[R-sig-ME] LogLikelihood

[Steve Walker]

Hope this helps clear things up:

with(getME(mod0, c("n", "L", "X", "beta", "Z", "Lambda", "u", "y")), {
     mu <- as.numeric((X %*% beta) + (Z %*% Lambda %*% u))
     r2 <- sum((y-mu)^2) + sum(u^2)
     ldL2 <- 2*determinant(L, logarithm = TRUE)$modulus
     -0.5*(ldL2 + n*(1 + log((2*pi*r2)/n)))
})
logLik(mod0)

Other useful references include the lme4pureR package and the lmer paper:

https://github.com/lme4/lme4pureR/blob/master/R/JSS.R
http://arxiv.org/pdf/1406.5823v1.pdf

Equation 34 of the paper is minus twice the log-likelihood.

Cheers,
Steve


On 2015-01-25 12:27 PM, bbonit at tin.it wrote:
>
>
> Dear list, my name is Gianluca Bonitta
> I'm trying to build up the Loglikelihood of the following model.
> For check it I had used logLik(mod0,REML=F) like "gold standard"
> Like You see there is a difference   # diff   logLik(mod0,REML=F) - mylog = 0.6339805
> Can somebody help to resolve my mistake ?
> Maybe professor Bolker or professor Bates that are the "fathers" of lme4 pack
> thank You in advance
> Best
> Gianluca
>
> ########################################################################################
> 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  +( x | group ), data = dat,REML="F")
> ########################################################################################
>
>    q <- 2                                          # number of random effects
>    n <- nrow(dat)                              # number of individuals
>    m <- length(unique(dat$group))      # number of groups
>    Y <- dat$y                                    # response vector
>    R <- diag(1,nrow(dat))*summary(mod0)$sigma^2    # covariance matrix of residuals
>    beta <- as.numeric(fixef(mod0))                 # fixed effects vector (p x 1)
>    a<-rep(c(597.1903,60.05023),m)                  # variance rand effects
>    ranef(mod0)$group
>    b <-c(17.94432, -3.753130,-33.31148, 10.294328,15.36716, -6.541198) # random effect estimated
>    D <-matrix(-0.97,6,6)                           # random effect estimated correlation
>    diag(D) <-a
>    X <- cbind(rep(1,n), dat$x)                     # model matrix of fixed effects (n x p)
>    Z.sparse<- getME(mod0,"Z")                   # model matrix of random effect (sparse format)
>    Z <- as.matrix(Z.sparse)
>    V <-Z%*% D %*% t(Z) + R                   # (total) covariance matrix of Y
>    # check: values in Y can be perfectly matched using lmer's information
>    Y.test <- X %*% beta + Z %*% b + resid(mod0)
>    cbind(Y, Y.test)
>    mu = X %*% beta + Z %*% b
> ###############################################################################################
>     ll = -n/2*log(2*pi) - sum(log(diag(chol(V)))) -  .5 * t(Y- mu) %*% chol2inv(chol(V)) %*% (Y-mu);
>     logLik(mod0,REML=F)
>     ll
> ####################################à
> # diff   'log Lik.' 0.6339805 (df=6)
>
>     logLik(mod0,REML=F) -ll
> 	[[alternative HTML version deleted]]
>
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