# 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!).

The R package lme4 is capable of fitting linear, generalized and nonlinear mixed effects models. Here, I am interested in linear mixed models exclusively. A linear mixed model fit is performed in lme4 with an lmer function call. For example:

library(lme4)
data(sleepstudy)
fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)


Thus, the first function to dissect is lmer. The function definition of lmer is located in the file lmer.R. The code is confusing. So, let’s go through it step-by-step.

# General overview

The general steps taken in lmer are:

1. Set some parameters in the local environment. In particular, deal with the function argument control, which usually is a list inheriting from class merControl (but control can be defined in other ways too, and the code deals with all possibilities in a multitude of lines). It includes general parameters such as the optimizer to be used, model- and data-checking specifications, and all parameters to be passed to the optimizer.

2. Parse data and formula. At this step the fixed effects matrix $X$, the random effects matrix $Z$, the parameter vector $\theta$, the covariance factor $\Lambda\subscript{\theta}$, etc. are created from the input data. Moreover, the REML flag is set, formula is rewritten in the preferred form, and warnings from checks for the random effects (e.g. about the number of levels, dimension of $Z$, rank of $Z$) are generated. This all is performed by the function lFormula, which is located in modular.R.

3. Create the deviance function to be minimized. Call the function mkLmerDevfun, which returns a function devfun to calculate the profiled deviance. Implicitly mkLmerDevfun also returns an environment required to evaluate devfun. The function definition of mkLmerDevfun can be found in modular.R.

4. Optimize the deviance function w.r.t. $\theta$. Optimize the deviance devfun with respect to the covariance parameters $\theta$. This is performed by the function optimizeLmer (located in modular.R), which returns the result of the optimization.

5. Check convergence criteria. Convergence check according to the convergence check options specified in control, performed by the function checkConv, which is implemented in the file checkConv.R.

6. Set up a useful output object. Package the results into a merMod object to return. This is performed by the function mkMerMod, located in the file utilities.R.

Step 2-6 perform function calls to other sophisticated functions. We will dissect each of those separately in what follows.

# Processing the formula - lFormula

Defined as:

lFormula <- function(formula, data=NULL, REML = TRUE,
subset, weights, na.action, offset, contrasts = NULL,
control=lmerControl(), ...)


It proceeds with the following steps:

• Check the input arguments. Call checkArgs on the given input arguments, in order to produces some warnings (about “family” and “method” being deprecated, and extra unused arguments) if necessary. Check that the input for check.formula.LHS is a valid value via the function checkCtrlLevels. The function checkArgs is defined in utilities.R, and checkCtrlLevels is defined in modular.R.

• Check and adjust the given formula and data frame. Check the provided formula and data with checkFormulaData from utilities.R (e.g. check missing data, check if formula has a left hand side, etc.). From the right hand side of a formula for a mixed-effects model, expand terms with || into separate, independent random effect terms written with | (expandDoubleVerts is defined in utilities.R, RHSForm is defined in modular.R). Generate a data frame with only the variables needed to use the given formula.

• Create the random effects model matrix $Z$, its covariance factor $\Lambda\subscript{\theta}$, as well as the parametrization $\theta$, etc. This is performed by the function mkReTrms, which is defined in utilities.R. Additionally, check that all grouping structures have at least 2 levels, that for each random effect $Z$ has more columns than rows, that the rank of $Z$ is not greater than $n$, etc. with the functions checkNlevels, checkZdims, checkZrank (all defined in modular.R).

• Create the fixed effects design matrix $X$. Only basic R functions like model.matrix used here.

• Return a data frame with variables required to use the formula. That is, fixed effects matrix $X$; reTrms containing the random effects matrix $Z$, covariance factor $\Lambda\subscript{\theta}$, etc.; REML flag; the formula; warnings from checks for the random effects (number of levels, dimension of $Z$, rank of $Z$, etc.).

Written on May 10, 2015
Tags: #lme4