How to Test the Parametric Fit of the Complementary Log Log Model to the Data?

Abstract

In this study, commands written on the basis of Uniform Confidence Bands (UCB) in the new windows version of the XploRe package for testing the validity of the link function assumed for binary parametric complementary log log model were introduced. Models including only continuous and both continuous and discrete (mixed) explanatory variables cases were discussed, separately. I intended here to present researchers an easier way for testing the accuracy of the assumed parametric complementary log log model for the data that could not be tested by the existing standard statistical packages. The applicability of the commands was shown over an artificial and a real data set on gastric cancer.    

 

 

    Key Words:  Complementary log log model; model validity test; binary dependent variable; semi-parametric

   approach; uniform confidence band.

 

Keywords

• Complementary log log model; model validity test; binary dependent variable; semi-parametric

References

1. Hardle, W., Klinke, S., Turlach, B.A., “XploRe: An interactive statistical computing environment and state-of-the-art density and regression smoothing”, Stat Comput, 3:23-26 (2007).
2. Hardle, W., Müller, M., Sperlich, S., Werwatz, A., “Nonparametric and Semiparametric Models”, Springer-Verlag, New York (2004).
3. Hardle, W., Hlavka, Z., Klinke, S., “XploRe Application Guide”. MD Tech, Springer-Verlag, New York (2003).
4. Hardle, W., “XploRe-A computing environment for exploratory regression and density smoothing”, Stat Softw Newsl, 14:113-119 (1988).
5. Horowitz, J.L., “Semiparametric Methods in Econometrics”. Springer-Verlag, New York (1998).
6. Horowitz, J.L, Hardle, W., “Direct semiparametric estimation of single-index models with discrete covariates”, J Am Stat Assoc, 91:1632-1640 (1996).
7. Horowitz, J.L, Hardle, W., “Testing a parametric model against a semiparametric alternative”, Econ Theory, 10:821-848 (1994).
8. GU J Sci, 25(3):665-675(2012)/ Özge AKKUŞ♠

9. Klinke, S., Golubev, Y., Hardle, W., Neuman, M., “Teaching wavelets in XploRe”, Comput Stat, 13:141-151 (1997).
10. McCullagh, P., Nelder, J.A., “Generalized Linear Models”, Monogr Stat Appl Probab 37, Chapman and Hall, London (1989). [10] Müller, M., Ronz, B., semiparametric “Computerassisted
11. linear models”, Comput Stat, 12:153-172 (1997). generalized [11] Powell, J.L, Stock, J.H., Stoker, T.M.,
12. “Semiparametric estimation of index coefficients”,
13. Econometrica, 57(6):1403-1430 (1989).
14. Proença, I., Werwatz, A., “Comparing parametric and semiparametric binary response models”, Sonderforschungsbereich 373 2000-20. Humboldt Universitaet. Berlin, Available via DIALOG. ftp://amadeus.wiwi.hu- berlin.de/pub/papers/sfb373 (1994).
15. Wang, X., Dey, D.K., “A flexible skewed link function for binary response data”, Technical Report, Department of Statistics. University of Connecticut, http://www.samsi.info/TR/tr2008-05.pdf (2008). via DIALOG.