Usage
alr(formula = formula(data), id = id, weights = NULL, data
= sys.parent(), subset, na.action, contrasts = NULL, z
= 0, zmast = 0, zid = 0, zlocs = 0, binit = NULL,
ainit, bweight = "full", depmodel = "general",
subclust = 0, clnames = NULL, tol = 0.001, maxiter =
25, silent = TRUE)Arguments
formula
typical model formula instance for binary logistic regression
id
cluster discriminator: N-vector
weights
vector of observation-specific weights
data
data frame for bindings of variables in formula
subset
typical subset expression
na.action
missing data handler
contrasts
optional list as in model.matrix.default
contrasts.arg
z
matrix of predictors for pairwise log odds ratio regression.
this may be omitted for certain choices of "depmodel",
see below. if used,
this matrix may take one of two forms. it may specify
directly, for each cluster, the form of the dependency
design. in this case, it has dimension (sum_i(n_i*(n_i - 1))) x q.
on the other hand, if the data to be analyzed are replicated
(possibly subject to missingness), then if n is the size of a complete
cluster, z has dimension (n*(n-1)) x q. see zmast and
zlocs below
zmast
if 1, then z is a "master" design for pairwise log oddsratio
regression. each cluster is a replicate of this master
design, but clusters may have missing elements, thus
missing pairs. the missing information is extracted from
zlocs, below. if 0, then z has dimension (sum_i(n_i*(n_i-1))) x q
zid
cluster discriminators for the z matrix, used only if zmast == 0.
if used, has dimension (sum_i(n_i *(n_i-1))) x 1.
zlocs
used only if zmast == 1. this is an N-vector of "locations" in
the dependency design. if replication is perfect and complete,
and n is the cluster size, and there are C clusters, then
this vector should have the value rep(1:n,C).
binit
p-vector of initial values for beta -- required; should
be obtained from a logistic regression fit assuming independence
ainit
q-vector of initial values for alpha -- difficult to
recommend starting values here, but rep(.01,q) often
works
tol
maximum relative change in parameter tolerated before
asserting convergence
bweight
currently takes one of two values: "full" or "independence".
if "independence", then the estimating equation for
estimating regression parameters beta uses a diagonal
weighting matrix, and the estimated beta should be
identical to the GLIM estimate. if "full", then
the estimating equation for beta uses the estimated
covariance (nxn) matrix of the outcomes as weight.
the "independence" setting may be useful for very
large clusters (n>50?) with sparse outcomes, in which the
weighting matrix can tend to singularity.
depmodel
currently takes one of three values: "general", "exchangeable",
"1-nested". The "general" setting uses a Z matrix (see above)
to specify the dependency model. The "exchangeable" setting
uses no Z matrix, but assumes a common pairwise log-odds ratio
for all cluster elements. The "1-nested" setting estimates
a log-odds ratio regression with first parameter the log
pairwise odds ratio for any two elements in a cluster,
the second parameter is the incremental dependency between
members of the same subcluster. subclusters are identified
through the "subclust" vector; see below.
subclust
N-vector discriminating subclusters within clusters. Thus
two 8-clusters might have id=c(1,1,1,1,1,1,1,2,2,2,2,2,2,2,2),
subclust=c(10,10,11,11,11,11,11,11,20,20,20,20,21,21,21,21).
the first cluster falls into 2 subclusters, the first is size
2, the second size 6; the second has 2 subclusters each of
size 4. the 1-nested model says that the log-pairwise
odds ratios between elements of the same cluster is a0+a1
if the two elements are ALSO of the same subcluster, and
a0 if they are from different subclusters.