } n <- 1000 dat_obs <- generate_data(n) # generate a data set with n observations Y <- dat_obs$Y
W_A <- dat_obs %>% select(-Y) # remove the outcome to make a matrix of predictors (A, W1, W2, W3, W4) for SuperLearner

### Step 1: Estimate Q
Q <- SuperLearner(Y = Y, # Y is the outcome vector
X = W_A, # W_A is the matrix of W1, W2, W3, W4, and A
family=binomial(), # specify we have a binary outcome
SL.library = sl_libs) # specify our superlearner library of LASSO, RF, and MARS
Q_A <- as.vector(predict(Q)$pred) # obtain predictions for everyone using the treatment they actually received W_A1 <- W_A %>% mutate(A = 1) # data set where everyone received treatment Q_1 <- as.vector(predict(Q, newdata = W_A1)$pred) # predict on that everyone-exposed data set
W_A0 <- W_A %>% mutate(A = 0) # data set where no one received treatment
Q_0 <- as.vector(predict(Q, newdata = W_A0)$pred) dat_tmle <- tibble(Y = dat_obs$Y, A = dat_obs$A, Q_A, Q_0, Q_1) ### Step 2: Estimate g and compute H(A,W) A <- dat_obs$A
W <- dat_obs %>% select(-Y, -A) # matrix of predictors that only contains the confounders W1, W2, W3, and W4
g <- SuperLearner(Y = A, # outcome is the A (treatment) vector
X = W, # W is a matrix of predictors
family=binomial(), # treatment is a binomial outcome
SL.library=sl_libs) # using same candidate learners; could use different learners

g_w <- as.vector(predict(g)$pred) # Pr(A=1|W) H_1 <- 1/g_w H_0 <- -1/(1-g_w) # Pr(A=0|W) is 1-Pr(A=1|W) dat_tmle <- # add clever covariate data to dat_tmle dat_tmle %>% bind_cols( H_1 = H_1, H_0 = H_0) %>% mutate(H_A = case_when(A == 1 ~ H_1, # if A is 1 (treated), assign H_1 A == 0 ~ H_0)) # if A is 0 (not treated), assign H_0 ### Step 3: Estimate fluctuation parameter glm_fit <- glm(Y ~ -1 + offset(qlogis(Q_A)) + H_A, data=dat_tmle, family=binomial) # fixed intercept logistic regression eps <- coef(glm_fit) # save the only coefficient, called epsilon in TMLE lit ### Step 4: Update Q's H_A <- dat_tmle$H_A # for cleaner code in Q_A_update
Q_A_update <- plogis(qlogis(Q_A) + eps*H_A) # updated expected outcome given treatment actually received
Q_1_update <- plogis(qlogis(Q_1) + eps*H_1) # updated expected outcome for everyone receiving treatment
Q_0_update <- plogis(qlogis(Q_0) + eps*H_0) # updated expected outcome for everyone not receiving treatment

### Step 5: Compute ATE
tmle_ate <- mean(Q_1_update - Q_0_update) # mean diff in updated expected outcome estimates

### Step 6: compute standard error, CIs and pvals
infl_fn <- (Y - Q_A_update) * H_A + Q_1_update - Q_0_update - tmle_ate # influence function
tmle_se <- sqrt(var(infl_fn)/nrow(dat_obs)) # standard error
conf_low <- tmle_ate - 1.96*tmle_se # 95% CI
conf_high <- tmle_ate + 1.96*tmle_se
pval <- 2 * (1 - pnorm(abs(tmle_ate / tmle_se))) # p-value at alpha .05

tmle_ate
conf_low
conf_high
sessionInfo()
## R version 4.0.3 (2020-10-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
##
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base
##
## other attached packages:
##  [1] SuperLearner_2.0-26 nnls_1.4            kableExtra_1.3.1
##  [4] forcats_0.5.0       stringr_1.4.0       dplyr_1.0.2
## [10] tibble_3.0.4        ggplot2_3.3.2       tidyverse_1.3.0
##
## loaded via a namespace (and not attached):
##  [1] httr_1.4.2         jsonlite_1.7.2     viridisLite_0.3.0  splines_4.0.3
##  [5] foreach_1.5.1      modelr_0.1.8       Formula_1.2-4      assertthat_0.2.1
##  [9] highr_0.8          cellranger_1.1.0   yaml_2.2.1         pillar_1.4.7
## [13] backports_1.2.1    lattice_0.20-41    glue_1.4.2         digest_0.6.27
## [17] rvest_0.3.6        colorspace_2.0-0   htmltools_0.5.0    Matrix_1.2-18
## [21] pkgconfig_2.0.3    broom_0.7.2        earth_5.3.0        haven_2.3.1
## [25] bookdown_0.21      scales_1.1.1       webshot_0.5.2      ranger_0.12.1
## [29] TeachingDemos_2.12 generics_0.1.0     ellipsis_0.3.1     withr_2.3.0
## [33] ROCR_1.0-11        cli_2.2.0          survival_3.2-7     magrittr_2.0.1
## [37] crayon_1.3.4       readxl_1.3.1       evaluate_0.14      fs_1.5.0
## [41] fansi_0.4.1        xml2_1.3.2         cabinets_0.6.0     blogdown_0.21
## [45] tools_4.0.3        hms_0.5.3          lifecycle_0.2.0    munsell_0.5.0
## [49] reprex_0.3.0       glmnet_4.0-2       plotrix_3.7-8      compiler_4.0.3
## [53] rlang_0.4.9        plotmo_3.6.0       grid_4.0.3         iterators_1.0.13
## [57] rstudioapi_0.13    rmarkdown_2.5      gtable_0.3.0       codetools_0.2-16
## [61] DBI_1.1.0          R6_2.5.0           lubridate_1.7.9.2  knitr_1.30
## [65] shape_1.4.5        stringi_1.5.3      tmle_1.5.0-1       Rcpp_1.0.5
## [69] vctrs_0.3.5        dbplyr_2.0.0       tidyselect_1.1.0   xfun_0.19
##### Katherine Hoffman
###### Research Biostatistician

