Recursive partitioning imputation versus full information maximum likelihood in finite mixture modeling

Abstract

It is well established that omitting important variables that are related to the propensity for missingness can lead to biased parameter estimates and invalid inference. Nevertheless, researchers conducting a person-centered analysis ubiquitously adopt a full information maximum likelihood (FIML) approach to treat missing data in a manner that assumes the missingness is only related to the observed indicators and is not related to any external variables. Such an assumption is generally considered overly restrictive in the behavioral sciences where the data are observational in nature. At the same time, previous research has discouraged the adoption of multiple imputation to treat missing data in person-centered analyses because traditional imputation models make a single-class assumption and do not reflect the multiple group structure of data with latent subpopulations (Enders & Gottschall, 2011). However, more modern imputation models that rely on recursive partitioning do not impose a single-class structure to the data. Focusing on latent profile analysis, we demonstrate in simulations that in samples of N = 1,200 or greater, recursive partitioning imputation algorithms can effectively incorporate external information from auxiliary variables to attenuate nonresponse bias better than FIML and multivariate normal imputation. Moreover, we find that recursive imputation models lead to confidence intervals with adequate coverage and they better recover posterior class probabilities than alternative missing data strategies. Taken together, our findings point to the promise and potential of multiple imputation in person-centered analyses once remaining methodological gaps around pooling and class enumeration are filled.