A Novel Bayesian Approach for Latent Variable Modeling from Mixed Data with Missing Values

TL;DR

This paper introduces a Bayesian Gaussian copula factor (BGCF) method for estimating latent variable models from mixed continuous and ordinal data with missing values, demonstrating superior performance over existing approaches.

Contribution

The paper presents a novel BGCF approach that is consistent and robust for latent variable modeling with mixed data and missing values, outperforming current methods.

Findings

BGCF outperforms state-of-the-art alternatives in simulations.

BGCF is robust to violations of model assumptions.

BGCF shows favorable results over robust maximum likelihood on real data.

Abstract

We consider the problem of learning parameters of latent variable models from mixed (continuous and ordinal) data with missing values. We propose a novel Bayesian Gaussian copula factor (BGCF) approach that is consistent under certain conditions and that is quite robust to the violations of these conditions. In simulations, BGCF substantially outperforms two state-of-the-art alternative approaches. An illustration on the `Holzinger & Swineford 1939' dataset indicates that BGCF is favorable over the so-called robust maximum likelihood (MLR) even if the data match the assumptions of MLR.