lrm.fit {Design} | R Documentation

## 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` 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

`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)

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