TY - JOUR TT - Comparative simulation study for model adequancy with binary response variable under multicollinearity – nonparametric approaches AU - Kan Kılınç, Betül AU - Çavuş, Mustafa PY - 2017 DA - April Y2 - 2016 DO - 10.16984/saufenbilder.297002 JF - Sakarya University Journal of Science JO - SAUJS PB - Sakarya University WT - DergiPark SN - 2147-835X SP - 169 EP - 177 VL - 21 IS - 2 KW - toplamsal modeller KW - lojistik regresyon KW - toplamsal lojistik regresyon N2 - Regressionmodels used to explore the importance of several explanatory variables inestimation, classification and analytical tools play an efficient role for manydata analysis. Although the classical linear model is quite easy to use, it isoften not sufficient for many real data sets as the relationships betweenvariables do not hold the assumption of the linearity of the relationshipbetween dependent and explanatory variables. Under this study, a nonparametricmodel fitting that does not require to form a strict mathematical relationshipbetween dependent and explanatory variables will be discussed on the contrarythe assumption in multiple linear regression. In this study, the relationshipbetween a binary dependent variable and the explanatory variables will beexamined in a conducted simulation study by using generalized linear, theadditive logistic regression in case of classical logistic regression model anddecision trees to explore the cause and effect relationship. The methods in questionand the simulation study will be performed for small, medium and large datasets when multicollinearity problem exists and will be compared with eachother. CR - [1] A. Erar, “Çoklu bağlantı varlığında doğrusal regresyon modellerinde değişken seçimi” Ankara, Hacettepe Üniversitesi, İstatistik Bölümü, 1994. CR - [2] A. Erar, “Bağlanım (Regresyon) Çözümlemesi Ders Notları” İstanbul, Mimar Sinan Güzel Sanatlar Üniversitesi, 2006. CR - [3] B. Kan Kılınç, “Yanıt Yüzeyi Modellerine MARS Yaklaşımı”, Eskişehir, Anadolu Üniversitesi, İstatistik Bölümü, 2010. CR - [4] Y. Kaşko, “Çoklu Bağlantı Durumunda İkili Lojistik Regresyon Modelinde Gerçekleşen 1.Tip Hata ve Testin Gücü”, Ankara, Ankara Üniversitesi, Biyometri ve Genetik Anabilim Dalı, 2007. CR - [5] G. Wahba and J. Wendelberger, “Some new mathematical methods for variational objective analysis using splines and cross validation”, Monthly Weather Review, vol.108, pp. 1122-1145, 1980. CR - [6] S. Wood, “Generalized Additive Models: An introduction to R”, Chapman and Hall/CRC, 2006. CR - [7] L. Breiman, J. Friedman, R. Olshen, and C. Stone, “Classification and Regression Trees”, Wadsworth, 1984. CR - [8] H. Christian, “Smoothing by spline functions”, Journal of Numerische Mathematic, vol.10, no.3, pp. 177-183, 1967. CR - [9] J. Duchon, “Splines minimizing rotation-invariant semi-norms in Sobolev spaces”, Constructive Theory of Functions of Several Variables, Springer, 1977. CR - [10] R. De Veaux and L. Ungar, “Multicollinearity: A tail of two nonparametric regressions”, Lecture Notes in Statistics: Selecting Models from Data, pp. 393-402, 2007. CR - [11] M. Hutchinson and R. Bischof, “A new method for estimating the spatial distribution of mean seasonal and annual rainfall applied to the Huner Valley, New South Wales”, Australian Meteorological Magazine , vol.31, no.3, pp.179-184, 1983. CR - [12] T. Hastie, R. Tibshirani and F. Friedman, “The Elements of Statistical Learning”, Springer, 2009. CR - [13] S. Kovalchik and R. Varadhan, “Fitting additive binomial regression models with the R package blm”, Journal of Statistical Software, vol.54, no.1, pp.1-18, 2013. CR - [14] L. Ma and X. Yan, “Examining the nonparametric effect of drivers' age in rear-end accidents through an additive logistic regression model”, Accident Analysis and Prevention, vol.67, pp.129-136, 2014. CR - [15] D. McFadden, “Conditional logit analysis of qualitative choice behavior”, Frontiers in Econometrics ,Academic Press, pp.105-142, 1974. CR - [16] J. Meinguet, “Multivariate interpolation at arbitrary points made simple”, Journal of Applied Mathematics and Physics, vol.30, pp.370-384,1979. CR - [17] C. Montgomery, E. Peck and G. Vining, “ Introduction to Linear Regression Analysis”, Wiley, 2012. CR - [18] W. Press, B. Flannery, S. Teukolsky and W. Vetterling, “Cubic Spline Interpolation. The Art of Scientific Computing”, Cambridge University Press, 1992. CR - [19] S. Silvey, “Multicollinearity and imprecise information”, Journal of Royal Statistics Society vol.31, pp.539-552, 1969. CR - [20] J. Shen and S. Gao, “A solution to seperation and multicollinearity in multiple logistic regression”, Journal of Data Science, vol.6, no.4, pp.515-531, 2008. CR - [21] B. Ripley, “Pattern Recognation and Neural Networks”, Cambridge University Press, 1996. UR - https://doi.org/10.16984/saufenbilder.297002 L1 - https://dergipark.org.tr/en/download/article-file/282234 ER -