Addressing nonresponse for categorical data items using full information maximum likelihood with Latent GOLD 5.0

Abstract

Full information maximum likelihood (FIML) is an important approach to compensating for nonresponse in data analysis. Unfortunately, only a few software packages implement FIML and even fewer have the capability to compensate for missing not at random (MNAR) nonresponse. One of these packages is Statistical Innovations’ Latent GOLD; however, the user documentation for Latent GOLD provides no mention of this capability. The purpose of this paper is to provide guidance for fitting MNAR FIML models for categorical data items using the Latent GOLD 5.0 software. By way of comparison, we also provide guidance on fitting FIML models for nonresponse missing at random (MAR) using the methods of Fuchs (1982) and Fay (1986), who incorporated item nonresponse indicators within a structural modeling framework. We compare both FIML for MAR and FIML for MNAR nonresponse models for independent and dependent variables. Also, we provide recommendations for future applications of FIML using Latent GOLD.