Estimating Latent Variable Interactions With Nonnormal Observed Data: A Comparison of Four Approaches

Heining Cham, Stephen West, Yue Ma, Leona S. Aiken

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

A Monte Carlo simulation was conducted to investigate the robustness of 4 latent variable interaction modeling approaches (Constrained Product Indicator [CPI], Generalized Appended Product Indicator [GAPI], Unconstrained Product Indicator [UPI], and Latent Moderated Structural Equations [LMS]) under high degrees of nonnormality of the observed exogenous variables. Results showed that the CPI and LMS approaches yielded biased estimates of the interaction effect when the exogenous variables were highly nonnormal. When the violation of nonnormality was not severe (normal; symmetric with excess kurtosis < 1), the LMS approach yielded the most efficient estimates of the latent interaction effect with the highest statistical power. In highly nonnormal conditions, the GAPI and UPI approaches with maximum likelihood (ML) estimation yielded unbiased latent interaction effect estimates, with acceptable actual Type I error rates for both the Wald and likelihood ratio tests of interaction effect at N ≥ 500. An empirical example illustrated the use of the 4 approaches in testing a latent variable interaction between academic self-efficacy and positive family role models in the prediction of academic performance.

Original languageEnglish (US)
Pages (from-to)840-876
Number of pages37
JournalMultivariate Behavioral Research
Volume47
Issue number6
DOIs
StatePublished - Nov 2012

Fingerprint

Latent Variables
Self Efficacy
Interaction Effects
Structural Equations
Interaction
Non-normality
Estimate
Self-efficacy
Statistical Power
Type I Error Rate
Kurtosis
Likelihood Ratio Test
Maximum Likelihood Estimation
Biased
Excess
Monte Carlo Simulation
Robustness
Testing
Prediction
Modeling

ASJC Scopus subject areas

  • Experimental and Cognitive Psychology
  • Statistics and Probability
  • Arts and Humanities (miscellaneous)

Cite this

Estimating Latent Variable Interactions With Nonnormal Observed Data : A Comparison of Four Approaches. / Cham, Heining; West, Stephen; Ma, Yue; Aiken, Leona S.

In: Multivariate Behavioral Research, Vol. 47, No. 6, 11.2012, p. 840-876.

Research output: Contribution to journalArticle

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