Nagelkerke and Estrella are not provided because are designed for discrete dependent variables. Cox and Snell is preferred and pseudo-R^2 should be preferred, because McFadden's index could be negative.
Original fitted model
Data used in update statement
A function described by using-fit-indices. You could retrieve following indices:
Provided by betareg by default
Cox and Snell(1989).
Cox, D. R., & Snell, E. J. (1989). The analysis of binary data (2nd ed.). London, UK: Chapman and Hall.
Estrella, A. (1998). A new measure of fit for equations with dichotomous dependent variables. Journal of Business & Economic Statistics, 16(2), 198-205. doi: 10.1080/07350015.1998.10524753.
McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.), Frontiers in econometrics (pp. 104-142). New York, NY: Academic Press.
Shou, Y., & Smithson, M. (2015). Evaluating Predictors of Dispersion:A Comparison of Dominance Analysis and Bayesian Model Averaging. Psychometrika, 80(1), 236-256.
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