Abstract: Parameter Influence In Structural Equation Models

Multivariate Behavioral Research
Taehun Lee, Robert C MacCallum

Abstract

In applications of SEM, investigators obtain and interpret parameter estimates that are computed so as to produce optimal model fit in the sense that the obtained model fit would deteriorate to some degree if any of those estimates were changed. This property raises a question: to what extent would model fit deteriorate if parameter estimates were changed? And which parameters have the greatest influence on model fit? This is the idea of parameter influence. The present paper will cover two approaches to quantifying parameter influence. Both are based on the principle of likelihood displacement (LD), which quantifies influence as the discrepancy between the likelihood under the original model and the likelihood under the model in which a minor perturbation is imposed ( Cook, 1986 ). One existing approach for quantifying parameter influence is a vector approach ( Lee & Wang, 1996 ) that determines a vector in the parameter space such that altering parameter values simultaneously in this direction will cause maximum change in LD. We propose a new approach, called influence mapping for single parameters, that determines the change in model fit under perturbation of a single parameter holding other parameter estimates constant. An ...Continue Reading

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