Testing differences between nested covariance structure models: Power analysis and null hypotheses.

For comparing nested covariance structure models, the standard procedure is the likelihood ratio test of the difference in fit, where the null hypothesis is that the models fit identically in the population. A procedure for determining statistical power of this test is presented where effect size is based on a specified difference in overall fit of the models. A modification of the standard null hypothesis of zero difference in fit is proposed allowing for testing an interval hypothesis that the difference in fit between models is small, rather than zero. These developments are combined yielding a procedure for estimating power of a test of a null hypothesis of small difference in fit versus an alternative hypothesis of larger difference.

[1]  K. Yuan.  Fit Indices Versus Test Statistics , 2005, Multivariate behavioral research.

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

[3]  S. Manne,et al.  Perceived control, coping efficacy, and avoidance coping as mediators between spouses' unsupportive behaviors and cancer patients' psychological distress. , 2000, Health psychology : official journal of the Division of Health Psychology, American Psychological Association.

[4]  T. W. Anderson,et al.  Asymptotic Chi-Square Tests for a Large Class of Factor Analysis Models , 1990 .

[5]  Ronald C. Serlin,et al.  Rationality in psychological research: The good-enough principle. , 1985 .

[6]  K. Bollen,et al.  The Noncentral Chi-square Distribution in Misspecified Structural Equation Models: Finite Sample Results from a Monte Carlo Simulation , 2002, Multivariate behavioral research.

[7]  A. Satorra,et al.  Scaled test statistics and robust standard errors for non-normal data in covariance structure analysis: a Monte Carlo study. , 1991, The British journal of mathematical and statistical psychology.

[8]  D. Heisey,et al.  The Abuse of Power , 2001 .

[9]  A. Satorra,et al.  Power of the likelihood ratio test in covariance structure analysis , 1985 .

[10]  Kenneth A. Bollen,et al.  Finite Sampling Properties of the Point Estimates and Confidence Intervals of the RMSEA , 2003 .

[11]  S. Manne,et al.  Perceived control, coping efficacy, and avoidance coping as mediators between spousal unsupportive behaviors and psychological distress. , 2000 .

[12]  S. West,et al.  The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. , 1996 .

[13]  Spiridon Penev,et al.  Nested structural equation models: Noncentrality and power of restriction test , 1998 .

[14]  Karl G. Jöreskog,et al.  Lisrel 8: User's Reference Guide , 1997 .

[15]  R. MacCallum,et al.  Power analysis and determination of sample size for covariance structure modeling. , 1996 .

[16]  D. Zuroff,et al.  Self-critical perfectionism and daily affect: dispositional and situational influences on stress and coping. , 2003, Journal of personality and social psychology.

[17]  W. Meredith.  Measurement invariance, factor analysis and factorial invariance , 1993 .

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

[19]  Jeff Joireman,et al.  The aggression paradox: understanding links among aggression, sensation seeking, and the consideration of future consequences. , 2003, Journal of personality and social psychology.

[20]  James H. Steiger,et al.  A note on multiple sample extensions of the RMSEA fit index , 1998 .

[21]  M. Browne,et al.  Automated Fitting of Nonstandard Models. , 1992, Multivariate behavioral research.

[22]  R. MacCallum,et al.  Power Analysis in Covariance Structure Modeling Using GFI and AGFI. , 1997, Multivariate behavioral research.

[23]  Y Kano,et al.  Can test statistics in covariance structure analysis be trusted? , 1992, Psychological bulletin.

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

[25]  B. Muthén,et al.  A comparison of some methodologies for the factor analysis of non‐normal Likert variables: A note on the size of the model , 1992 .

[26]  A. Shapiro,et al.  On the multivariate asymptotic distribution of sequential Chi-square statistics , 1985 .

[27]  M. Browne.  Asymptotically distribution-free methods for the analysis of covariance structures. , 1984, The British journal of mathematical and statistical psychology.

[28]  A. Shapiro,et al.  Robustness of normal theory methods in the analysis of linear latent variate models. , 1988 .

[29]  Erik Woody,et al.  Is who you are who you're talking to? Interpersonal style and complementarity in mixed-sex interactions. , 2003, Journal of personality and social psychology.