Employing a Monte Carlo algorithm in expectation maximization restricted maximum likelihood estimation of the linear...

Area of Science:

• Quantitative Genetics
• Statistical Genomics
• Animal Breeding

Background:

• Estimating variance components in multiple-trait and random regression models requires solving numerous equations.
• Traditional methods involving matrix inversion or decomposition become computationally intensive with increasing model complexity.
• Need for efficient algorithms to handle large-scale genetic analyses.

Purpose of the Study:

• To propose and evaluate a Monte Carlo Expectation Maximization Restricted Maximum Likelihood (MC EM REML) method for variance component estimation.
• To compare the performance of MC EM REML against analytical EM REML for multiple-trait linear mixed models.
• To develop a robust convergence criterion for MC EM REML.

Main Methods:

• Implementation of MC EM REML using full-model sampling for prediction error variances.
• Comparison of MC EM REML and analytical EM REML using simulated and field data.
• Development of a convergence criterion accounting for sampling variation.

Main Results:

• MC EM REML results closely matched analytical EM REML results on field data, even with minimal MC samples.
• Standard error estimates were influenced by the calculation formula and MC sample size.
• MC EM REML demonstrated superior performance in computing time and memory usage compared to analytical EM REML for field data.

Conclusions:

• MC EM REML provides a computationally efficient and memory-sparing alternative for estimating variance components in complex genetic models.
• The proposed convergence criterion effectively monitors MC EM REML algorithm convergence.
• MC EM REML is a viable and advantageous method for large-scale genetic data analysis.