Exploratory analyses to improve model fit: Errors due to misspecification and a strategy to reduce their occurrence

Two Lagrange multiplier (LM) methods may be used in specification searches for adding parameters to models: one based on univariate LM tests and respecification of the model (LM‐respecified method) and the other based on a partitioning of multivariate LM tests (LM‐incremental method). These methods may result in extraneous parameters being included in models due to either sampling error or the model being misspecified. A 2‐stage specification search may be used to reduce errors due to misspecification. In the 1st stage, parameters are added to models based on LM tests to maximize fit. Second, parameters added in the 1st stage are deleted if they are no longer necessary to maintain model fit. Illustrations are presented to demonstrate that errors due to misspecification occur with the LM‐respecified method and are even more likely with the LM‐incremental approach. These illustrations also show how the deletion stage can help eliminate some of these errors.

[1]  P. Bentler,et al.  Model Modification in Covariance Structure Modeling: A Comparison among Likelihood Ratio, Lagrange Multiplier, and Wald Tests. , 1990, Multivariate behavioral research.

[2]  Robert C. MacCallum,et al.  SPECIFICATION SEARCHES IN COVARIANCE STRUCTURE MODELING , 1986 .

[3]  S. Green,et al.  A Monte Carlo Investigation of Methods for Controlling Type I Errors with Specification Searches in Structural Equation Modeling. , 1998, Multivariate behavioral research.

[4]  R. MacCallum,et al.  Model modifications in covariance structure analysis: the problem of capitalization on chance. , 1992, Psychological bulletin.

[5]  D. Kaplan.  Evaluating and Modifying Covariance Structure Models: A Review and Recommendation. , 1990, Multivariate behavioral research.

[6]  E. Pedhazur.  Multiple Regression in Behavioral Research: Explanation and Prediction , 1982 .

[7]  Willem E. Saris,et al.  The Detection and Correction of Specification Errors in Structural Equation Models , 1987 .

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

[9]  Gregory R. Hancock.  A sequential Scheffé‐type respecification procedure for controlling type I error in exploratory structural equation model modification , 1999 .

[10]  S. Green,et al.  Control of Type I Errors with Multiple Tests of Constraints in Structural Equation Modeling. , 1997, Multivariate behavioral research.

[11]  Thomas J. Page,et al.  Causal modelling in nonexperimental research : an introduction to the LISREL approach , 1985, American Political Science Review.

[12]  Peter M. Bentler,et al.  EQS : structural equations program manual , 1989 .

[13]  Zvi Drezner,et al.  Model specification searches in structural equation modeling using tabu search , 1998 .

[14]  Richard G. Lomax,et al.  A Beginner's Guide to Structural Equation Modeling , 2022 .

[15]  Peter M. Bentler,et al.  Model Search With TETRAD II and EQS , 1990 .