A Statistically Justified Pairwise ML Method for Incomplete Nonnormal Data: A Comparison With Direct ML and Pairwise ADF

Abstract

This article proposes a new approach to the statistical analysis of pairwise-present covariance structure data. The estimator is based on maximizing the complete data likelihood function, and the associated test statistic and standard errors are corrected for misspecification using Satorra-Bentler corrections. A Monte Carlo study was conducted to compare the proposed method (pairwise maximum likelihood [ML]) to 2 other methods for dealing with incomplete nonnormal data: direct ML estimation with the Yuan-Bentler corrections for nonnormality (direct ML) and the asymptotically distribution free (ADF) method applied to available cases (pairwise ADF). Data were generated from a 4-factor model with 4 indicators per factor; sample size varied from 200 to 5,000; data were either missing completely at random (MCAR) or missing at random (MAR); and the proportion of missingness was either 15% or 30%. Measures of relative performance included model fit, relative accuracy in parameter estimates and their standard errors, and efficiency of parameter estimates. The results generally favored direct ML over either of the pairwise methods, except at N = 5,000, when ADF outperformed both ML methods with MAR data. The inferior performance of the 2 pairwise methods was primarily due to inflated test statistics. Among the unexpected findings was that ADF did better at estimating factor covariances in all conditions, and that MCAR data presented more problems for all methods than did MAR data, in terms of convergence, performance of test statistics, and relative accuracy of parameter estimates.