modular.RdModular functions for mixed model fits
glFormula(formula, data = NULL, family = gaussian,
subset, weights, na.action, offset, contrasts = NULL,
start, mustart, etastart, control = glmerControl(), ...)a two-sided linear formula object
describing both the fixed-effects and random-effects parts
of the model, with the response on the left of a ~
operator and the terms, separated by + operators,
on the right. Random-effects terms are distinguished by
vertical bars ("|") separating expressions for
design matrices from grouping factors.
an optional data frame containing the
variables named in formula. By default the
variables are taken from the environment from which
lmer is called. While data is optional, the
package authors strongly recommend its use,
especially when later applying methods such as
update and drop1 to the fitted model
(such methods are not guaranteed to work properly
if data is omitted). If data is omitted,
variables will be taken from the environment of
formula (if specified as a formula) or from the
parent frame (if specified as a character vector).
an optional expression indicating the
subset of the rows of data that should be used in
the fit. This can be a logical vector, or a numeric
vector indicating which observation numbers are to be
included, or a character vector of the row names to be
included. All observations are included by default.
an optional vector of ‘prior weights’ to be used
in the fitting process. Should be NULL or a numeric vector.
a function that indicates what should
happen when the data contain NAs. The default
action (na.omit, inherited from the 'factory
fresh' value of getOption("na.action")) strips any
observations with any missing values in any variables.
this can be used to specify an a priori known
component to be included in the linear predictor during
fitting. This should be NULL or a numeric vector of length
equal to the number of cases. One or more offset
terms can be included in the formula instead or as well, and if
more than one is specified their sum is used. See
model.offset.
an optional list. See the
contrasts.arg of model.matrix.default.
a list giving
[g]lFormula:all
options for running the model, see lmerControl;
mkLmerDevfun,mkGlmerDevfun:options for the inner optimization step;
optimizeLmer and optimizeGlmer:control
parameters for nonlinear optimizer (typically inherited from the
... argument to lmerControl).
starting values (see lmer;
for glFormula, should be just a numeric vector of
fixed-effect coefficients)
optional starting values on the scale of
the conditional mean; see glm for details.
optional starting values on the scale of
the unbounded predictor; see glm for details.
other potential arguments; for optimizeLmer and
optimizeGlmer, these are passed to internal function
optwrap, which has relevant parameters calc.derivs
and use.last.params (see lmerControl).
lFormula and glFormula return a list containing
components:
model frame
fixed-effect design matrix
list containing information on random effects structure:
result of mkReTrms
mkLmerDevfun and mkGlmerDevfun return a function to
calculate deviance (or restricted deviance) as a function of the
theta (random-effect) parameters. updateGlmerDevfun
returns a function to calculate the deviance as a function of a
concatenation of theta and beta (fixed-effect) parameters. These
deviance functions have an environment containing objects required
for their evaluation. CAUTION: The environment of
functions returned by mk(Gl|L)merDevfun contains reference
class objects (see ReferenceClasses,
merPredD-class, lmResp-class), which
behave in ways that may surprise many users. For example, if the
output of mk(Gl|L)merDevfun is naively copied, then
modifications to the original will also appear in the copy (and
vice versa). To avoid this behavior one must make a deep copy (see
ReferenceClasses for details).
optimizeLmer and optimizeGlmer return the results of an
optimization.
These functions make up the internal components of an [gn]lmer fit.
[g]lFormula takes the arguments that would normally be
passed to [g]lmer, checking for errors and processing the
formula and data input to create a list of objects required to fit a
mixed model.
mk(Gl|L)merDevfun takes the output of the previous
step (minus the formula component) and creates a
deviance function
optimize(Gl|L)mer takes a
deviance function and optimizes over theta (or
over theta and beta, if stage is set
to 2 for optimizeGlmer
updateGlmerDevfun takes the first stage of a GLMM
optimization (with nAGQ=0, optimizing over theta only)
and produces a second-stage deviance function
mkMerMod takes the environment of a
deviance function, the results of an optimization, a list of
random-effect terms, a model frame, and a model all and produces a
[g]lmerMod object.
