A Monte Carlo-based pseudo-coefficient of determination for generalized linear models with binary outcome

References

• J.H. Aldrich and F.D. Nelson, Linear Probability, Logit and Probit Models, Sage Publications, London, 1984.
   Google Scholar
• T. Amemiya, Qualitative response models: A survey, J. Econ. Lit. 19 (1981), pp. 1483–1536.
   Web of Science ®Google Scholar
• J.G. Cragg and R.S. Uhler, The demand for automobiles, Canad. J. Econ. 3 (1970), pp. 386–406. doi: 10.2307/133656
   Web of Science ®Google Scholar
• A. DeMaris, Explained variance in logistics regression: A Mone Carlo study of proposed measures, Sociol. Methods Res. 31 (2002), pp. 27–74. doi: 10.1177/0049124102031001002
   Web of Science ®Google Scholar
• P.J. Dhrymes, Handbook of Econometrics, Elsevier Science Publishers BV, Amsterdam, 1986.
   Google Scholar
• B. Efron, Regression and ANOVA with zero-one data: Measure of residual variation, J. Amer. Statist. Assoc. 73 (1978), pp. 113–121. doi: 10.1080/01621459.1978.10480013
   Web of Science ®Google Scholar
• A. Estrella, A new measure of fit for equations with dichotomous dependent variables, J. Bus. Econ. Stat. 16 (1998), pp. 198–205.
   Web of Science ®Google Scholar
• J. Freese and J. Long, Regression Models for Categorical Dependent Variables Using Stata, Stata Press, College Station, 2006.
   Google Scholar
• T.M. Hagle and G.E. Mitchell-II, Goodness-of-fit measures for probit and logit, Amer. J. Polit. Sci. 36 (1992), pp. 762–784. doi: 10.2307/2111590
   Web of Science ®Google Scholar
• J.R. Koza, Genetic Programming: on the Programming of Computers by Means of Natural Selection, MIT Press, Cambridge,1992.
   Google Scholar
• T. Kvalseth, Cautionary note about R2, Amer. Statist. 39 (1985), pp. 279–285.
   Web of Science ®Google Scholar
• M. Lacy, An explained variation measure for ordinal response models with comparisons to other ordinal R2 measures, Sociol. Methods Res. 34 (2006), pp. 469–520. doi: 10.1177/0049124106286329
   Web of Science ®Google Scholar
• C. Lave, The demand for urban mass transportation, Rev. Econ. Stat. 52 (1970), pp. 320–323. doi: 10.2307/1926301
   Web of Science ®Google Scholar
• S. Lee, M. Goddard, N. Wray and P. Visscher, A better coefficient of determination for genetic profile analysis, Genetic Epidemiol. 36 (2012), pp. 214–224. doi: 10.1002/gepi.21614
   PubMed Web of Science ®Google Scholar
• J.S. Long, Regression Models for Categorical and Limited Dependent Variables, Sage Publications, Thousand Oaks, CA, 1997.
   Google Scholar
• G.S. Maddala, A perspective on the use of limited-dependent and qualitative variables, Amer. J. Polit. Sci. 36 (1992), pp. 762–784. doi: 10.2307/2111590
   Web of Science ®Google Scholar
• L. Magee, R2 measures based on wald and likelihood ratio joint significance test, Amer. Statist. 44 (1990), pp. 250–253.
   Web of Science ®Google Scholar
• P. McCullagh and J.A. Nelder, Generalized Linear Models, Chapman and Hall, London, 1989.
   Google Scholar
• D. McFadden, Conditional logit analysis of qualitative choice behavior, in Frontiers in Econometrics, P. Zarembka, ed., Chapter 4, Academic Press, New York, 1973, pp. 105–142.
   Google Scholar
• R.D. McKelvey and W. Zavoina, A statistical model for the analysis of ordinal level dependent variables, J. Math. Sociol. 4 (1975), pp. 103–120. doi: 10.1080/0022250X.1975.9989847
   Web of Science ®Google Scholar
• N. Meinel, Comparison of performance measures for multivariate discrete models, AStA Adv. Statist. Anal. 93 (2009), pp. 159–174. doi: 10.1007/s10182-008-0078-x
   Web of Science ®Google Scholar
• M. Mittlbock and M. Schemper, Explained variation for logistic regression, Stat. Med. 15 (1996), pp. 1987–1997. doi: 10.1002/(SICI)1097-0258(19961015)15:19<1987::AID-SIM318>3.0.CO;2-9
   PubMed Web of Science ®Google Scholar
• N. Nagelkerke, A note on a general definition of the coefficient of determination, Biometrika 78 (1991), pp. 691–692. doi: 10.1093/biomet/78.3.691
   Web of Science ®Google Scholar
• J. Neter and E.S. Maynes, On the appropriateness of the correlation coefficient with a 0, 1 dependent variable, J. Amer. Statist. Assoc. 65 (1970), pp. 501–509. doi: 10.1080/01621459.1970.10481099
   Web of Science ®Google Scholar
• D. Rizopoulos, Point-biserial correlation. Available at http://rss.acs.unt.edu/Rdoc/library/ltm/html/biserial.cor.html [Accessed 3 January 2013].
   Google Scholar
• M. Schmidt and H. Lipson, Distilling free-form natural laws from experimental data, Science 324 (2009), pp. 81–85. doi: 10.1126/science.1165893
   PubMed Web of Science ®Google Scholar
• M. Schmidt and H. Lipson, Eureqa (version 0.98 beta) software. Available at http://www.nutonian.com [Accessed 13 February 2014].
   Google Scholar
• G. Shorack, Probability for Statisticians, Springer, New York, 2000.
   Google Scholar
• L. Spector and M. Mazzeo, Probit analysis and economic education, J. Econ. Edu. 11 (1980), pp. 37–44. doi: 10.1080/00220485.1980.10844952
   Web of Science ®Google Scholar
• R. Tate, Correlation between a discrete and a continuous variable-point-biserial correlation, Ann. Math. Stat. 25 (1954), pp. 603–607. doi: 10.1214/aoms/1177728730
   Google Scholar
• R. Tate, The theory of correlation between two continuous variables when one is dichotomized, Biometrika 42 (1955), pp. 205–216. doi: 10.1093/biomet/42.1-2.205
   Web of Science ®Google Scholar
• M.R. Veall and K.F. Zimmermann, Evatuating pseudo-R2's for binary probit models, Qual. Quantity 28 (1994), pp. 151–164. doi: 10.1007/BF01102759
   Web of Science ®Google Scholar
• M.R. Veall and K.F. Zimmermann, Pseudo-R2 measures for some common limited dependent variable models, J. Econ. Surv. 10 (1996), pp. 241–259. doi: 10.1111/j.1467-6419.1996.tb00013.x
   Google Scholar
• F. Windmeijer, Goodness of fit measures in binary choice models, Econometr. Rev. 14 (1995), pp. 101–116. doi: 10.1080/07474939508800306
   Google Scholar