Structural Equation Models and the Regression Bias for Measuring Correlates of Change

ANCOVA and regression both exhibit a directional bias when measuring correlates of change. This bias confounds the comparison of changes between naturally occurring groups with large pretest differences (ANCOVA), or for identifying predictors of change when the predictor is correlated with pretest (regression). This bias is described in some detail. A computer simulation study is presented, which shows that properly identified structural equation models are not susceptible to this bias. Neither gain scores (posttest minus pretest) nor structural equation models exhibit the “regression bias.” Other factors, such as skewness, that may confound measurement of change are also discussed.

[1]  R. Darlington,et al.  Regression and Linear Models , 1990 .

[2]  Bradley E. Huitema,et al.  The analysis of covariance and alternatives , 1980 .

[3]  J. Jamieson,et al.  Dealing with baseline differences: two principles and two dilemmas. , 1999, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[4]  N. Schneiderman,et al.  The reliability and specificity of delta versus residualized change as measures of cardiovascular reactivity to behavioral challenges. , 1991, Psychophysiology.

[5]  K. Schaie,et al.  Methodological issues in aging research , 1990 .

[6]  Mark Shevlin,et al.  Effects of sample size, model specification and factor loadings on the GFI in confirmatory factor analysis , 1998 .

[7]  T. Raykov A Structural Equation Model for Measuring Residualized Change and Discerning Patterns of Growth or Decline , 1993 .

[8]  David Rogosa,et al.  Myths about longitudinal research. , 1988 .

[9]  D. W. Zimmerman,et al.  Are Simple Gain Scores Obsolete? , 1996 .

[10]  H. Wainer Adjusting for differential base rates: Lord's paradox again. , 1991, Psychological bulletin.

[11]  Tenko Raykov,et al.  Structural models for studying correlates and predictors of change , 1992 .

[12]  The law of initial values: five factors or two? , 1993, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[13]  P. Bentler,et al.  Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives , 1999 .

[14]  M. Eid,et al.  Modeling true intraindividual change: True change as a latent variable. , 1997 .

[15]  P. Bonate Analysis of pretest-posttest designs , 2000 .

[16]  J. Jamieson Measurement of Change and the Law of Initial Values: A Computer Simulation Study , 1995 .

[17]  D. Rubin,et al.  ON LORD'S PARADOX , 1982 .

[18]  The law of initial values: a four factor theory. , 1993, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[19]  Terry E. Duncan,et al.  Latent Variable Modeling of Longitudinal and Multilevel Substance Use Data. , 1997, Multivariate behavioral research.

[20]  James R. Craig,et al.  Methods of psychological research , 1979 .

[21]  J. S. Long,et al.  Testing Structural Equation Models , 1993 .

[22]  F. Lord A paradox in the interpretation of group comparisons. , 1967, Psychological bulletin.

[23]  L. Low,et al.  The Analysis of Covariance and Alternatives , 1983 .

[24]  B. Thompson,et al.  EFFECTS OF SAMPLE SIZE, ESTIMATION METHODS, AND MODEL SPECIFICATION ON STRUCTURAL EQUATION MODELING FIT INDEXES , 1999 .

[25]  E. Maris Covariance adjustment versus gain scores-revisited , 1998 .

[26]  John B. Willett,et al.  Measuring change: What individual growth modeling buys you. , 1997 .

[27]  R. MacCallum,et al.  Studying Multivariate Change Using Multilevel Models and Latent Curve Models. , 1997, Multivariate behavioral research.

[28]  John B. Willett,et al.  Understanding correlates of change by modeling individual differences in growth , 1985 .

[29]  M. Browne,et al.  Alternative Ways of Assessing Model Fit , 1992 .

[30]  John McLeod,et al.  Change and Development , 1991 .

[31]  J. Jamieson Correlates of reactivity: problems with regression based methods. , 1994, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[32]  T. Raykov Simultaneous study of individual and group patterns of latent longitudinal change using structural equation modeling , 1997 .

[33]  G. Hancock,et al.  Assessing Change over Time Using Latent Growth Modeling. , 1998 .

[34]  Tenko Raykov,et al.  Studying Correlates and Predictors of Longitudinal Change Using Structural Equation Modeling , 1994 .

[35]  Karl G. Jöreskog,et al.  LISREL 7: A guide to the program and applications , 1988 .