Moderated multiple regression for interactions involving categorical variables: a statistical control for heterogeneous variance across two groups.

Moderated multiple regression (MMR) arguably is the most popular statistical technique for investigating regression slope differences (interactions) across groups (e.g., aptitude-treatment interactions in training and differential test score-job performance prediction in selection testing). However, heterogeneous error variances can greatly bias the typical MMR analysis, and the conditions that cause heterogeneity are not uncommon. Statistical corrections that have been developed require special calculations and are not conducive to follow-up analyses that describe an interaction effect in depth. A weighted least squares (WLS) approach is recommended for 2-group studies. For 2-group studies, WLS is statistically accurate, is readily executed through popular software packages (e.g., SAS Institute, 1999; SPSS, 1999), and allows follow-up tests.

[1]  Herman Aguinis,et al.  Heterogeneity of Error Variance and the Assessment of Moderating Effects of Categorical Variables: A Conceptual Review , 1998 .

[2]  J. Fox.  Applied Regression Analysis, Linear Models, and Related Methods , 1997 .

[3]  Ralph A. Alexander,et al.  Alternative procedures for testing regression slope homogeneity when group error variances are unequal. , 1996 .

[4]  S. West,et al.  Experimental personality designs: analyzing categorical by continuous variable interactions. , 1996, Journal of personality.

[5]  James Jaccard,et al.  Measurement error in the analysis of interaction effects between continuous predictors using multiple regression: Multiple indicator and structural equation approaches. , 1995 .

[6]  C. Judd,et al.  Data analysis: continuing issues in the everyday analysis of psychological data. , 1995, Annual review of psychology.

[7]  Ralph A. Alexander,et al.  A New and Simpler Approximation for ANOVA Under Variance Heterogeneity , 1994 .

[8]  Ralph A. Alexander,et al.  Effect of error variance heterogeneity on the power of tests for regression slope differences. , 1994 .

[9]  M. Bartlett.  Properties of Sufficiency and Statistical Tests , 1992 .

[10]  S. West,et al.  Multiple Regression: Testing and Interpreting Interactions , 1991 .

[11]  J. Jaccard,et al.  Interaction effects in multiple regression , 1992 .

[12]  G. Vining,et al.  Data Analysis: A Model-Comparison Approach , 1989 .

[13]  A. H. Studenmund.  Using Econometrics: A Practical Guide , 1987 .

[14]  L. Humphreys.  An analysis and evaluation of test and item bias in the prediction context. , 1986 .

[15]  R. Snow,et al.  Lecture 2: Toward a Theory of Cognitive Aptitude for Learning from Instruction , 1984 .

[16]  Thad W. Mirer.  Economic Statistics and Econometrics , 1983 .

[17]  J. Neter,et al.  Applied Linear Regression Models , 1983 .

[18]  J. Levin,et al.  Testing for regression homogeneity under variance heterogeneity , 1982 .

[19]  R. Schuler.  Fairness in selecting employees , 1979 .

[20]  Wayne F. Cascio,et al.  Applied psychology in personnel management , 1978 .

[21]  T. Cleary.  TEST BIAS: PREDICTION OF GRADES OF NEGRO AND WHITE STUDENTS IN INTEGRATED COLLEGES , 1968 .

[22]  D. M. Ellis,et al.  Applied Regression Analysis , 1968 .

[23]  L. A. Marascuilo.  Large-sample multiple comparisons. , 1966, Psychological bulletin.

[24]  Seymour Geisser,et al.  Statistical Principles in Experimental Design , 1963 .

[25]  G. S. James.  THE COMPARISON OF SEVERAL GROUPS OF OBSERVATIONS WHEN THE RATIOS OF THE POPULATION VARIANCES ARE UNKNOWN , 1951 .

[26]  A. Aspin,et al.  An examination and further development of a formula arising in the problem of comparing two mean values. , 1948, Biometrika.

[27]  B. L. Welch.  THE SIGNIFICANCE OF THE DIFFERENCE BETWEEN TWO MEANS WHEN THE POPULATION VARIANCES ARE UNEQUAL , 1938 .