Abstract
The rank-based method is a well-known robust estimation
technique in analyzing linear models, it serves as an alternative to Restricted Maximum Likelihood Estimation (REML) for non-normal error
distribution. It is based on minimizing a pseudo-norm and can be upgraded by selecting a suitable score function according to the probability
distribution of the error term. Some generic score functions are recommended in the literature for specific shapes of the error distributions in
linear models. In this study, the efficiency of score functions is examined through simulations for various level-1 and level-2 sample sizes applied on a random intercept multilevel model for symmetric, asymmetric,
and light-tailed to heavy-tailed error distributions. Score functions like
wscores, nscores, Bentscores1, and Bentscores4 show minimum SE only
when the level-2 sample size is 10 or more. Bentscores1 and Bentscores3
are more suitable than other score functions even for the smallest sample
size and their magnitudes reduce as sample size increases for right-skewed
and left-skewed error distributions, respectively. Another selection criterion based on Hogg type adaptive scheme is also applied for the same
class of error distribution. The efficiency rank-based fit with the selected
score function is compared with the Wilcoxon score based on minimum
standard error (SE).For the case of right-skewed, moderately heavy-tailed
and light-tailed distribution, selected fit from the adaptive scheme is more
precise than Wilcoxon fit. For contaminated normal distribution selectedfit is more precise in small sample sizes only. In group size 30 or more,
the selection of score function does not make a significant change in SE.
Sehar Saleem, Rehan Ahmad Khan Sherwani. (2020) Selecting and Estimating Rank Score Functions Based on Residuals for Linear Mixed Models, Punjab University Journal of Mathematics, Volume 52 , Issue 9.
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