computes the summary measures of predictive strength (i.e., pseudo-R2s) of several categorical outcome models.
Rsquared(model, measure)single model object for which R2 is determined.
selects any of the different measures available.
the name of the R-squared calculated.
realized value of the computed R2.
adjusted R2, only available when McFadden's R2 is computed.
Modified R2 with a square root penalty, only available when the Ugba & Gertheiss's R2 is computed.
Modified R2 with a logarithmic penalty, only available when the Ugba & Gertheiss's is computed.
Rsquared provides different R2 indices for both binary and
multi-categorical response models. Supported classes include: glm,
vglm, clm, polr, multinom, mlogit,
serp. In other words, mainly models with binary or multi-categorical
outcomes are supported. The non-likelihood based measures, including the Mckelvey,
Tjur and Efron R2s are only available for binary models, while the rest of the
measures (likelihood-based) are all available for both binary and
multi-categorical models. The Ugba & Gertheiss's R2 in particular, computes
the recently proposed modification of the popular Mcfadden's R2. The likelihood
ratio index in the said R2 is penalized using either a square-root or logarithmic
stabilizing function of the response category. The two approaches yield practically
the same result.
Long, J.S. (1997). Regression Models for Categorical and Limited Dependent Variables. California: Sage Publications.
Ugba, E. R. and Gertheiss, J. (2018). An Augmented Likelihood Ratio Index for Categorical Response Models. In Proceedings of 33rd International Workshop on Statistical Modelling, Bristol, 293-298.
require(serp)
pom <- serp(ordered(RET) ~ DIAB + GH + BP, link="logit",
slope = "parallel", reverse = TRUE, data = retinopathy)
Rsquared(pom, measure = "mcfadden")
#>
#> McFadden's R2:
#> 0.18922
#>
#> adj.R2
#> 0.18027
Rsquared(pom, measure = "ugba")
#>
#> Ugba & Gertheiss' R2:
#>
#> (sqrt)
#> 0.40178
#>
#> (log)
#> 0.41854