Poisson Multilevel Models with Small Samples

Research output: Contribution to journalArticle

Abstract

Recent methodological studies have investigated the properties of multilevel models with small samples. Previous work has primarily focused on continuous outcomes and little attention has been paid to count outcomes. The estimation of count outcome models can be difficult because the likelihood has no closed-form solution, meaning that approximation methods are required. Although adaptive Gaussian quadrature (AGQ) is generally seen as the gold standard, its comparative performance has been investigated with larger samples. AGQ approximates the full likelihood, a function that is known to produce biased estimates with small samples with continuous outcomes. Conversely, penalized quasi-likelihood (PQL) is considered to be a less desirable approximation; however, it can approximate the restricted likelihood function, a function that is known to perform well with smaller samples with continuous outcomes. The goal of this paper is to compare the small sample bias of full likelihood methods to the linearization bias of PQL with restricted likelihood. Simulation results indicate that the linearization bias of PQL is preferable to the finite sample bias of AGQ with smaller samples.

Original languageEnglish (US)
JournalMultivariate Behavioral Research
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Multilevel Models
Poisson Model
Small Sample
Likelihood Functions
Penalized Quasi-likelihood
Adaptive Quadrature
Gaussian Quadrature
Likelihood
Linearization
Count
Likelihood Methods
Likelihood Function
Closed-form Solution
Approximation Methods
Gold
Biased
Approximation
Estimate
Simulation

Keywords

  • generalized linear modeling
  • mixed models
  • Multilevel modeling
  • small sample

ASJC Scopus subject areas

  • Statistics and Probability
  • Experimental and Cognitive Psychology
  • Arts and Humanities (miscellaneous)

Cite this

Poisson Multilevel Models with Small Samples. / McNeish, Daniel.

In: Multivariate Behavioral Research, 01.01.2019.

Research output: Contribution to journalArticle

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