rms (version 4.5-0)

lrm.fit: Logistic Model Fitter

Description

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=0, initial, est, maxit=12, eps=.025, tol=1e-7, trace=FALSE, penalty.matrix=NULL, weights=NULL, normwt=FALSE, scale=FALSE)

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. If the $-2 log$ likelihood gets worse by eps/10 while the maximum absolute first derivative of $-2 log$ likelihood is below 1e-9, convergence is still declared. This handles the case where the initial estimates are MLEs, to prevent endless step-halving.

tol

Singularity criterion. Default is 1e-7

trace

set to TRUE to print -2 log likelihood, step-halving fraction, change in -2 log likelihood, maximum absolute value of first derivative, and vector of first derivatives 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 TRUE to scale weights so they sum to the length of y; useful for sample surveys as opposed to the default of frequency weighting

scale

set to TRUE to subtract column means and divide by column standard deviations of x before fitting, and to back-solve for the un-normalized covariance matrix and regresion coefficients. This can sometimes make the model converge for very large sample sizes where for example spline or polynomial component variables create scaling problems leading to loss of precision when accumulating sums of squares and crossproducts.

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, the Brier probability score with respect to computing the probability that $y >$ the mid level less one, the $g$-index, $gr$ (the $g$-index on the odds ratio scale), and $gp$ (the $g$-index on the probability scale using the same cutoff used for the Brier score). 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

See Also

lrm, glm, matinv, solvet, cr.setup, gIndex

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)