I am passionate about meaningful, reproducible medical research.


text:
# What is clean limit and dirty limit?

In superconductor there has two limits, one called as clean and other one called dirty limit. But what are that meaning? What means clean and dirty? How the coherence length depends on the electron mean free path, what are these limit using for? For that I had read sth, in which the surface energy was mentioned. What kind of influences this energy has for superconductor? I hope you can understand my English.

Clean and dirty limits refer to the comparison of the carriers mean free path ($$\ell$$) to the coherence length of the pairs ($$\xi$$). Note that $$\xi$$ is, roughly speaking, the size of the Cooper pair (superconducting state), and that $$\ell$$ refers to unpaired carriers.
The clean limit is the case where $$\xi \ll \ell$$ and the dirty limit is, obviously, the case $$\xi \gg \ell$$.


text:
# Records: [Texmaster] Special and Sudden Ti

Thread in 'Competition' started by aperturegrillz, 27 Feb 2008.

1. ### makalaka

Aim for whatever gets you to 500. Then aim for whatever gets you to 500 under 2:20, etc

2. ### Red_Star

okay thanks kotetsu. i think i'm getting the hang of it slightly, i really like how fast paced sudden is.

Ti sudden-158- 1:06:56

3. ### cdsboyUnregistered

For 999 i'm gonna with first the rank, then who survives the end roll the longest, then how fast they did the whole thing.

5. ### Billmaan

Special TI - S9, 999, 9:18:95

6. ### jujubeUnregistered

it might help if you try holding your first piece regardless. if you place a few pieces before using hold for the first time it can throw off your rhythm with seeing the previews because you're taking 2 pieces from the previews and only placing 1. but if you hold the first piece, you're doing it before you get into a rhythm. and it becomes easier after the first hold because you're always making 1 placement per preview whether you use hold or not.

7. ### AmnesiaPiece of Cake

Don't worry mushroom, I just begin to master it, that comes faster than you think..Force yourself to use it and it will become natural very soon..

Practice simple HOLD and IHS (Initial Hold System)

One weeks ago I was yet thinking :

"DAMN I hate this f**** HOLD !! I will never use it anymore !!"

When I began on Heboris, 2 weeks ago now with my friend Bou, I could not use it in DOOM..Now even Bou can use it in DOOM..

8. ### AmnesiaPiece of Cake

Code:
Amnesia ---------- M2   999  7:24:90

Now I can focuse only on sudden ti and lockjaw..Before the end of my life I will beat him..

ah.. humm...sorry..

9. ### deepdorp

without further ado, here's my score for Texmaster beta2 special Ti mode:

-deep-

10. ### AmnesiaPiece of Cake

Code:
Edo -------------- M5   903  05:50:31
Amnesia ---------- M1   999  07:24:90
Kotetsu ---------- M1   999  06:39:10

AAAHHHRR !!!
M2 !! not M1 !

11. ### Red_Star

Ti Special-- 696 --08:45:03

Edit: oops forgot to say that it's still S1 rank.

12. ### eksUnregistered

Ti Special - 453 - 2 - 06:16:91

one game/day isnt paying off

13. ### mycophobia

Special Ti - S1 - 352 - 4:14:48

Video

A series of failed recoveries that somehow gets S1. On the bright side, I got three sectional cools for the first time! Still not using hold, though...

Also, DAMN this game is addictive.

14. ### cdsboyUnregistered

Sorry Amnesia! its fixed now

15. ### mycophobia

I died at 352, not 453.

16. ### cdsboyUnregistered

erm... ya... Ok no more leader board editing at 6 am...

17. ### deepdorp

new screen for special Ti:

-deep-

18. ### AmnesiaPiece of Cake

This game is stupid, try to follow the required conditions and you will be rewarded by a bit higher grad..

