Internals of Mixed Models

Linear mixed models are widely used in Agriculture and Plant Breeding, as of recent. With access to genotype data high resolution phenotype data, it has become more of a requirement to use this family of model.

Mixed models allow for experimental (design or outcome) variables’ parameter estimates to have probabilistic distributions – most commonly normal – with opportunity to specify different variance-covariance components among the levels of those variables. In this post, I wish to discuss on some of the popular mixed modeling tools and techniques in the R community with links and discussion of the concepts surrounding variations of modeling techniques.

Logistic Regression: Part I - Fundamentals

Likelihood theory

Probit models were the first of those being used to analyze non-normal data using non-linear models. In an early example of probit regression, Bliss(1934) describes an experiment in which nicotine is applied to aphids and the proportion killed is recorded. As an appendix to a paper Bliss wrote a year later (Bliss, 1935), Fisher (1935) outlines the use of maximum likelihood to obtain estimates of the probit model.