Nageena Nazir

Extension of Basic Linear Mixed Effect Model to Incorporate Heterocedasticity

The linear mixed effect model allows considerable flexibility in the specification of the random effects structure but restricts the within group errors to be independent, identically distributed random variables with mean zero and constant variance. This basic linear mixed effects model provides an adequate model for many different types of grouped data observed in practice. However, there are many applications involving grouped data for which the within group errors are heteroscedastic (i.e. have unequal variances), correlated or both. The lme() function of nlme library due to pinherio and bates 2000 is used to fit the extended linear mixed-effects model. The complexity of linear mixed-effects (LME) models means that traditional diagnostics are rendered less effective. This is due to a breakdown of asymptotic results, boundary issues, and visible patterns in residual plots that are introduced by the model fitting process. Loy et al., has proposed adjustment to some of the well-known issues (Loy, 2013). International Journal of Current Microbiology and Applied Sciences ISSN: 2319-7706 Volume 7 Number 06 (2018) Journal homepage: http://www.ijcmas.com

A New Approach of Ratio Estimation in Sample Surveys

This article deals with the estimation of population mean under simple random sampling using a new form of ratio estimator. The expression for mean square error and bias has been obtained. An efficiency comparison is considered for proposed estimator with the classical ratio, product and exponential ratio estimator. Finally an empirical study is also carried out to judge the performance of proposed estimator.