It is important to well know your current limit an abilities, for example, judging by your time, you should be able to valid the 3 or 4 first section time conditions to get 3 or 4 grads..

Then try to valid the 2 first tetris conditions :

3 on the 0-100

6 on the 100-199..

Then, when the game is a bit too fast for you, try to perform quietly the 4 required tetris by sections, or try to increase your speed to valid few required section time..

Don't hesitate to keep in mind the list of condition in the wiki when you are playing..

http://www.tetrisconcept.com/wiki/index ... RET_System

19. ### DIGITALUnregistered

My advice: just play. 3 previews and hold make the game very forgiving. As long as you play fast and cleanly, which should be worlds easier than in TAP (excluding speed timings of course), you'll get high grades.

Special TI:


text:
• This work is on the Physics of the B Factories. Part A of this book contains a brief description of the SLAC and KEK B Factories as well as their detectors, BaBar and Belle, and data taking related issues. Part B discusses tools and methods used by the experiments in order to obtain results. The results themselves can be found in Part C. Please note that version 3 on the archive is the auxiliary version of the Physics of the B Factories book. This uses the notation alpha, beta, gamma for the angles of the Unitarity Triangle. The nominal version uses the notation phi_1, phi_2 and phi_3. Please cite this work as Eur. Phys. J. C74 (2014) 3026.
• ### The HERMES Recoil Detector(1302.6092)

May 6, 2013 hep-ex, physics.ins-det
For the final running period of HERA, a recoil detector was installed at the HERMES experiment to improve measurements of hard exclusive processes in charged-lepton nucleon scattering. Here, deeply virtual Compton scattering is of particular interest as this process provides constraints on generalised parton distributions that give access to the total angular momenta of quarks within the nucleon. The HERMES recoil detector was designed to improve the selection of exclusive events by a direct measurement of the four-momentum of the recoiling particle. It consisted of three components: two layers of double-sided silicon strip sensors inside the HERA beam vacuum, a two-barrel scintillating fibre tracker, and a photon detector. All sub-detectors were located inside a solenoidal magnetic field with an integrated field strength of 1 T. The recoil detector was installed in late 2005. After the commissioning of all components was finished in September 2006, it operated stably until the end of data taking at HERA end of June 2007. The present paper gives a brief overview of the physics processes of interest and the general detector design. The recoil detector components, their calibration, the momentum reconstruction of charged particles, and the event selection are described in detail. The paper closes with a summary of the performance of the detection system.
• ### Beam-helicity asymmetry arising from deeply virtual Compton scattering measured with kinematically complete event reconstruction(1206.5683)

Nov. 28, 2012 hep-ex
The beam-helicity asymmetry in exclusive electroproduction of real photons by the longitudinally polarized HERA positron beam scattering off an unpolarized hydrogen target is measured at HERMES. The asymmetry arises from deeply virtual Compton scattering and its interference with the Bethe--Heitler process. Azimuthal amplitudes of the beam-helicity asymmetry are extracted from a data sample consisting of $ep\rightarrow ep\gamma$ events with detection of all particles in the final state including the recoiling proton. The installation of a recoil detector, while reducing the acceptance of the experiment, allows the elimination of background from $ep\rightarrow eN\pi\gamma$ events, which was estimated to contribute an average of about 12% to the signal in previous HERMES publications. The removal of this background from the present data sample is shown to increase the magnitude of the leading asymmetry amplitude by 0.054 +/- 0.016 to -0.328 +/- 0.027 (stat.) +/- 0.045 (syst.).
• ### The G0 Experiment: Apparatus for Parity-Violating Electron Scattering Measurements at Forward and Backward Angles(1103.0761)

March 3, 2011 nucl-ex, physics.ins-det
In the G0 experiment, performed at Jefferson Lab, the parity-violating elastic scattering of electrons from protons and quasi-elastic scattering from deuterons is measured in order to determine the neutral weak currents of the nucleon. Asymmetries as small as 1 part per million in the scattering of a polarized electron beam are determined using a dedicated apparatus. It consists of specialized beam-monitoring and control systems, a cryogenic hydrogen (or deuterium) target, and a superconducting, toroidal magnetic spectrometer equipped with plastic scintillation and aerogel Cerenkov detectors, as well as fast readout electronics for the measurement of individual events. The overall design and performance of this experimental system is discussed.
• ### Electromagnetic radiative corrections in parity-violating electron-proton scattering(hep-ph/0511229)

Nov. 18, 2005 hep-ph
QED radiative corrections have been calculated for leptonic and hadronic variables in parity-violating elastic ep scattering. For the first time, the calculation of the asymmetry in the elastic radiative tail is performed without the peaking-approximation assumption in hadronic variables configuration. A comparison with the PV-A4 data validates our approach. This method has been also used to evaluate the radiative corrections to the parity-violating asymmetry measured in the G0 experiment. The results obtained are here presented.