mlprof.fun {dosresmeta}  R Documentation 
These functions compute the value of the loglikelihood for randomeffects doseresponse metaanalysis, in terms of model parameters. They are meant to be used internally and not directly run by the users.
remlprof.fn(par, Xlist, Zlist, ylist, Slist, nalist, q, nall, ctrl)
remlprof.gr(par, Xlist, ylist, Slist, nalist, p, nall, ctrl)
mlprof.fn(par, Xlist, Zlist, ylist, Slist, nalist, q, nall, ctrl)
mlprof.gr(par, Xlist, ylist, Slist, nalist, p, nall, ctrl)
iter.igls(Psi, Xlist, Zlist, ylist, Slist, nalist, q)
par 
a vector representing the randomeffects parameters defining the betweenstudy (co)variance matrix. 
Xlist 
a mdimensional list of studyspecific design matrices for the fixedeffects part of the model. 
Zlist 
a mdimensional list of studyspecific design matrices for the randomeffects part of the model. 
ylist 
a mdimensional list of studyspecific of vectors of estimated outcomes. 
Slist 
a mdimensional list of withinstudy (co)variance matrices of estimated outcomes. 
nalist 
a mdimensional list of kdimensional studyspecific logical vectors, identifying missing outcomes. 
ctrl 
list of parameters for controlling the fitting process, usually internally set to default values by

p, q, nall 
numeric scalars: number of predictors, number of observations (excluding missing). 
Psi 
a p x p matrix representing the current estimate of the betweenstudy (co)variance matrix. 
These functions are called internally by the fitting functions dosresmeta.ml
and dosresmeta.reml
to
perform iterative optimization algorithms for estimating random effects metaanalytical models.
The maximization of the (restricted) likelihood starts with few runs of an iterative generalized least square algorithm implemented in iter.igls
.
This can be regarded as a fast and stable way to get starting values close to the maximum for the QuasiNewton iterative algorithm, implemented in
optim
. Alternatively, starting values can be provided by the user in the control list (see mvmeta.control
).
These functions actually specify the profiled version of the (restricted) likelihood, expressed only in terms of randomeffects parameters, while the
estimate of the fixedeffects coefficients is provided at each iteration by the internal function glsfit
, based on the current value of
the betweenstudy (co)variance matrix. At convergence, the value of this profiled version is identical to the full (restricted) likelihood.
This approach is computationally efficient, as it reduces the number of parameters in the optimization routine.
The parameterization of the betweenstudy (co)variance matrix ensures the positivedefiniteness of the estimated matrix. A Cholesky decomposition is then performed on the marginal (co)variance matrix in order to reexpress the problem as standard least square equations, an approach which speeds up the computation of matrix inverses and determinants. These equations are finally solved through a QR decomposition, which guarantees stability.
mlprof.fn
and remlprof.fn
return the value of the (restricted) loglikelihood for a given set of
parameters in par
. iter.igls
returns an updated estimate of Psi
given its initial value or the value at
the previous iteration.
Alessio Crippa, alessio.crippa@ki.se
dosresmeta
, mvmeta.fit
, dosresmeta.control
, mlprof.fn