modEvA (version 3.5)

Dsquared: Proportion of deviance explained by a GLM

Description

This function calculates the (adjusted) amount of deviance accounted for by a generalized linear model.

Usage

Dsquared(model = NULL, obs = NULL, pred = NULL, family = NULL, 
adjust = FALSE, npar = NULL, na.rm = TRUE, rm.dup = FALSE)

Value

This function returns a numeric value indicating the (adjusted) proportion of deviance accounted for by the model.

Arguments

model

a model object of class "glm". If this argument is provided, 'obs' and 'pred' will be extracted with mod2obspred. Alternatively, you can input the 'obs' and 'pred' arguments instead of 'model'.

obs

alternatively to 'model' and together with 'pred', a numeric 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 vector with the corresponding predicted values of presence probability, habitat suitability, environmental favourability or alike. 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.

family

a character vector (i.e. in quotes) of length 1 specifying the family of the GLM. This argument is ignored if model is provided; otherwise (i.e. if 'obs' and 'pred' are provided rather than a model object), only families 'binomial' (logit link) and 'poisson' (log link) are currently implemented.

adjust

logical, whether or not to adjust the D-squared value for the number of observations and parameters in the model (see Details). The default is FALSE; TRUE requires either providing the model object, or specifying the number of parameters in the model that produced the pred values.

npar

an integer vector indicating the number of parameters in the model. This argument is ignored if model is provided or if adjust = FALSE.

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.

Author

A. Marcia Barbosa

Details

Linear models come with an R-squared value that measures the proportion of variation that the model accounts for. The R-squared is provided with summary(model) in R. For generalized linear models (GLMs), the equivalent is the amount of deviance accounted for (D-squared; Guisan & Zimmermann 2000), but this value is not normally provided with the model summary. The Dsquared function calculates it. There is also an option to calculate the adjusted D-squared, which takes into account the number of observations and the number of predictors, thus allowing direct comparison among different models (Weisberg 1980, Guisan & Zimmermann 2000).

References

Guisan, A. & Zimmermann, N.E. (2000) Predictive habitat distribution models in ecology. Ecological Modelling 135: 147-186

Weisberg, S. (1980) Applied Linear Regression. Wiley, New York

See Also

glm, plotGLM

Examples

# load sample models:
data(rotif.mods)

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

Dsquared(model = mod)

Dsquared(model = mod, adjust = TRUE)


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

presabs <- mod$y
prediction <- mod$fitted.values
parameters <- attributes(logLik(mod))$df

Dsquared(obs = presabs, pred = prediction, family = "binomial")

Dsquared(obs = presabs, pred = prediction, family = "binomial",
adjust = TRUE, npar = parameters)


# 'obs' can also be a table of presence point coordinates
# and 'pred' a SpatRaster of predicted values