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Characteristics of Dichotomous Variable Estimators

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Effective Investments on Capital Markets

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Abstract

The article covers the following probability models used in dichotomous variable analysis: logit, probit, and raybit—the last one proposed by the author. In the article, the following characteristics of estimators are derived: bias, variance, and mean squared error, which links them. The method of probability estimation which minimizes relative root mean squared error (RRMSE) is proposed. It is also shown that the goodness-of-fit measures of mean square error (MSE) and mean absolute error (MAE) models present in the field literature lead to the similar results.

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References

  1. Purczyński, J., Bednarz-Okrzyńska, K.: The raybit model and the assessment of its quality in comparison with the logit and probit models. Przegląd Statystyczny 3, 305–322 (2017)

    Google Scholar 

  2. Gruszczyński, M.: Empiryczne finanse przedsiębiorstw. Mikroekonometria finansowa. Difin, Warszawa (2012)

    Google Scholar 

  3. Barniv, R., McDonald, J.B.: Review of categorical models for classification issues in accounting and finance. Rev. Quant. Financ. Account. 13, 39–62 (1999)

    Article  Google Scholar 

  4. Ye, F., Lord, D.: Comparing three commonly used crash severity models on sample size requirements: multinomial logit, ordered probit and mixed logit models. Anal. Methods Accid. Res. 1, 72–85 (2014)

    Article  Google Scholar 

  5. Cramer, J.S.: Logit Models from Economics and Other Fields. Cambridge University Press (2003)

    Google Scholar 

  6. Hoetker, G.: The use logit and probit models in strategic management research: critical use. Strateg. Manag. J. 28, 331–343 (2007)

    Article  Google Scholar 

  7. Shin, H., Yin, G.: Boosting conditional logit model. J. Choice Model. 26, 48–63 (2018)

    Article  Google Scholar 

  8. D’Haultfœuille, X., Iaria, A.: A convenient method for the estimation of the multinomial logit model with fixed effects. Econ. Lett. 141, 77–79 (2016)

    Article  Google Scholar 

  9. Jones, J.M., Landwehr, J.T.: Removing heterogeneity bias from logit model estimation. Mark. Sci. 7, 41–59 (1988)

    Article  Google Scholar 

  10. Chamberlain, G.: Asymptotic efficiency in estimation with conditional moment restrictions. J. Econom. 34(3), (March 1987)

    Article  Google Scholar 

  11. Hausman, J., McFadden, D.: Specification tests for the multinomial logit model. Econometrica 52, 1219–1240 (1984)

    Article  Google Scholar 

  12. Hausman, J.: Specification test in econometrics. Econometrica 46, 1251–1272 (1978)

    Article  Google Scholar 

  13. Jones, S., Hensher, D.A.: Predicting firm financial distress: a mixed logit model. Account. Rev. 79, 1011–1038 (2004)

    Article  Google Scholar 

  14. Fox, J.T., Kim, K., Ryan, S.P., Bajari, P.: The random coefficients logit model is identified. J. Econ. 166, 204–212 (2012)

    Article  Google Scholar 

  15. Li, S., Wang, S.: A financial early warning logit model and its efficiency verification approach. Knowl. Based Syst. 70, 78–87 (2014)

    Article  Google Scholar 

  16. Brezigar-Masten, A., Masten, I.: CART-based selection of bankruptcy predictors for the logit model. Expert Syst. Appl. 39, 10153–10159 (2012)

    Article  Google Scholar 

  17. Antunes, A., Bonfim, D., Monteiro, N., Rodrigues, P.M.M.: Forecasting banking crises with dynamic panel probit models. Int. J. Forecast. 34, 249–275 (2018)

    Article  Google Scholar 

  18. Ng, E.C.Y.: Forecasting US recessions with various risk factors and dynamic probit models. J. Macroecon. 34, 112–125 (2012)

    Article  Google Scholar 

  19. Soyer, R., Sung, M.: Bayesian dynamic probit models for the analysis of longitudinal data. Comput. Stat. Data Anal. 68, 388–398 (2013)

    Article  Google Scholar 

  20. Proaño, C.R., Tarassow, A.: Evaluating the predicting power of ordered probit models for multiple business cycle phases in the US and Japan. J. Japan. Int. Econ. (in press), 1–28 (2018)

