# A (naive) application of linear mixed models to genetics

The following shows an application of class LMM from the Ruby gem mixed_models to SNP data (single-nucleotide polymorphism) with known pedigree structures. The family information is prior knowledge that we can model in the random effects of a linear mixed effects model.

# P-values and confidence intervals

A few days ago I started working on hypotheses tests and confidence intervals for my project mixed_models, and I got pretty surprised by certain things.

# MixedModels Formula Interface and Categorical Variables

I made some more progress on my Google Summer of Code project MixedModels. The linear mixed models fitting method is now capable of handling non-numeric (i.e., categorical) predictor variables, as well as interaction effects. Moreover, I gave the method a user friendly R-formula-like interface. I will present these new capabilities of the Ruby gem with an example. Then I will briefly describe their implementation.

# Model specification for linear mixed model

Last week I wrote about my implementation of an algorithm that fits a linear mixed model in Ruby using the gem MixedModels, that I am working on right now. See, first rudimentary LMM fit.

# A rudimentary first linear mixed model fit

During the last two weeks I made some progress on my Google Summer of Code project. The Ruby gem is now capable of fitting linear mixed models. In this short blog post I want to give an example, and compare the results I get in Ruby to those obtained by lme4 in R.

# Dissecting lme4's lmer function. Part 3.

This is the final part of my analysis of the function lmer, which is used to fit linear mixed models in the R package lme4. In two previous blog posts, we have seen the general layout of the function lmer, the dealings with the R model formula, and the setting up of the objective function for the optimization (see part 1 and part 2).

# Dissecting lme4's lmer function. Part 2.

Last time I started to analyze the function lmer that is used to fit linear mixed models in the R package lme4. I have delineated the general steps taken by lmer, and looked at the employed formula module in more detail. The formula module evaluates the provided R model formula to model matrices, vectors and parameters. The next step is to use these to define the objective function that needs to be minimized, which is the profiled deviance or the profiled REML criterion in this case. The objective function is returned by the function mkLmerDevfun which is dissected in what follows.

# Dissecting lme4's lmer function. Part 1.

This blog posts marks the start of my Google Summer of Code project with the Ruby Science Foundation, where I will develop mixed linear models software for Ruby. As a preparation for my GSoC project, I will dedicate a couple of blog posts to a meticulous analysis of lme4 code (so that I can steal all the ideas from it!).