Multiple Group Comparisons of the Fixed and Random Effects from the Generalized Linear Mixed Model

SAGE Publications. 2455 Teller Road, Thousand Oaks, CA 91320. Tel: 800-818-7243; Tel: 805-499-9774; Fax: 800-583-2665; e-mail: [email protected]; Web site: https://sagepub.com

Y

57

Models; Achievement Tests; Foreign Countries; International Assessment; Reading Achievement; Reading Tests; Grade 4; Elementary Secondary Education; Mathematics Achievement; Mathematics Tests; Science Achievement; Science Tests; Regression (Statistics); Statistical Inference; Maximum Likelihood Statistics

Progress in International Reading Literacy Study; Trends in International Mathematics and Science Study

10.1177/0049124120986182

0049-1241
1552-8294

In this article, we extend Liao's test for across-group comparisons of the fixed effects from the generalized linear model to the fixed and random effects of the generalized linear mixed model (GLMM). Using as our basis the Wald statistic, we developed an asymptotic test statistic for across-group comparisons of these effects. The test can be applied when the fixed and random effects are multivariate normally distributed, and it works well for any link function and conditional distribution of the dependent variable of the GLMM. We also derived the asymptotic properties of this test, and because power information does not exist for either our new test statistic or Liao's test, we implemented a power study to demonstrate the superiority of these tests over the alternatively proposed F test. Using an example, we show the application of the test and then discuss its possible restrictions with respect to the distribution of the random effects.

As Provided

2024

EJ1411242