On Insensitivity of the Chi-Square Model Test to Nonlinear Misspecification in Structural Equation Models

By A. Mooijaart, A. Satorra. 2008

54 citations recorded by the source corpus.

In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of misspecifications, but even the theoretical (chi-square) distribution of the test is not distorted when severe interaction term misspecification is present in the postulated model. We explain this phenomenon by exploiting results on asymptotic robustness in structural equation models. The importance of this paper is to warn against the conclusion that if a proposed linear model fits the data well according to the chi-quare goodness-of-fit test, then the underlying model is linear indeed; it will be shown that the underlying model may, in fact, be severely nonlinear. In addition, the present paper shows that such insensitivity to nonlinear terms is only a particular instance of a more general problem, namely, the incapacity of the classical chi-square goodness-of-fit test to detect deviations from zero correlation among exogenous regressors (either being them observable, or latent) when the structural part of the model is just saturated.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b8276c7d99a99967d9c052712cd0bdda34e099bc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

An Alternative Approach for Nonlinear Latent Variable Models (2010, background): “This test is important because ML can yield incorrect conclusions on the necessity of an interaction term ( Mooijaart & Satorra, 2009a , 2009b).”
Probing for the Multiplicative Term in Modern Expectancy-Value Theory: A Latent Interaction Modeling Study. (2012, unknown): “It should also be noted that conventional model test statistics and fit indices cannot be used to test latent interaction effects because they are insensitive to nonlinear misspecifications (Mooijaart & Satorra, 2009).”