Fits a binary or ordinal logistic model for a given design matrix and response
vector with no missing values in either. Ordinary or penalized maximum
likelihood estimation is used.
USAGE:
lrm.fit(x, y, offset, initial, est, maxit=12, eps=.025,
tol=1E-7, trace=FALSE, penalty.matrix, weights, normwt)
ARGUMENTS:
x
design matrix with no column for an intercept
y
response vector, numeric, categorical, or character
offset
optional numeric vector containing an offset on the logit scale
initial
vector of initial parameter estimates, beginning with the
intercept
est
indexes of
x to fit in the model (default is all columns of
x).
Specifying
est=c(1,2,5) causes columns 1,2, and 5 to have
parameters estimated. The score vector
u and covariance matrix
var
can be used to obtain score statistics for other columns
maxit
maximum no. iterations (default=
12). Specifying
maxit=1
causes logist to compute statistics at initial estimates.
eps
difference in
-2 log likelihood for declaring convergence.
Default is
.025.
tol
Singularity criterion. Default is 1E-7
trace
set to
TRUE to print -2 log likelihood, step-halving
fraction, and rank of variance matrix at each iteration
penalty.matrix
a self-contained ready-to-use penalty matrix - see
lrm
weights
a vector (same length as
y) of possibly fractional case weights
normwt
set to code{TRUE} to scale
weights so they sum to the length of
y; useful for sample surveys as opposed to the default of
frequency weighting
VALUE:
a list with the following components:
call
calling expression
freq
table of frequencies for
y in order of increasing
y
stats
vector with the following elements: number of observations used in the
fit, maximum absolute value of first
derivative of log likelihood, model likelihood ratio chi-square, d.f.,
P-value,
c index (area under ROC curve), Somers' D_{xy},
Goodman-Kruskal gamma, and Kendall's tau-a
rank correlations
between predicted probabilities and observed response, the
Nagelkerke R^2 index, and the Brier probability score with
respect to computing the probability that y > lowest level.
Probabilities are rounded to the nearest 0.002
in the computations or rank correlation indexes.
When
penalty.matrix is present, the chi-square,
d.f., and P-value are not corrected for the effective d.f.
fail
set to
TRUE if convergence failed (and
maxiter>1)
coefficients
estimated parameters
var
estimated variance-covariance matrix (inverse of information matrix).
Note that in the case of penalized estimation,
var is not the
improved sandwich-type estimator (which
lrm does compute).
u
vector of first derivatives of log-likelihood
deviance
-2 log likelihoods.
When an offset variable is present, three
deviances are computed: for intercept(s) only, for
intercepts+offset, and for intercepts+offset+predictors.
When there is no offset variable, the vector contains deviances for
the intercept(s)-only model and the model with intercept(s) and predictors.
est
vector of column numbers of
X fitted (intercepts are not counted)
non.slopes
number of intercepts in model
penalty.matrix
see above
AUTHOR(S):
Frank Harrell
Department of Biostatistics, Vanderbilt University
f.harrell@vanderbilt.edu
SEE ALSO:
,
,
,
,
EXAMPLES:
#Fit an additive logistic model containing numeric predictors age,
#blood.pressure, and sex, assumed to be already properly coded and
#transformed
#
# fit <- lrm.fit(cbind(age,blood.pressure,sex), death)