\name{modular}
\title{Modular Functions for Mixed Model Fits}
\alias{glFormula}
\alias{lFormula}
\alias{mkGlmerDevfun}
\alias{mkLmerDevfun}
\alias{modular}
\alias{optimizeGlmer}
\alias{optimizeLmer}
\alias{updateGlmerDevfun}
\usage{
lFormula(formula, data = NULL, REML = TRUE,
    subset, weights, na.action, offset, contrasts = NULL,
    control = lmerControl(), ...)

mkLmerDevfun(fr, X, reTrms, REML = TRUE, start = NULL,
    verbose = 0, control = lmerControl(), ...)

optimizeLmer(devfun,
             optimizer    = formals(lmerControl)$optimizer,
             restart_edge = formals(lmerControl)$restart_edge,
             boundary.tol = formals(lmerControl)$boundary.tol,
             start = NULL, verbose = 0L,
             control = list(), ...)

glFormula(formula, data = NULL, family = gaussian,
    subset, weights, na.action, offset, contrasts = NULL,
    start, mustart, etastart, control = glmerControl(), ...)

mkGlmerDevfun(fr, X, reTrms, family, nAGQ = 1L,
              verbose = 0L, maxit = 100L, control = glmerControl(), ...)

optimizeGlmer(devfun,
    optimizer = if(stage == 1) "bobyqa" else "Nelder_Mead",
    restart_edge = FALSE,
    boundary.tol = formals(glmerControl)$boundary.tol,
    verbose = 0L, control = list(),
    nAGQ = 1L, stage = 1, start = NULL, ...)

updateGlmerDevfun(devfun, reTrms, nAGQ = 1L)
}
\arguments{
  \item{formula}{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 \code{~}
    operator and the terms, separated by \code{+} operators,
    on the right.  Random-effects terms are distinguished by
    vertical bars (\code{"|"}) separating expressions for
    design matrices from grouping factors.}

  \item{data}{an optional data frame containing the
    variables named in \code{formula}.  By default the
    variables are taken from the environment from which
    \code{lmer} is called. While \code{data} is optional, the
    package authors \emph{strongly} recommend its use,
    especially when later applying methods such as
    \code{update} and \code{drop1} to the fitted model
    (\emph{such methods are not guaranteed to work properly
      if \code{data} is omitted}). If \code{data} is omitted,
    variables will be taken from the environment of
    \code{formula} (if specified as a formula) or from the
    parent frame (if specified as a character vector).}

  \item{REML}{(logical) indicating to fit \bold{re}stricted maximum
    likelihood model.}

  \item{subset}{an optional expression indicating the
    subset of the rows of \code{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.}

  \item{weights}{an optional vector of \sQuote{prior weights} to be used
    in the fitting process.  Should be \code{NULL} or a numeric vector.}

  \item{na.action}{a function that indicates what should
    happen when the data contain \code{NA}s.  The default
    action (\code{na.omit}, inherited from the 'factory
    fresh' value of \code{getOption("na.action")}) strips any
    observations with any missing values in any variables.}

  \item{offset}{this can be used to specify an \emph{a priori} known
    component to be included in the linear predictor during
    fitting.  This should be \code{NULL} or a numeric vector of length
    equal to the number of cases.  One or more \code{\link{offset}}
    terms can be included in the formula instead or as well, and if
    more than one is specified their sum is used.  See
    \code{\link{model.offset}}.}

  \item{contrasts}{an optional \code{\link{list}}.  See the
    \code{contrasts.arg} of \code{\link{model.matrix.default}}.}

  \item{control}{a list giving
    \describe{
      \item{for \code{[g]lFormula}:}{all
	options for running the model, see \code{\link{lmerControl}};}
      \item{for \code{mkLmerDevfun,mkGlmerDevfun}:}{options
	for the inner optimization step;}
      \item{for \code{optimizeLmer} and \code{optimizeGlmer}:}{control
	parameters for nonlinear optimizer (typically inherited from the
	\dots argument to \code{\link{lmerControl}}).}
	% FIXME: reference optCtrl
    }
  }
  \item{fr}{A model frame containing the variables needed to create an
    \code{\link{lmerResp}} or \code{\link{glmResp}} instance.}
  \item{X}{fixed-effects design matrix}
  \item{reTrms}{information on random effects structure (see
    \code{\link{mkReTrms}}).}
  \item{start}{starting values (see \code{\link{lmer}};
    for \code{glFormula}, should be just a numeric vector of
    fixed-effect coefficients)}
  \item{verbose}{print output?}
  \item{maxit}{maximal number of Pwrss update iterations.}
  \item{devfun}{a deviance function, as generated by \code{\link{mkLmerDevfun}}}
  \item{nAGQ}{number of Gauss-Hermite quadrature points}
  \item{stage}{optimization stage (1: nAGQ=0, optimize over theta only;
    2: nAGQ possibly >0, optimize over theta and beta)}
  \item{optimizer}{character - name of optimizing
    function(s).  A character vector or list of functions:
    length 1 for \code{lmer} or \code{glmer}, possibly length
    2 for \code{glmer}.  The built-in optimizers are
    \code{"\link{Nelder_Mead}"} and \code{"\link[minqa]{bobyqa}"}
    (from the \CRANpkg{minqa} package).  Any minimizing function
    that allows box constraints can be used provided that it
    \enumerate{
      \item{takes input parameters \code{fn} (function to be
	optimized), \code{par} (starting parameter values),
	\code{lower} (lower bounds) and \code{control} (control
	parameters, passed through from the \code{control}
	argument) and}
      \item{returns a list with (at least) elements
	\code{par} (best-fit parameters), \code{fval} (best-fit
	function value), \code{conv} (convergence code) and
	(optionally) \code{message} (informational message, or
	explanation of convergence failure)}.
    }
    Special provisions are made for \code{\link{bobyqa}},
    \code{\link{Nelder_Mead}}, and optimizers wrapped in the
    \CRANpkg{optimx} package; to use \pkg{optimx} optimizers
    (including \code{L-BFGS-B} from base \code{\link{optim}}
    and \code{\link{nlminb}}), pass the \code{method}
    argument to \code{optim} in the \code{control} argument.

