|Brian O'Connor||UBCO Psychology||UBCO|
All-in-one programs for exploring interactions in moderated multiple regression
O'Connor, B. P. (1998). All-in-one programs for exploring interactions in moderated multiple regression. Educational and Psychological Measurement, 58, 833-837.
1) All significance levels are two-tailed.
2) The SIMPLE programs process raw score data. Any centering, standardization, or other transformation of raw scores should be performed before running the programs. Aiken & West (1991) recommend centering the predictors (the IDV and MOD variables). When users are primarily interested in standardized betas rather than raw betas, Aiken & West (1991, p. 44) recommend standardizing the IDV and MOD before computing product terms (a procedure first described by Friedrich, 1982).
3) The effect sizes of interactions are usually reported in terms of Rsquare change coefficients for the product variable(s). However, Rsquared change is not linearly related to effect size (Aiken & West, 1991, p. 157), and f-squared is the proper index (see also Cohen & Cohen, 1983, p. 155). Cohen's guidelines for interpreting f-squared are as follows:
f2 = .02 is small, f2 = .15 is medium, f2 = .35 is large.
4) The variance-covariance matrix of the coefficients from the overall equation can be obtained by entering a "PRINT Sb" command after the computation for Sb.
5) The standard errors for the raw betas for the simple slopes are computed but not printed in the output (in order to save space). To view them, insert a PRINT command after the compute SEslopes statement, or simply divide the raw beta by the t-value on the output.
6) For categorical moderators, users may notice that the standard errors of the simple slopes and t values are lower than the values that are obtained from simple regressions of the DV on the IDV for individual groups. The reason is that the mean square error and variance-covariance matrix of regression coefficients must be used in computing standard errors in moderated regression analyses of simple slopes (see Aiken & West, 1991, p. 131; Rogosa, 1980, Psych. Bull. 88 p. 317).
7) See Darlington, 1990, p. 126 for information on confidence intervals for slopes.
8) Aiken & West (1991, Chapter 7), Huitema (1980), and Pedhazur (p. 469) are the best sources of information on regions of significance.
9) See Nye & Witt (1995, Ed. Psych. Meas., 55, p. 27) for information on values of the moderator at which simple slopes become zero.
10) Sometimes in the plots it will appear that a symbol is missing for one end of one of the simple regression lines. This occurs when two symbols fall on the same spot, and SAS/SPSS can only print one symbol on the same spot.
11) The programs do not permit entry of additional "covariates" (only IDVs, Moderators, Interaction Terms, and DVs can be specified). However, the results for analyses involving additional covariates are easily obtained by first statistically partialling out any additional covariates from each of the variables involved in the interaction analyses. The residualized variables are then entered into the desired SIMPLE program. For example, in SPSS, first run a separate regression for the covariate(s) and each of the primary variables, requesting that the residuals be saved. e.g.:
regression var = covariates idv / dependent = idv / enter / save resid(ridv) .
regression var = covariates mod / dependent = mod / enter / save resid(rmod) .
compute x = idv * mod.
regression var = covariates x/ dependent = x / enter / save resid(rx) .
regression var = covariates dv / dependent = dv / enter / save resid(rdv) .
Then enter the residualized variables (e.g., ridv, rmod, rx, rdv) into the setup for the SIMPLE program of your choice, as in:
/var= ridv rmod rx rdv
/statistics=defaults zpp bcov
/enter ridv rmod
/test (rx) .
The slopes should be identical to the slopes obtained from analyses of the original (non-residualized) variables, but most other statistics from the residualized variable analyses will be slightly different. The coefficients from analyses of the original (non-residualized) variables are the correct ones. The analyses of the residualized variables are conducted merely as a way of determining the nature of the interaction.
12) SAS users can store any simple program as a module that can be CALLed and run with just a couple of command lines. See the SAS/IML Software manual for information on modulestorage and calls. Here is an example of how to do it. First create a library where the modules can be stored. Then:
libname cc 'csaslib';
ENTER THE RELEVANT SIMPLE PROGRAM HERE, FROM IMMEDIATELY AFTER THE PROC IML STATEMENT TO IMMEDIATELY BEFORE THE QUIT STATEMENT
store module =simple-1;
TO USE THE MODULE, RUN THE PROC REG PROCEDURE THEN RUN THESE COMMANDS:
THE FILENAME USED ON THE OUTSSCP STATEMENT IN PROC REG MUST BE THE
SAME AS THE FILENAME USED WHEN CREATING A MODULE
13) DISCLAIMER: The SIMPLE programs have been carefully tested; however, the author assumes no responsibility for errors that may result from their use.
Brian P. O'Connor
Department of Psychology
University of British Columbia - Okanagan
Kelowna, British Columbia, Canada