Three Likelihood-Based Methods for Mean and Covariance Structure Analysis with Nonnormal Missing Data

Bibliographic Data

ID8019691
AuthorsKe-Hai Yuan (0000-0003-0610-1745, University of North Texas), Peter M Bentler (0000-0002-9440-721X, University of California, Los Angeles)
Year2000
Volume30
Issue1
Pages165-200
Publication date2000-08-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueSociological Methodology (JOURNAL)
Journal identifiersISSN: 0081-1750 • E-ISSN: 1467-9531
PublisherSAGE Publishing (PUBLISHER • US)
DOI10.1111/0081-1750.00078
OpenAlexW2095968500
LanguageEN
Citations received465
References cited56

Survey and longitudinal studies in the social and behavioral sciences generally contain missing data. Mean and covariance structure models play an important role in analyzing such data. Two promising methods for dealing with missing data are a direct maximum-likelihood and a two-stage approach based on the unstructured mean and covariance estimates obtained by the EM-algorithm. Typical assumptions under these two methods are ignorable nonresponse and normality of data. However, data sets in social and behavioral sciences are seldom normal, and experience with these procedures indicates that normal theory based methods for nonnormal data very often lead to incorrect model evaluations. By dropping the normal distribution assumption, we develop more accurate procedures for model inference. Based on the theory of generalized estimating equations, a way to obtain consistent standard errors of the two-stage estimates is given. The asymptotic efficiencies of different estimators are compared under various assumptions. We also propose a minimum chi-square approach and show that the estimator obtained by this approach is asymptotically at least as efficient as the two likelihood-based estimators for either normal or nonnormal data. The major contribution of this paper is that for each estimator, we give a test statistic whose asymptotic distribution is chisquare as long as the underlying sampling distribution enjoys finite fourth-order moments. We also give a characterization for each of the two likelihood ratio test statistics when the underlying distribution is nonnormal. Modifications to the likelihood ratio statistics are also given. Our working assumption is that the missing data mechanism is missing completely at random. Examples and Monte Carlo studies indicate that, for commonly encountered nonnormal distributions, the procedures developed in this paper are quite reliable even for samples with missing data that are missing at random

Asymptotic analysis · Asymptotic distribution · Covariance · Econometrics · Empirical likelihood · Estimating equations · Estimator · Inference · Likelihood-ratio test · Maximum likelihood · Missing data · Normal distribution · Normality · Restricted maximum likelihood · Statistical hypothesis testing · Statistics · Test statistic · Advanced Statistical Methods and Models · Computer Science · Mathematics · Statistical Methods and Bayesian Inference · Statistical Methods and Inference

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