Transcription of Fitting Linear Mixed-Effects Models using lme4
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Fitting Linear Mixed-Effects Models using lme4
Fitting Linear Mixed-Effects Models using lme4 Douglas BatesUniversity of Wisconsin-MadisonMartin M chlerETH ZurichBenjamin M. BolkerMcMaster UniversitySteven C. WalkerMcMaster UniversityAbstractMaximum likelihood or restricted maximum likelihood (REML) estimates of the pa-rameters in Linear Mixed-Effects Models can be determined using thelmerfunction in thelme4package forR. As for most model - Fitting functions inR, the model is described inanlmercall by a formula, in this case including both fixed- and random-effects formula and data together determine a numerical representation of the model fromwhich the profiled deviance or the profiled REML criterion can be evaluated as a functionof some of the model parameters. The appropriate criterion is optimized, using one ofthe constrained optimization functions inR, to provide the parameter estimates.
In a linear model the distribution of Y is multivariate normal, Y ∼ N(Xβ +o,σ2W−1), (1) where n is the dimension of the response vector, W is a diagonal matrix of known prior weights, β is a p-dimensional coefficient vector, X is an n×p model matrix, and o is a vector of known prior offset terms. The parameters of the model are the ...
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