RsqGLM: R-squared measures for GLMs

In modEvA: Model Evaluation and Analysis

R-squared measures for GLMs

Description

This function calculates some (pseudo) R-squared statistics for binomial Generalized Linear Models.

Usage

RsqGLM(model = NULL, obs = NULL, pred = NULL, use = "pairwise.complete.obs",
plot = TRUE, plot.type = "lollipop", na.rm = TRUE, rm.dup = FALSE, 
verbosity = 2, ...)

Arguments

model	a binary-response model object of class "glm". Alternatively, you can input the 'obs' and 'pred' arguments instead of 'model'.
obs	alternatively to 'model' and together with 'pred', a vector of observed presences (1) and absences (0) of a binary response variable. Alternatively (and if 'pred' is a 'SpatRaster'), a two-column matrix or data frame containing, respectively, the x (longitude) and y (latitude) coordinates of the presence points, in which case the 'obs' vector will be extracted with ptsrast2obspred. This argument is ignored if 'model' is provided.
pred	alternatively to 'model' and together with 'obs', a numeric vector with the corresponding predicted values of presence probability. Must be of the same length and in the same order as 'obs'. Alternatively (and if 'obs' is a set of point coordinates), a 'SpatRaster' map of the predicted values for the entire evaluation region, in which case the 'pred' vector will be extracted with ptsrast2obspred. This argument is ignored if 'model' is provided.
use	argument to be passed to cor for handling mising values.
plot	logical value indicating whether or not to display a bar chart or (by default) a lollipop chart of the calculated measures.
plot.type	character value indicating the type of plot to produce (if plot=TRUE). Can be "lollipop" (the default) or "barplot".
na.rm	Logical value indicating whether missing values should be ignored in computations. Defaults to TRUE.
rm.dup	If TRUE and if 'pred' is a SpatRaster and if there are repeated points within the same pixel, a maximum of one point per pixel is used to compute the presences. See examples in ptsrast2obspred. The default is FALSE.
verbosity	integer specifying the amount of messages to display. Defaults to the maximum implemented; lower numbers (down to 0) decrease the number of messages.
...	additional arguments to pass to the plotting function (see Examples).

Details

Implemented measures include the R-squared metrics of McFadden (1974), Cox-Snell (1989), Nagelkerke (1991, which corresponds to the corrected Cox-Snell, eliminating its upper bound), and Tjur (2009). See Allison (2014) for a brief review of these measures.

Note that pseudo R-squared values tend to be considerably lower than those of the R-squared for ordinary regression analysis, and they should not be judged by the same standards for a "good fit". For example, for McFadden's R-squared, values of 0.2 to 0.4 represent an excellent fit (McFadden, 1979).

Value

The function returns a named list of the calculated R-squared values.

Note

Tjur's R-squared can only be calculated for models with binomial response variable; otherwise, NA will be returned.

Author(s)

A. Marcia Barbosa

References

Allison P. (2014) Measures of fit for logistic regression. SAS Global Forum, Paper 1485-2014

Cox, D.R. & Snell E.J. (1989) The Analysis of Binary Data, 2nd ed. Chapman and Hall, London

McFadden, D. (1974) Conditional logit analysis of qualitative choice behavior. In: Zarembka P. (ed.) Frontiers in Economics. Academic Press, New York

McFadden, D. (1979) Quantitative Methods for Analyzing Travel Behaviour on Individuals: Some Recent Developments. Chapter 15 in Behavioural Travel Modelling. Edited by David Hensher and Peter Stopher.

Nagelkerke, N.J.D. (1991) A note on a general definition of the coefficient of determination. Biometrika, 78: 691-692

Tjur T. (2009) Coefficients of determination in logistic regression models - a new proposal: the coefficient of discrimination. The American Statistician, 63: 366-372.

See Also

Dsquared, AUC, threshMeasures, HLfit

Examples

# load sample models:
data(rotif.mods)

# choose a particular model to play with:
mod <- rotif.mods$models[[1]]

RsqGLM(model = mod)


# you can also use RsqGLM with vectors of observed and predicted values
# instead of a model object:

RsqGLM(obs = mod$y, pred = mod$fitted.values)


# plotting arguments can be modified:

par(mar = c(6, 3, 2, 1))

RsqGLM(obs = mod$y, pred = mod$fitted.values, col = "seagreen", border = NA,
ylim = c(0, 1), main = "Pseudo-R-squared values")

modEvA documentation built on May 12, 2025, 3:01 p.m.