Estimating Latent Variable Interactions with Missing Data

Investigating interaction effect is very popular in psychological research. The present study is concerned with a special kind of interaction effect, which is essentially the interaction effect between two continuous latent variables and hence is refereed to as latent variable interaction effect in this study. The goal of the present study is to investigate the estimation of such interaction effect in the context of missing data. Two estimation approaches, direct maximum likelihood and multiple imputation, are proposed for estimating such interactions with missing data. A Monte Carlo simulation study is sequentially conducted to examine the behavior of these two estimation approaches across different data distributions, sample sizes, reliabilities of measures, and missing data rates and mechanisms. Specifically, their performances are examined with respect to both parameter estimation and model fit evaluation.To summarize the empirical findings in a succinct manner, the simulation results indicate that all of above factors affect, with varying degree, the parameter estimates and model fit statistics from both approaches. Direct maximum likelihood approach yields acceptable estimation results when the missing data are missing completely at random. It also exhibits limited robustness when the data are nonnormal and missing at random. Parameter estimates from multiple imputation approach tend to exhibit severe negative biases when the rates of missing data are high, regardless of missing data mechanism. Issues related to these findings are discussed in detail.