Abstract
Rank-based analysis of linear models is based on selecting an appropriate score function. The information about the shape of the underlying distribution is necessary for the optimal selection; leading towards asymptotically efficient analysis. In this study, we analyzed the multilevel model with cluster-correlated error terms following a family of skew-t distribution with the rank-based approach based on score function derived for the class of skew-normal distribution. The rank fit is compared with the Restricted Maximum Likelihood (REML) estimation in terms of validity and efficiency for different sample sizes. A Monte Carlo simulation study is carried out over skewed-t and contaminated-t distribution with a range of skewness parameter from moderately to highly skewed. The standard error of regression coefficients is significantly reduced in the rank-based approach and further reduces for a large sample size. Rank-based fit appeared asymptotically efficient than REML for each shape parameter of skewness in skew-t and contaminated-t distribution computed through a calculation of precision. The empirical validity of fixed effects is obtained up to the nominal level 0.95 in REML but not rank-based with skew-normal score function.
Highlights
Several experimental and observational studies often occur resulting in cluster-correlated data, for example in clinical designs with multiple centers known as clusters, repeated measurement designs where individuals are supposed as clusters
This study is focused on rank-based analysis with score function that is suitable for skew-normal (SN) class of distributions of the error term in linear models
Table-1 summarizes the results of simulations, comprising rank-based and Restricted Maximum Likelihood (REML) analysis of skewed-t distribution
Summary
Several experimental and observational studies often occur resulting in cluster-correlated data, for example in clinical designs with multiple centers known as clusters, repeated measurement designs where individuals are supposed as clusters. This study is focused on rank-based analysis with score function that is suitable for skew-normal (SN) class of distributions of the error term in linear models. We applied the score function suitable for skew-normal error distribution from this package and skew-t error terms are generated from multilevel models. We performed a Monte Carlo simulation study to discuss the robustness and efficiency of rank-based procedures developed for skew-normal and applied over a class of skew-t distributions at different sample sizes. The findings of this study confirm the outclass performance of skew-normal procedure over the traditional approach REML in the neighborhood of the correct applied on skew-t level-1 and level-2 random errors in the multilevel model
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