A comparison of likelihood ratio tests and Rao's score test for three separable covariance matrix structures

Katarzyna Filipiak, Daniel Klein, Anuradha Roy

Research output: Research - peer-reviewArticle

Abstract

The problem of testing the separability of a covariance matrix against an unstructured variance-covariance matrix is studied in the context of multivariate repeated measures data using Rao's score test (RST). The RST statistic is developed with the first component of the separable structure as a first-order autoregressive (AR(1)) correlation matrix or an unstructured (UN) covariance matrix under the assumption of multivariate normality. It is shown that the distribution of the RST statistic under the null hypothesis of any separability does not depend on the true values of the mean or the unstructured components of the separable structure. A significant advantage of the RST is that it can be performed for small samples, even smaller than the dimension of the data, where the likelihood ratio test (LRT) cannot be used, and it outperforms the standard LRT in a number of contexts. Monte Carlo simulations are then used to study the comparative behavior of the null distribution of the RST statistic, as well as that of the LRT statistic, in terms of sample size considerations, and for the estimation of the empirical percentiles. Our findings are compared with existing results where the first component of the separable structure is a compound symmetry (CS) correlation matrix. It is also shown by simulations that the empirical null distribution of the RST statistic converges faster than the empirical null distribution of the LRT statistic to the limiting χ2 distribution. The tests are implemented on a real dataset from medical studies.

LanguageEnglish (US)
Pages192-215
Number of pages24
JournalBiometrical Journal
Volume59
Issue number1
DOIs
StatePublished - Jan 1 2017

Fingerprint

Rao's Score Test
Likelihood Ratio Test
Covariance matrix
Likelihood ratio test
Score test
Test statistic
Test Statistic
Null Distribution
Likelihood Ratio Test Statistic
Empirical Distribution
Correlation Matrix
Separability
Context
Correlation matrix
Empirical distribution
Compound Symmetry
Multivariate Normality
Measure Data
Variance-covariance Matrix
Repeated Measures

Keywords

  • Empirical null distribution
  • Likelihood ratio test
  • Maximum likelihood estimates
  • Rao’s score test
  • Separable covariance structure

ASJC Scopus subject areas

  • Statistics and Probability
  • Medicine(all)
  • Statistics, Probability and Uncertainty

Cite this

A comparison of likelihood ratio tests and Rao's score test for three separable covariance matrix structures. / Filipiak, Katarzyna; Klein, Daniel; Roy, Anuradha.

In: Biometrical Journal, Vol. 59, No. 1, 01.01.2017, p. 192-215.

Research output: Research - peer-reviewArticle

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