Analyses of Two Different Regression Models and Bootstrapping

Regression methods are used to explain the relationship between a single response variable and one or more explanatory variables. Graphical methods are generally the first step and are used to identify models that can be explored to describe the relationship. Although linear models are frequently used and they are user friendly, many important associations are not linear and require considerably more analytical effort. This study is focused on such nonlinear models. To perform statistical inference in this context, we need to account for the error structure of the data. The experimental design for the nutrition data that we use called for each subject to be studied under two different values of the explanatory variable. However, some participants did not complete the entire study and, as a result, the data are available for only one value of the explanatory variable for them. In the analysis section, the bootstrapping method will be used to re-sample the data points with replacement, which will then be used with a nonlinear parametric model. The confidence intervals for the parameters of the nonlinear model will be calculated with the reflection method for the nutrition data set. In addition, the break point of the spline regression will be determined for the same data set. Although the nutrition data set will be used for this study, the basic ideas can be used in many other fields such as education, engineering and biology.


CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization
Weber, Gerhard-Wilhelm; Batmaz, İnci; Köksal, Gülser; Taylan, Pakize; Yerlikaya-Ozkurt, Fatma (2012-01-01)
Regression analysis is a widely used statistical method for modelling relationships between variables. Multivariate adaptive regression splines (MARS) especially is very useful for high-dimensional problems and fitting nonlinear multivariate functions. A special advantage of MARS lies in its ability to estimate contributions of some basis functions so that both additive and interactive effects of the predictors are allowed to determine the response variable. The MARS method consists of two parts: forward an...
Fuzzy versus statistical linear regression
Kim, KJ; Moskowitz, H; Köksalan, Mustafa Murat (1996-07-19)
Statistical linear regression and fuzzy linear regression have been developed from different perspectives, and thus there exist several conceptual and methodological differences between the two approaches. The characteristics of both methods, in terms of basic assumptions, parameter estimation, and application are described and contrasted. Their descriptive and predictive capabilities are also compared via a simulation experiment to identify the conditions under which one outperforms the other. It turns out...
Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method
Yerlikaya-Ozkurt, F.; Vardar Acar, Ceren; Yolcu-Okur, Y.; Weber, G. -W. (2014-03-15)
In this study, we develop an alternative method for estimating the Hurst parameter using the conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solutions of stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm). Our approach is superior to others in that it not only estimates the Hurst parameter but also finds spline parameters of the stochastic process in an adaptive way. We examine the performance of our estimations using simulated tes...
Batmaz, İnci; Kartal-Koc, Elcin; Köksal, Gülser (2010-02-04)
Multivariate Adaptive Regression Splines (MARS) is a very popular nonparametric regression method particularly useful for modeling nonlinear relationships that may exist among the variables. Recently, we developed CMARS method as an alternative to backward stepwise part of the MARS algorithm. Comparative studies have indicated that CMARS performs better than MARS for modeling nonlinear relationships. In those studies, however, only main and two-factor interaction effects were sufficient to model the nonline...
Parameter estimation in generalized partial linear models with conic quadratic programming
Çelik, Gül; Weber, Gerhard Wilhelm; Department of Scientific Computing (2010)
In statistics, regression analysis is a technique, used to understand and model the relationship between a dependent variable and one or more independent variables. Multiple Adaptive Regression Spline (MARS) is a form of regression analysis. It is a non-parametric regression technique and can be seen as an extension of linear models that automatically models non-linearities and interactions. MARS is very important in both classification and regression, with an increasing number of applications in many areas...
Citation Formats
F. Gökalp Yavuz, Analyses of Two Different Regression Models and Bootstrapping. 2011, p. 242.