# \donttest{
library(lme4)
### Fitting a linear mixed model in 4 modularized steps
## 1. Parse the data and formula:
lmod <- lFormula(Reaction ~ Days + (Days|Subject), sleepstudy)
names(lmod)
#> [1] "fr" "X" "reTrms" "REML" "formula" "wmsgs"
## 2. Create the deviance function to be optimized:
(devfun <- do.call(mkLmerDevfun, lmod))
#> function (theta)
#> .Call(lmer_Deviance, pp$ptr(), resp$ptr(), as.double(theta))
#> <environment: 0x558a01d507c0>
ls(environment(devfun)) # the environment of 'devfun' contains objects
#> [1] "lmer_Deviance" "lower" "pp" "resp"
# required for its evaluation
## 3. Optimize the deviance function:
opt <- optimizeLmer(devfun)
opt[1:3]
#> $par
#> [1] 0.96674177 0.01516906 0.23090995
#>
#> $fval
#> [1] 1743.628
#>
#> $feval
#> [1] 43
#>
## 4. Package up the results:
mkMerMod(environment(devfun), opt, lmod$reTrms, fr = lmod$fr)
#> Linear mixed model fit by REML ['lmerMod']
#> REML criterion at convergence: 1743.628
#> Random effects:
#> Groups Name Std.Dev. Corr
#> Subject (Intercept) 24.741
#> Days 5.922 0.07
#> Residual 25.592
#> Number of obs: 180, groups: Subject, 18
#> Fixed Effects:
#> (Intercept) Days
#> 251.41 10.47
### Same model in one line
lmer(Reaction ~ Days + (Days|Subject), sleepstudy)
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + (Days | Subject)
#> Data: sleepstudy
#> REML criterion at convergence: 1743.628
#> Random effects:
#> Groups Name Std.Dev. Corr
#> Subject (Intercept) 24.741
#> Days 5.922 0.07
#> Residual 25.592
#> Number of obs: 180, groups: Subject, 18
#> Fixed Effects:
#> (Intercept) Days
#> 251.41 10.47
### Fitting a generalized linear mixed model in six modularized steps
## 1. Parse the data and formula:
glmod <- glFormula(cbind(incidence, size - incidence) ~ period + (1 | herd),
data = cbpp, family = binomial)
#.... see what've got :
str(glmod, max=1, give.attr=FALSE)
#> List of 6
#> $ fr :'data.frame': 56 obs. of 3 variables:
#> $ X : num [1:56, 1:4] 1 1 1 1 1 1 1 1 1 1 ...
#> $ reTrms :List of 10
#> $ family :List of 13
#> $ formula:Class 'formula' language cbind(incidence, size - incidence) ~ period + (1 | herd)
#> $ wmsgs : chr(0)
## 2. Create the deviance function for optimizing over theta:
(devfun <- do.call(mkGlmerDevfun, glmod))
#> function (theta)
#> {
#> resp$updateMu(lp0)
#> pp$setTheta(theta)
#> p <- pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GHrule(0L),
#> compDev = compDev, maxit = maxit, verbose = verbose)
#> resp$updateWts()
#> p
#> }
#> <environment: 0x558a17ce1418>
ls(environment(devfun)) # the environment of devfun contains lots of info
#> [1] "compDev" "lower" "lp0" "maxit" "pp"
#> [6] "pwrssUpdate" "resp" "tolPwrss" "verbose"
## 3. Optimize over theta using a rough approximation (i.e. nAGQ = 0):
(opt <- optimizeGlmer(devfun))
#> parameter estimates: 0.641838555349172
#> objective: 184.108693002453
#> number of function evaluations: 18
## 4. Update the deviance function for optimizing over theta and beta:
(devfun <- updateGlmerDevfun(devfun, glmod$reTrms))
#> function (pars)
#> {
#> resp$setOffset(baseOffset)
#> resp$updateMu(lp0)
#> pp$setTheta(as.double(pars[dpars]))
#> spars <- as.numeric(pars[-dpars])
#> offset <- if (length(spars) == 0)
#> baseOffset
#> else baseOffset + pp$X %*% spars
#> resp$setOffset(offset)
#> p <- pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat,
#> compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose)
#> resp$updateWts()
#> p
#> }
#> <environment: 0x558a17ce1418>
## 5. Optimize over theta and beta:
opt <- optimizeGlmer(devfun, stage=2)
str(opt, max=1) # seeing what we'got
#> List of 7
#> $ fval : num 184
#> $ par : num [1:5] 0.642 -1.398 -0.992 -1.128 -1.58
#> $ convergence: num 0
#> $ NM.result : int 3
#> $ message : chr "parameter values converged to within tolerance"
#> $ control :List of 17
#> $ feval : num 285
#> - attr(*, "optimizer")= chr "Nelder_Mead"
#> - attr(*, "control")=List of 3
#> - attr(*, "warnings")= list()
#> - attr(*, "derivs")=List of 2
## 6. Package up the results:
(fMod <- mkMerMod(environment(devfun), opt, glmod$reTrms, fr = glmod$fr))
#> Generalized linear mixed model fit by maximum likelihood (Laplace
#> Approximation) [glmerMod]
#> Family: binomial ( logit )
#> AIC BIC logLik -2*log(L) df.resid
#> 194.0531 204.1799 -92.0266 184.0531 51
#> Random effects:
#> Groups Name Std.Dev.
#> herd (Intercept) 0.6421
#> Number of obs: 56, groups: herd, 15
#> Fixed Effects:
#> (Intercept) period2 period3 period4
#> -1.3983 -0.9919 -1.1282 -1.5797
### Same model in one line
fM <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
data = cbpp, family = binomial)
all.equal(fMod, fM, check.attributes=FALSE, tolerance = 1e-12)
#> [1] TRUE
# ---- -- even tolerance = 0 may work
# }