Colr {tram}

Continuous Outcome Logistic Regression

Description

A proportional-odds model for continuous variables

Usage

Colr(formula, data, subset, weights, offset, cluster, na.action = na.omit, ...)

Arguments

formula

an object of class "formula": a symbolic description of the model structure to be fitted. The details of model specification are given under tram and in the package vignette.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula).

subset

an optional vector specifying a subset of observations to be used in the fitting process.

weights

an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector. If present, the weighted log-likelihood is maximised.

offset

this can be used to specify an _a priori_ known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases.

cluster

optional factor with a cluster ID employed for computing clustered covariances.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset.

...

additional arguments to tram.

Details

Simultaneous estimation of all possible binary logistic models obtained by dichotomisation of a continuous response. The regression coefficients can be constant allowing for an interpretation as log-odds ratios.

The model is defined with a positive shift term, thus exp(coef()) is the multiplicative change of the odds ratio (conditional odds of treatment or for a one unit increase in a numeric variable divided by conditional odds of reference). Large values of the linear predictor correspond to small values of the conditional expectation response (but this relationship is nonlinear).

Value

An object of class Colr, with corresponding coef, vcov, logLik, estfun, summary, print, plot and predict methods.

References

Tina Lohse, Sabine Rohrmann, David Faeh and Torsten Hothorn (2017), Continuous Outcome Logistic Regression for Analyzing Body Mass Index Distributions, F1000Research, 6(1933), doi:10.12688/f1000research.12934.1.

Torsten Hothorn, Lisa Moest, Peter Buehlmann (2018), Most Likely Transformations, Scandinavian Journal of Statistics, 45(1), 110–134, doi:10.1111/sjos.12291.

Examples

  data("BostonHousing2", package = "mlbench")

  lm(cmedv ~ crim + zn + indus + chas + nox + rm + age + dis + 
             rad + tax + ptratio + b + lstat, data = BostonHousing2)

  Colr(cmedv ~ chas + crim + zn + indus + nox + 
               rm + age + dis + rad + tax + ptratio + b + lstat, 
               data = BostonHousing2)