Estimating longitudinal change in latent variable means: a comparison of non-negative matrix factorization and other item non-response methods

Abstract

Estimates of longitudinal change in the parameters of latent (i.e. unobserved) variables, including means, are affected by non-response on the items or indicators of the latent variable. This study used Monte Carlo simulation and a numeric example to compare four ordinal item non-response methods: non-negative matrix factorization (NNMF), multiple imputation with conditional proportional odds model (POM), full information maximum likelihood (FIML) and complete-case analysis, when estimating the longitudinal change in latent variable means. The mean squared error for the NNMF method was more than 40% lower than for the FIML and POM methods when the latent variable correlations over time were strong, percentage of missing data was 25% or more, and sample size was large. The NNMF method is a promising method to address item non-response. It is relatively efficient when sample size is large, and the percentage of missing data is high but has limitations under other data-analytic conditions.