    For \code{glmer}, if \code{length(optimizer)==2}, the
    first element will be used for the preliminary (random
    effects parameters only) optimization, while the second
    will be used for the final (random effects plus fixed
    effect parameters) phase. See \code{\link{modular}} for
    more information on these two phases.
  }
  \item{restart_edge}{see \code{\link{lmerControl}}}
  \item{boundary.tol}{see \code{\link{lmerControl}}}
  \item{family}{a GLM family; see \code{\link[stats]{glm}}
    and \code{\link[stats]{family}}.}
  \item{mustart}{optional starting values on the scale of
    the conditional mean; see \code{\link[stats]{glm}} for details.}
  \item{etastart}{optional starting values on the scale of
    the unbounded predictor; see \code{\link[stats]{glm}} for details.}
  \item{\dots}{other potential arguments; for \code{optimizeLmer} and
    \code{optimizeGlmer}, these are passed to internal function
    \code{optwrap}, which has relevant parameters \code{calc.derivs}
    and \code{use.last.params} (see \code{\link{lmerControl}}).}
}
\value{
  \code{lFormula} and \code{glFormula} return a list containing
  components:

  \describe{
    \item{fr}{model frame}
     \item{X}{fixed-effect design matrix}
     \item{reTrms}{list containing information on random effects structure:
     result of \code{\link{mkReTrms}}}
     \item{REML}{(lFormula only): logical indicating if restricted maximum
     likelihood was used (Copy of argument.)}
  }

  \code{mkLmerDevfun} and \code{mkGlmerDevfun} return a function to
      calculate deviance (or restricted deviance) as a function of the
      theta (random-effect) parameters.  \code{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 \code{\link{environment}} of
      functions returned by \code{mk(Gl|L)merDevfun} contains reference
      class objects (see \code{\link{ReferenceClasses}},
      \code{\link{merPredD-class}}, \code{\link{lmResp-class}}), which
      behave in ways that may surprise many users. For example, if the
      output of \code{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
      \code{\link{ReferenceClasses}} for details).

  \code{optimizeLmer} and \code{optimizeGlmer} return the results of an
  optimization.
}
\description{
  Modular functions for mixed model fits
}
\details{
  These functions make up the internal components of an [gn]lmer fit.
  \itemize{
    \item \code{[g]lFormula} takes the arguments that would normally be
    passed to \code{[g]lmer}, checking for errors and processing the
    formula and data input to create a list of objects required to fit a
    mixed model.
    \item \code{mk(Gl|L)merDevfun} takes the output of the previous
    step (minus the \code{formula} component) and creates a
    deviance function
    \item \code{optimize(Gl|L)mer} takes a
    deviance function and optimizes over \code{theta} (or
    over \code{theta} and \code{beta}, if \code{stage} is set
    to 2 for \code{optimizeGlmer}
    \item \code{updateGlmerDevfun} takes the first stage of a GLMM
    optimization (with \code{nAGQ=0}, optimizing over \code{theta} only)
    and produces a second-stage deviance function
    \item \code{\link{mkMerMod}} takes the \emph{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
    \code{[g]lmerMod} object.
  }
}
\examples{
### Fitting a linear mixed model in 4 modularized steps

## 1.  Parse the data and formula:
lmod <- lFormula(Reaction ~ Days + (Days|Subject), sleepstudy)
names(lmod)
## 2.  Create the deviance function to be optimized:
(devfun <- do.call(mkLmerDevfun, lmod))
ls(environment(devfun)) # the environment of 'devfun' contains objects
                        # required for its evaluation
## 3.  Optimize the deviance function:
opt <- optimizeLmer(devfun)
opt[1:3]
## 4.  Package up the results:
mkMerMod(environment(devfun), opt, lmod$reTrms, fr = lmod$fr)


### Same model in one line
lmer(Reaction ~ Days + (Days|Subject), sleepstudy)


### 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)
## 2.  Create the deviance function for optimizing over theta:
(devfun <- do.call(mkGlmerDevfun, glmod))
ls(environment(devfun)) # the environment of devfun contains lots of info
## 3.  Optimize over theta using a rough approximation (i.e. nAGQ = 0):
(opt <- optimizeGlmer(devfun))
## 4.  Update the deviance function for optimizing over theta and beta:
(devfun <- updateGlmerDevfun(devfun, glmod$reTrms))
## 5.  Optimize over theta and beta:
opt <- optimizeGlmer(devfun, stage=2)
str(opt, max=1) # seeing what we'got
## 6.  Package up the results:
(fMod <- mkMerMod(environment(devfun), opt, glmod$reTrms, fr = glmod$fr))

### 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)
        # ----  --  even tolerance = 0  may work
}
\keyword{models}