R-squared for Latent Variable Models
R-squared goodness of fit for latent variable models, such as cumulative link models. Some software such as Stata call the quantity the McKelvey–Zavoina R-squared, which was proposed in their 1975 paper for cumulative probit models.
R2latvar(object)
object |
A |
Models such as the proportional odds model have
a latent variable interpretation
(see, e.g., Section 6.2.6 of Agresti (2018),
Section 14.4.1.1 of Yee (2015),
Section 5.2.2 of McCullagh and Nelder (1989)).
It is possible to summarize the predictive power of
the model by computing R^2 on the transformed
scale, e.g., on a standard normal distribution for
a probitlink link.
For more details see Section 6.3.7 of Agresti (2018).
The R^2 value. Approximately, that amount is the variability in the latent variable of the model explained by all the explanatory variables. Then taking the positive square-root gives an approximate multiple correlation R.
Thomas W. Yee
Agresti, A. (2018). An Introduction to Categorical Data Analysis, 3rd ed., New York: John Wiley & Sons.
McKelvey, R. D. and W. Zavoina (1975). A statistical model for the analysis of ordinal level dependent variables. The Journal of Mathematical Sociology, 4, 103–120.
pneumo <- transform(pneumo, let = log(exposure.time)) (fit <- vglm(cbind(normal, mild, severe) ~ let, propodds, data = pneumo)) R2latvar(fit)
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