Development of a new modified hogg type adaptive scheme for multilevel models with diverse error distributions

Abstract

The rank-based method is a well-known robust estimation technique in analyzing the linear models for non normal error distributions. The efficiency of rank-based analysis can be upgraded by selecting a suitable score function according to the probability distribution of the error term. In this study, a modified version of Hogg’s type adaptive scheme is developed by introducing a new set of cutoff values. The novel idea is to use the rank-based estimation by using the score functions selected through Hogg’s and modified Hogg’s schemes for multilevel models that generate cluster-correlated errors. The efficiency of both schemes is compared for symmetric, asymmetric, and light-tailed to heavy-tailed error distributions under various sample sizes through simulation study based on bias, variance, mean square error, the selected score function, and precision. The modified Hogg’s scheme produces a more efficient rank-based fit than Hogg’s scheme in case of skewed error distribution and produces equal efficiency for symmetric heavy, moderate, and light-tailed distributions. The empirical comparison of score selection through both schemes is also illustrated via a real example. The modified Hogg’s scheme considered the skewness and selected an appropriate score function, giving a more efficient fit than Hogg’s scheme that ignores the skewness.