EFFECTS OF MISSPECIFYING AN EXPLANATORY VARIABLE ON COEFFICIENTS OF DETERMINATION IN LOGISTIC REGRESSION

Yıl 2014, Cilt: 3 Sayı: 1, 1 - 10, 17.03.2014

Suay Ereeş Suay Erees Aylin Alın

https://doi.org/10.20290/btdb.14728

Öz

Misspecifying an explanatory variable is a common problem in logistic regression as it is for all members of generalized linear models. Categorizing a continuous explanatory variable, using wrong functional form of an explanatory variable and omitting an explanatory variable from the model are commonly made misspecifications in logistic regression analysis. Studies show that all of these cases cause a loss in efficiency for test statistics. In this paper, the effects of these types of misspecification on asymptotic relative efficiency of different coefficients of determination are investigated. All calculations and comparisons are based on extensive simulation study using bootstrap methods

Anahtar Kelimeler

Misspecification; R-square; Asymptotic relative efficiency; Logistic regression; Bootstrapping

LOJİSTİK REGRESYONDA BİR AÇIKLAYICI DEĞİŞKENİN YANLIŞ TANUMLANMASININ BELİRTME KATSAYILARI ÜZERİNDEKİ ETKİLERİ

Öz

Anahtar Kelimeler

Belirleme hatası, R-kare, asimtotik göreli etkinlik, lojistik regresyon, bootstrap

Kaynakça

• Begg, M.D. and Lagakos, S. (1990). On The Consequences of Model Misspecification in Logistic Regression. Environmental Health Perspectives, 87: 69-75.
• Begg, M.D. and Lagakos, S. (1992). Effects of Mismodelling on Tests of Association Based on Logistic Regression Models. The Annals of Statistics, 20(4): 1929-1952.
• Begg, M.D. and Lagakos, S. (1993). Loss in Efficiency Caused By Omitting Covariates and Misspecifying Exposure in Logistic Regression Models. Journal of The American Statistical Association, 88(421): 166-170.
• Cox, D.R. (1957). Note on Grouping. Journal of the American Statistical Association, 53(280): 543- 547.
• Cox, D.R. and Snell, E.J. (1989). The Analysis of Binary Data. London: Chapman and Hall.
• Erees, S. and Demirel, N. (2012). Omitted Variable Bias and Detection with Reset Test in Regression Analysis. Anadolu University Journal of Science and Technology -B- Theoretical Sciences, 2(1): 1-19.
• Hu, B., Palta, M., Shao, J. (2006). Properties of R Statistics for Logistic Regression. Statistics in
• Statistics for Logistic Regression. Statistics in
• Medicine, 25: 1383-1395.
• Keele, L.J. (2008). Semiparametric Regression for The Social Sciences. Wiley.
• Kvalseth, T.O. (1985). Cautionary Note About R. The American Statistician, 39: 279-285.
• Lagakos, S.W. (1988). Effects of Mismodelling and Mismeasuring Explanatory Variables on Tests of Their Association with A Response Variable. Statistics in Medicine, 7: 257-274.
• Leightner, J. E., and Inoue, T. (2007). Tackling The Omitted Variables Problem Without The Strong Assumptions of Proxies. European Journal of Operational Research, 178: 819–840.
• Menard, S. (2000). Coefficients of Determination for Multiple Logistic Regression Analysis. The American Statistician, 54(1): 17-24.
• Menard, S. (2002). Applied Logistic Regression Analysis, Second Edition. SAGE.
• McFadden, D. (1974). The Measurement of Urban Travel Demand. Journal of Public Economies, 3:303-328.
• Mittlböck, M. and Schemper, M. (1996). Explained Variation for Logistic Regression. Statistics in Medicine, 15: 1987-1997.
• Nagelkerke, N.J.D. (1991). A Note on A General Definition of The Coefficient of Determination. Biometrica, 78: 691-692.
• Nemes, S., Jonasson, J.M., Genell, A. and Steineck, G. (2009). Bias in Odds Ratios By Logistic Regression Modeling and Sample Size. BMC Medical Research Methodology, 9(56).
• Tosteson, T.D. and Tsiatis, A.A. (1988). The Asymptotic Relative Efficiency of Score Tests in A Generalized Linear Model with Surrogate Covariates. Biometrica, 75(3): 507-514.