TY - JOUR
T1 - Estimating Latent Variable Interactions With Nonnormal Observed Data
T2 - A Comparison of Four Approaches
AU - Cham, Heining
AU - West, Stephen
AU - Ma, Yue
AU - Aiken, Leona S.
N1 - Funding Information:
We thank Mark Roosa, Jenn-Yun Tein, and La Familia (The Family Project) [National Institute of Mental Health (NIMH) Grant R01 MH68920; culture, context, and Mexican American mental health], at the Prevention Research Center, Arizona State University, who generously provided data for the example. Stephen G. West was partially supported by a Forschungspreis (research prize) from the Alexander von Humboldt Foundation.
PY - 2012/11
Y1 - 2012/11
N2 - 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.
AB - 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.
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U2 - 10.1080/00273171.2012.732901
DO - 10.1080/00273171.2012.732901
M3 - Article
AN - SCOPUS:84872554193
SN - 0027-3171
VL - 47
SP - 840
EP - 876
JO - Multivariate Behavioral Research
JF - Multivariate Behavioral Research
IS - 6
ER -