Estimation of the likelihood function in linear mixed models (lme4)

I am currently writing a script to evaluate the (limited) log-likelihood function for use in linear mixed models. I need this to calculate the probability of a model with some parameters fixed to arbitrary values. Perhaps this script is also useful for some of you!

I use lmer()from lme4and logLik()to check if my script is working. And, as it seems, this is not so! Since my educational experience was not really related to this level of statistics, I lost a little when I discovered an error.

Below you will find a short example script using sleepstudy data:

  # * * * * * * * * * * * * * * * * * * * * * * * * 
  # * example data

  library(lme4)
  data(sleepstudy)
  dat <- sleepstudy[ (sleepstudy$Days %in% 0:4) & (sleepstudy$Subject %in% 331:333) ,]
  colnames(dat) <- c("y", "x", "group")

  mod0 <- lmer( y ~ 1 + x + ( 1 | group ), data = dat)  


  # + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + #
  #                                                             #
  #   Evaluating the likelihood-function for a LMM              #
  #   specified as: Y = X*beta + Z*b + e                        #
  #                                                             #
  # + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 

  # * * * * * * * * * * * * * * * * * * * * * * * * 
  # * the model parameters

  # n is total number of individuals
  # m is total number of groups, indexed by i
  # p is number of fixed effects
  # q is number of random effects

  q <- nrow(VarCorr(mod0)$group)                  # number of random effects
  n <- nrow(dat)                                  # number of individuals
  m <- length(unique(dat$group))                  # number of goups
  Y <- dat$y                                      # response vector

  X <- cbind(rep(1,n), dat$x)                     # model matrix of fixed effects (n x p)
  beta <- as.numeric(fixef(mod0))                 # fixed effects vector (p x 1)

  Z.sparse <- t(mod0@Zt)                          # model matrix of random effect (sparse format)
  Z <- as.matrix(Z.sparse)                        # model matrix Z (n x q*m)
  b <- as.matrix(ranef(mod0)$group)               # random effects vector (q*m x 1)

  D <- diag(VarCorr(mod0)$group[1:q,1:q], q*m)    # covariance matrix of random effects
  R <- diag(1,nrow(dat))*summary(mod0)@sigma^2    # covariance matrix of residuals
  V <- Z %*% D %*% t(Z) + R                       # (total) covariance matrix of Y

  # check: values in Y can be perfectly matched using lmer information
  Y.test <- X %*% beta + Z %*% b + resid(mod0)
  cbind(Y, Y.test)

  # * * * * * * * * * * * * * * * * * * * * * * * * 
  # * the likelihood function

  # profile and restricted log-likelihood (Harville, 1997)
  loglik.p <- - (0.5) * (  (log(det(V))) + t((Y - X %*% beta)) %*% solve(V) %*% (Y - X %*% beta)  )
  loglik.r <- loglik.p - (0.5) * log(det( t(X) %*% solve(V) %*% X ))

  #check: value of above function does not match the generic (restricted) log-likelihood of the mer-class object
  loglik.lmer <- logLik(mod0, REML=TRUE)
  cbind(loglik.p, loglik.r, loglik.lmer)

, LMM-, ? !

edit: BTW, LMM (1977), (), :

,