R: Penalized Minus Log Likelihood for Aster Models
penmlogl
R Documentation
Penalized Minus Log Likelihood for Aster Models
Description
Penalized minus log likelihood for an aster model, and its first and second
derivative. The penalization allows for (approximate) random effects.
These functions are called inside pickle,
pickle1, pickle2, pickle3,
and reaster.
Usage
penmlogl(parm, sigma, fixed, random, obj, y, origin)
penmlogl2(parm, alpha, sigma, fixed, random, obj, y, origin)
Arguments
parm
for penmlogl, parameter value (vector of regression
coefficients and rescaled random effects) at which we evaluate the
penalized log likelihood. For penmlogl2 the vector of rescaled
random effects only (see next item).
alpha
the vector of fixed effects. For penmlogl2, the
concatenation c(alpha, parm) is the same as parm that
is supplied to pemnmlogl.
sigma
vector of square roots of variance components, one component
for each group of random effects.
fixed
the model matrix for fixed effects. The number of rows
is nrow(obj$data).
The number of columns is the number of fixed effects.
random
the model matrix or matrices for random effects.
Each has the same number of rows as fixed. The number of columns
is the number of random effects in a group. Either a matrix or a list
of matrices.
obj
aster model object, the result of a call to aster.
y
response vector. May be omitted, in which case obj$x
is used. If supplied, must be a matrix of the same dimensions as
obj$x.
origin
origin of aster model. May be omitted, in which case
default origin (see aster) is used. If supplied, must be
a matrix of the same dimensions obj$x.
Details
Consider an aster model with random effects and canonical parameter vector
of the form
M alpha + Z[1] b[1] + … +
Z[k] b[k]
where M and each Z[j] are known matrices having the same
row dimension, where alpha is a vector of unknown parameters
(the fixed effects) and each b[j] is a vector of random effects
that are supposed to be (marginally) independent and identically distributed
mean-zero normal with variance sigma[j]^2.
These functions evaluate minus the “penalized log likelihood”
for this model, which considers the random effects as parameters but
adds a penalization term
To properly deal with random effects that are zero, random effects
are rescaled by their standard deviation.
The rescaled random effects are
c[i] = b[i] / sigma[i].
If sigma[i] = 0, then the corresponding rescaled
random effects c[i] are also zero.
Value
a list containing some of the following components:
value
minus the penalized log likelihood.
gradient
minus the first derivative vector of the penalized
log likelihood.
hessian
minus the second derivative matrix of the penalized
log likelihood.
argument
the value of the parm argument for this function.
scale
the vector by which parm must be scaled to obtain
the true random effects.
mlogl.gradient
gradient for evaluation of log likelihood;
gradient is this plus gradient of penalty.
mlogl.hessian
hessian for evaluation of log likelihood;
hessian is this plus hessian of penalty.
Note
Not intended for use by naive users. Use reaster,
which calls them.
See Also
For an example using this function see the example
for pickle.