Comparative GMM and GQL logistic regression models on hierarchical data

Bei Wang, Jeffrey Wilson

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We often rely on the likelihood to obtain estimates of regression parameters but it is not readily available for generalized linear mixed models (GLMMs). Inferences for the regression coefficients and the covariance parameters are key in these models. We presented alternative approaches for analyzing binary data from a hierarchical structure that do not rely on any distributional assumptions: a generalized quasi-likelihood (GQL) approach and a generalized method of moments (GMM) approach. These are alternative approaches to the typical maximum-likelihood approximation approach in Statistical Analysis System (SAS) such as Laplace approximation (LAP). We examined and compared the performance of GQL and GMM approaches with multiple random effects to the LAP approach as used in PROC GLIMMIX, SAS. The GQL approach tends to produce unbiased estimates, whereas the LAP approach can lead to highly biased estimates for certain scenarios. The GQL approach produces more accurate estimates on both the regression coefficients and the covariance parameters with smaller standard errors as compared to the GMM approach. We found that both GQL and GMM approaches are less likely to result in non-convergence as opposed to the LAP approach. A simulation study was conducted and a numerical example was presented for illustrative purposes.

Original languageEnglish (US)
Pages (from-to)1-17
Number of pages17
JournalJournal of Applied Statistics
DOIs
StateAccepted/In press - Jan 20 2017

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Generalized Method of Moments
Hierarchical Data
Quasi-likelihood
Logistic Regression Model
Laplace Approximation
Regression Coefficient
Estimate
Statistical Analysis
Generalized Linear Mixed Model
Binary Data
Alternatives
Standard error
Hierarchical Structure
Random Effects
Biased
Maximum Likelihood
Likelihood
Regression
Likely
Generalized method of moments

Keywords

  • binary response
  • correlated data
  • Generalized linear mixed model
  • Newton–Raphson
  • R

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Comparative GMM and GQL logistic regression models on hierarchical data. / Wang, Bei; Wilson, Jeffrey.

In: Journal of Applied Statistics, 20.01.2017, p. 1-17.

Research output: Contribution to journalArticle

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