    Google Scholar 

  21. Proaño, C.R.: Detecting and predicting economic accelerations, recessions, and normal growth periods in real-time. J. Forecast. 1, 26–42 (2017)

    Article  Google Scholar 

  22. Purczyński, J., Porada-Rochoń, M.: Ocena jakości modeli ze zmienną dychotomiczną. Logistyka 3, 4064–4073 (2015)

    Google Scholar 

  23. Maddala, G.S.: Limited-Dependent and Qualitative Variables in Econometrics. Cambridge University Press (1983)

    Google Scholar 

  24. Han, S., Vytlacil, E.J.: Identification in a generalization of bivariate probit models with dummy endogenous regressors. J. Econ. 199, 63–73 (2017)

    Article  Google Scholar 

  25. Mourifié, M., Méango, R.: A note on the identification in two equations probit model with dummy endogenous regressor. Econ. Lett. 125, 360–363 (2014)

    Article  Google Scholar 

  26. Papatla, P., Krishnamurthi, L.: A probit model of choice dynamics. Mark. Sci. 11, 189–206 (1992)

    Article  Google Scholar 

  27. Amemiya, T.: The estimation of a simultaneous equation generalized probit model. Econometrica 46, 1193–1205 (1978)

    Article  Google Scholar 

  28. Amemiya, T.: The estimation of a simultaneous equation Tobit model. Int. Econ. Rev. 1, 169–181 (1979)

    Article  Google Scholar 

  29. Amemiya, T.: Advanced Econometrics. Harvard University Press (1985)

    Google Scholar 

  30. Hausman, J., Wise, D.A.: A conditional probit model for qualitative choice: discrete decisions recognizing interdependence and heterogeneous preferences. Econometrica 46, 403–426 (1978)

    Article  Google Scholar 

  31. Eichengreen, B., Watson, M.W., Grossman, R.S.: Bank rate policy under the interwar gold standard: a dynamic probit model. Econ. J. 95, 725–745 (1985)

    Article  Google Scholar 

  32. Butler, J.S.: Estimating the correlation in censored probit models. Rev. Econ. Stat. 78, 356–358 (1966)

    Article  Google Scholar 

  33. Collett, D.: Modelling binary data, 2nd edn. In: Text in Statistical Science. Chapman & Hall/CRC (2003)

    Google Scholar 

  34. McFadden, D.: Conditional logit analysis of qualitative choice behavior, chap. 4. In: Analysis of Qualitative Choice Behavior, pp. 105–142 (1973)

    Google Scholar 

  35. McFadden, D., Train, K.: Mixed MNL models for discrete response. J. Appl. Econ. 15(5), 447–470 (2000)

    Article  Google Scholar 

  36. Judge, G.G., Griffiths, W.E., Hill, R.C., Lee, T.C.: Theory and Practice of Econometrics. Wiley, New York (1980)

    Google Scholar 

  37. Jajuga, K.: Modele z dyskretną zmienną objaśnianą. In: Bartosiewicz, S. (ed.) Estymacja modeli ekonometrycznych. PWE, Warszawa (1989)

    Google Scholar 

  38. Chow, G.C.: Econometrics. Mc-Graw-Hill Inc., New York (1983)

    Google Scholar 

  39. Krzyśko, M.: Statystyka matematyczna (Part II). UAM, Poznań (1997)

    Google Scholar 

  40. Guzik, B., Appenzeller, D., Jurek, W.: Prognozowanie i symulacje. Wybrane zagadnienia. Wydawnictwo Akademii Ekonomicznej w Poznaniu, Poznań (2005)

    Google Scholar 

  41. Amemiya, T.: Qualitative response models: a survey. J. Econ. Lit., 1483–1536 (1981)

    Google Scholar 

  42. Maddala, G.S.: Ekonometria. Wydawnictwo Naukowe PWN, Warszawa (2006)

    Google Scholar 

  43. Purczyński, J., Bednarz-Okrzyńska, K.: Goodness of fit measures of models with binary dependent variable which take into account heteroscedasticity of a random element. Folia Oeconomica Stetinensia 18, 182–194 (2018)

    Article  Google Scholar 

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Correspondence to Jan Purczyński .

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Purczyński, J. (2019). Characteristics of Dichotomous Variable Estimators. In: Tarczyński, W., Nermend, K. (eds) Effective Investments on Capital Markets. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-21274-2_21

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