rms (version 2.0-2)

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, 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 c

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 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 $\chi^2$, 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

concept

logistic regression model

See Also

lrm, glm, matinv, solvet, cr.setup

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)