Abstract
Linear mixed model (LMM) approaches have been widely applied in many areas of research data analysis because they offer great flexibility for different data structures and linear model systems. In this study, emphasis is placed on comparing the properties of two LMM approaches: restricted maximum likelihood (REML) and minimum norm quadratic unbiased estimation (MINQUE) with and without resampling techniques being included. Bias, testing power, Type I error, and computing time were compared between REML and MINQUE approaches with and without Jackknife technique based on 500 simulated data sets. Results showed that MINQUE and REML methods performed equally regarding bias, Type I error, and power. Jackknife-based MINQUE and REML greatly improved power compared to non-Jackknife based linear mixed model approaches. Results also showed that MINQUE is more time-saving compared to REML, especially with the use of resampling techniques and large data set analysis. Results from the actual cotton data analysis were in agreement with our simulated results. Therefore, Jackknife-based MINQUE approaches could be recommended to achieve desirable power with reduced time for a large data analysis and model simulations.
Highlights
Linear mixed models (LMM) are a generalization of various linear models covering simple linear regression models, ANOVA models, and complex genetic models
Emphasis is placed on comparing the properties of two LMM approaches: restricted maximum likelihood (REML) and minimum norm quadratic unbiased estimation (MINQUE) with and without resampling techniques being included
Bias, testing power, Type I error, and computing time were compared between REML and MINQUE approaches with and without Jackknife technique based on 500 simulated data sets
Summary
Linear mixed models (LMM) are a generalization of various linear models covering simple linear regression models, ANOVA models, and complex genetic models. ML and REML approaches have been integrated into SAS [4] and into R such as lme4 [5] [6] and ASReml [7] Due to their popularity and long-term availability, a wide range of applications in various areas, has occurred. Based on a recent google scholar search in May, 2016, more than 43,000 publications were available Both ML and REML approaches are based on the assumption that data are normally distributed (Laird and Ware, 1982) and require iterations [8]. MINQUE approaches do not require normally distributed data nor iterations [3] [9]. They could offer more flexibility with reduced computational intensity. Since 1989, MINQUE approaches have been widely used in quantitative genetics studies [10]-[19]
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