`formula`

.```
glmer(formula, data = NULL, family = gaussian, control = glmerControl(),
start = NULL, verbose = 0L, nAGQ = 1L, subset, weights, na.action,
offset, contrasts = NULL, mustart, etastart,
devFunOnly = FALSE, …)
```

formula

a two-sided linear formula object describing both the
fixed-effects and random-effects part 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.data

an optional data frame containing the variables named in
*strongly* recommend its use,
especially when later applying methods such as *such methods are not
guaranteed to work properly if *). If

`formula`

. By default the variables are taken from the
environment from which `lmer`

is called. While `data`

is
optional, the package authors `update`

and
`drop1`

to the fitted model (`data`

is omitted`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).control

a list (of correct class, resulting from

`lmerControl()`

or `glmerControl()`

respectively) containing control parameters, including the nonlinear
optimizer to be used and parameters to be passed through to the
nonlinear optimizer, see the `*lmerControl`

documentation for
details.start

a named list of starting values for the parameters in the
model, or a numeric vector. A numeric

`start`

argument will be
used as the starting value of `theta`

. If `start`

is a
list, the `theta`

element (a numeric vector) is used as the
starting value for the first optimization step (default=1 for
diagonal elements and 0 for off-diagonal elements of the lower
Cholesky factor); the fitted value of `theta`

from the first
step, plus `start[["fixef"]]`

, are used as starting values for
the second optimization step. If `start`

has both `fixef`

and `theta`

elements, the first optimization step is skipped.
For more details or finer control of optimization, see
`modular`

.verbose

integer scalar. If

`> 0`

verbose output is
generated during the optimization of the parameter estimates. If
`> 1`

verbose output is generated during the individual PIRLS
steps.nAGQ

integer scalar - the number of points per axis for
evaluating the adaptive Gauss-Hermite approximation to the
log-likelihood. Defaults to 1, corresponding to the Laplace
approximation. Values greater than 1 produce greater accuracy in
the evaluation of the log-likelihood at the expense of speed. A
value of zero uses a faster but less exact form of parameter
estimation for GLMMs by optimizing the random effects and the
fixed-effects coefficients in the penalized iteratively reweighted
least squares step. (See Details.)

subset

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.weights

an optional vector of ‘prior weights’ to be used
in the fitting process. Should be

`NULL`

or a numeric
vector.na.action

a function that indicates what should happen when the
data contain

`NA`

s. 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.offset

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`

.contrasts

an optional list. See the

`contrasts.arg`

of
`model.matrix.default`

.mustart

optional starting values on the scale of the
conditional mean, as in

`glm`

; see there for
details.etastart

optional starting values on the scale of the unbounded
predictor as in

`glm`

; see there for details.devFunOnly

logical - return only the deviance evaluation
function. Note that because the deviance function operates on
variables stored in its environment, it may not return
*exactly* the same values on subsequent calls (but the results
should always be within machine tolerance).

…

other potential arguments. A

`method`

argument was
used in earlier versions of the package. Its functionality has been
replaced by the `nAGQ`

argument.`merMod`

(more specifically,
an object of `glmerMod`

) for which many
methods are available (e.g. `methods(class="merMod")`

)`family`

. The expression for the likelihood of a mixed-effects model is an
integral over the random effects space. For a linear mixed-effects
model (LMM), as fit by `lmer`

, this integral can be
evaluated exactly. For a GLMM the integral must be approximated. The
most reliable approximation for GLMMs
is adaptive Gauss-Hermite quadrature,
at present implemented only for models with
a single scalar random effect. The
`nAGQ`

argument controls the number of nodes in the quadrature
formula. A model with a single, scalar random-effects term could
reasonably use up to 25 quadrature points per scalar integral.
`lmer`

(for details on formulas and
parameterization); `glm`

for Generalized Linear
Models (`nlmer`

for nonlinear mixed-effects models. `glmer.nb`

to fit negative binomial GLMMs.## generalized linear mixed model library(lattice) xyplot(incidence/size ~ period|herd, cbpp, type=c('g','p','l'), layout=c(3,5), index.cond = function(x,y)max(y)) (gm1 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd), data = cbpp, family = binomial)) ## using nAGQ=0 only gets close to the optimum (gm1a <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd), cbpp, binomial, nAGQ = 0)) ## using nAGQ = 9 provides a better evaluation of the deviance ## Currently the internal calculations use the sum of deviance residuals, ## which is not directly comparable with the nAGQ=0 or nAGQ=1 result. (gm1a <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd), cbpp, binomial, nAGQ = 9)) ## GLMM with individual-level variability (accounting for overdispersion) ## For this data set the model is the same as one allowing for a period:herd ## interaction, which the plot indicates could be needed. cbpp$obs <- 1:nrow(cbpp) (gm2 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd) + (1|obs), family = binomial, data = cbpp)) anova(gm1,gm2) ## glmer and glm log-likelihoods are consistent gm1Devfun <- update(gm1,devFunOnly=TRUE) gm0 <- glm(cbind(incidence, size - incidence) ~ period, family = binomial, data = cbpp) ## evaluate GLMM deviance at RE variance=theta=0, beta=(GLM coeffs) gm1Dev0 <- gm1Devfun(c(0,coef(gm0))) ## compare stopifnot(all.equal(gm1Dev0,c(-2*logLik(gm0)))) ## the toenail oncholysis data from Backer et al 1998 ## these data are notoriously difficult to fit ## Not run: ------------------------------------ # if (require("HSAUR2")) { # gm2 <- glmer(outcome~treatment*visit+(1|patientID), # data=toenail, # family=binomial,nAGQ=20) # } ## ---------------------------------------------