{'fraction_non_alphanumeric': 0.012745098039215686, 'fraction_numerical': 0.00196078431372549, 'mean_word_length': 5.1878787878787875, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Improving prediction by means of a two parameter approach in linear mixed models

In this article, two parameter estimator and two parameter predictor are defined via the penalized log-likelihood approach in linear mixed models. The recommended approach is quite useful when there is a strong linear relationship among the variables of fixed effects design matrix. The necessary and sufficient condition for the superiority of the two parameter predictor over the best linear unbiased predictor of linear combinations of fixed and random effects in the sense of matrix mean square error criterion is examined. Additionally, to enhance the practical utility of the two parameter estimator and the two parameter predictor, we focus on the selection issue of two biasing parameters. Thus, 10 different methods for choosing the unknown biasing parameters are offered. Two real data sets are analysed to test the performance of our new two parameter approach. In addition, a comprehensive Monte Carlo simulation is performed.