Rsquared {gofcat}

R-squared for Categorical Response Models

Description

computes the summary measures of predictive strength (i.e., pseudo-R2s) of several categorical outcome models.

Usage

Rsquared(model, measure)

Arguments

model

single model object for which R2 is determined.

measure

selects any of the different measures available.

Details

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.

Value

measure

the name of the R-squared calculated.

R2

realized value of the computed R2.

adj

adjusted R2, only available when McFadden's R2 is computed.

sqrt.R2

Modified R2 with a square root penalty, only available when the Ugba & Gertheiss's R2 is computed.

log.R2

Modified R2 with a logarithmic penalty, only available when the Ugba & Gertheiss's is computed.

References

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.

See Also

erroR

Examples

require(serp)

pom <- serp(ordered(RET) ~ DIAB + GH + BP, link="logit",
            slope = "parallel", reverse = TRUE, data = retinopathy)
Rsquared(pom, measure = "mcfadden")
Rsquared(pom, measure = "ugba")