Linear mixed models (LMMs) ensure a flexible and powerful tool for the analysis of grouped data, which arise in many areas as diverse as agriculture, biology, economics, manufacturing, and geophysics. Examples of grouped data include longitudinal data, repeated measures data, blocked designs data, hierarchical data and multilevel data. The most popularly used prediction methods are the best linear unbiased estimator (BLUE) and the best linear unbiased predictor (BLUP). But, prediction is very important problem when multicollinearity matter exists in the linear mixed models. And hence, these BLUE and BLUP methods become ill-balanced and give confusional results when multicollinearity is present. The ridge estimator and the ridge predictor have been broadly used as an alternative method to contend with under multicollinearity problem. This multicollinearity problem can also be handled by using some prior information. Taking account of this knowledge, we suggest the modified ridge estimator and the modified ridge predictor in this article. A widespread performance criterion, mean square error, is taken into consideration to compare the modified ridge estimator/ the modified ridge predictor with the ridge estimator/ the ridge predictor and the BLUE/ the BLUP. Finally, a real data analysis is applied to demonstrate the theoretical results in the article.
Anahtar Kelimeler: Linear mixed model, Multicollinearity, The best linear unbiased predictor, The ridge predictor, The modified ridge predictor