Deviance Function in Terms of Standard Deviations/Correlations

The deviance is profiled with respect to the fixed-effects parameters but not with respect to sigma; that is, the function takes parameters for the variance-covariance parameters and for the residual standard deviation. The random-effects variance-covariance parameters are on the standard deviation/correlation scale, not the theta (Cholesky factor) scale.

Usage

devfun2(fm, useSc = if(isLMM(fm)) TRUE else NA,
        transfuns = list(from.chol = Cv_to_Sv,
                           to.chol = Sv_to_Cv,
                             to.sd = identity),
        scale = c("sdcor", "varcov"), ...)

Arguments

fm: a fitted model inheriting from class "merMod".
useSc: (logical) indicating whether a scale parameter has been in the model or should be used.

transfuns: a list of functions for converting parameters to and from the Cholesky-factor scale
scale: a character string indicating the scale of the argument of the deviance function.
...: arguments passed to the internal profnames function (signames=TRUE to use old-style .sigxx names, FALSE uses (sd_cor|xx); also prefix=c("sd","cor"))

Value

Returns a function that takes a vector of standard deviations and correlations and returns the deviance (or REML criterion). The function has additional attributes

optimum: a named vector giving the parameter values at the optimum
basedev: the deviance at the optimum, (i.e., not the REML criterion).
thopt: the optimal variance-covariance parameters on the “theta” (Cholesky factor) scale
stderr: standard errors of fixed effect parameters

Note

Even if the original model was fitted using REML=TRUE as by default with lmer(), this returns the deviance, i.e., the objective function for maximum (log) likelihood (ML).

For the REML objective function, use getME(fm, "devfun") instead.

Examples

m1 <- lmer(Reaction~Days+(Days|Subject),sleepstudy)
dd <- devfun2(m1, useSc=TRUE)
pp <- attr(dd,"optimum")
## extract variance-covariance and residual std dev parameters
sigpars <- pp[grepl("^\\.sig",names(pp))]
all.equal(unname(dd(sigpars)),deviance(refitML(m1)))
#> [1] "Mean relative difference: 0.09681211"