Comparison of the estimators of the intra-cluster correlation for the nested error regression model

ABSTRACT

The intra-cluster correlation is insisted on nested error regression model that, in practice, is rarely known. This article demonstrates the size in generalized least squares (GLS) F-test using Fuller–Battese transformation and modification F-test. For the balanced case, the former using strictly positive, analysis of covariance (ANCOVA) and analysis of variance (ANOVA) estimators of intra-cluster correlation can control the size for moderate intra-cluster correlations. For small intra-cluster correlation, they perform well when the numbers of cluster are large. The latter using the ANOVA estimator performs well except for small numbers of cluster. When intra-cluster correlation is large, it cannot control the size. For the unbalanced case, the GLS F-test using the Fuller–Battese transformation and the modification F-test using the strictly positive, the ANCOVA and the ANOVA estimators maintain the significance level for small total sample size and small intra-cluster correlations when there is a large variation in cluster sizes, but they perform well in controlling the size for large total sample size and small different variation in cluster sizes. Besides, Henderson’s method 3 estimator maintains the significance level for a few situations.

KEYWORDS:

• ANCOVA estimator
• ANOVA estimator
• Henderson’s method 3 estimator
• Intra-cluster correlation
• Strictly positive estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F03
• 62F86

Funding

This work was supported by the Centre of Excellence in Mathematics, Commission on Higher Education, Thailand and the Faculty of Science, Mahidol University, Thailand.