Full Information Maximum Likelihood Estimation for Latent Variable Interactions With Incomplete Indicators

Abstract

Researchers have developed missing data handling techniques for estimating interaction effects in multiple regression. Extending to latent variable interactions, we investigated full information maximum likelihood (FIML) estimation to handle incompletely observed indicators for product indicator (PI) and latent moderated structural equations (LMS) methods. Drawing on the analytic work on missing data handling techniques in multiple regression with interaction effects, we compared the performance of FIML for PI and LMS analytically. We performed a simulation study to compare FIML for PI and LMS. We recommend using FIML for LMS when the indicators are missing completely at random (MCAR) or missing at random (MAR) and when they are normally distributed. FIML for LMS produces unbiased parameter estimates with small variances, correct Type I error rates, and high statistical power of interaction effects. We illustrated the use of these methods by analyzing the interaction effect between advanced cancer patients’ depression and change of inner peace well-being on future hopelessness levels.

A novel global urban typology framework for sustainable mobility futures

“…To handle missing data, full-information maximum likelihood was incorporated. In the estimation procedure, the conditional distributions of variables with missingness were therefore assumed to be multivariate normal on variables with complete observations across the sample, ensuring that all observations were utilized in model estimation (Hirose et al 2016, Cham et al 2017. The rate of missingness in the dataset is 15%, and we assumed that observations were missing at random.…”

Effects of school climate and teacher self-efficacy on job satisfaction of mostly STEM teachers: a structural multigroup invariance approach

“…These tests show no significant statistics for each components of the teacher self-efficacy (χ 2 = 302.98, df = 317, p = .750 at 0.1-0.5% missing), borderline significant statistics for job satisfaction (χ 2 = 195.79, df = 165, p = .051 at 1.6-2.0% missing), and significant statistics for school climate (χ 2 = 134.25, df = 97, p = .007 at 1.0-14.2% missing). Thus, for convenient use of these data in subsequence analysis, full information maximum likelihood (FIML) estimation with expectation maximum (EM) algorithm is utilized as opposed to multiple imputation to replace the missing data (Cham, Reshetnyak, Rosenfeld, & Breitbart, 2017).…”

Latent Interaction Modeling with Planned Missing Data Designs

“…Satorra-Bentler standard errors, typically used in cases of non-normality, offer little noticeable improvement with regard to bias when lower-order terms are normal or non-normal (Cham et al, 2012;Marsh et al, 2004). Huber-White standard errors, however, have not been systematically examined when used in latent interaction estimation (Cham et al, 2017(Cham et al, , 2012Enders et al, 2014;Lin et al, 2010). In Mplus, normal theory standard errors are the default for PI approaches whereas Huber-White standard errors are the default for the LMS approach (Muthén & Muthén, 2012).…”

“…When data are non-normally distributed, LMS suffers compared to product indicator approaches in bias and coverage (Cham et al, 2012). Whether or not these different estimation methods also perform differently under planned missingness has not been explored (Cham, Reshetnyak, Rosenfeld, & Breitbart, 2017;Enders, Baraldi, & Cham, 2014).…”