Primary and Secondary Effects

To evaluate the relative importance of primary and secondary effects, we use a method introduced in Erikson et al., 2005.  The basic steps are to:

1. Take the mean and standard deviation of the standardized performance scores for each group separately

2. Run the binary logistic regressions for each class separately (Y=transition (0/1), X=standardized performance score)

3. Use the results from (1.) and (2.) to create the graphs (i.e. substitute the mean and standard deviation of performance scores for each group into the equation for a normal distribution, substitute constant and coefficient from models for each group into the logistic regression probability equation)

4. Calculate the integrals for all ‘factual’ and ‘counterfactual’ combinations

5. Substitute the results of the integrals into the appropriate equations to find the relative importance of primary and secondary effects

The following files might be helpful if you plan to use the method

Methods

Use the numerical integration utility (by Waner and Costenoble) to calculate the integrals.  The equations should be of the form:

(0.464e^-(((x - .39)^2)/1.479))((e^(0.98+2.63x))/(1+e^(0.98+2.63x)))

 

Integrate between the limits of –4 and +4 (limits of performance distribution), using adaptive quadrature

Calculating the integrals

This Excel spreadsheet can be used to create the graphs for (3.).  Substitute your results in the appropriate places in the worksheet. 

Creating the graphs

Maarten Buis has created a Stata add-on which allows for quick calculation of the relative importance of primary and secondary effects.  This paper explains how to install and use the add-on, as well as providing a generalization of the Erikson et al. method.

Stata Add-On

This Excel spreadsheet can be used to calculate the relative importance of primary and secondary effects (5.).  Substitute your results in the appropriate places in the worksheet. 

Calculating the relative importance

An alternative decomposition method is discussed in a paper by Fairlie:

Farlie, R.W. (2005): ‘An Extension of the Blinder-Oaxaca Decomposition Technique to Logit and Probit Models’, Journal of Economic and Social Measurement, 30: 305-316.

Fairlie Method