Authors:
Ameena Karem Essa, Haifa Taha Abd,DOI NO:
https://doi.org/10.26782/jmcms.2020.07.00024Keywords:
Linear mixed model Non-parametric ,Kernel Smoothing,Bandwidth,Abstract
This study aims to test a new treatment that has been developed for type 2 diabetes, by estimating the response of diabetics by experimenting number of mixed linear models, non-parametric, where they were compared by relying on the coefficient of determination and the standard error for the random errors in order to determine the appropriate model and then measure the effectiveness This new treatment is for type 2 diabetes. Therefore, some non-parametric methods were used in estimating the average response for the mixed linear model. The method of the kernel smoothing function was used by employing the Gaussian and Epanchnikov family functions, as well as some formulas of the Cross Validation method. To estimate Bandwidth as Scott and Silverman. An experiment for a new treatment for type 2 diabetes was chosen as an application of the mixed linear model, by experimenting with this drug on a sample of patients who were divided into three different age groups and performing laboratory tests for a period of three months, and then estimating their response rates to the new drug through four models Different. The results demonstrated that the A mixed non-parametric linear model with (Gaussian) function and the (Scott) package was the best fit model for this study, as it gave the largest determination coefficient and the lowest standard deviation of the error, as well as the new drug, was not effective in regulating blood sugar level for all age groups of patients.Refference:
I. Carroll, R.J., Delaigle, A. and Hall, P. (2007). “Nonparametric Regression Estimation from Data Contaminated by a Mixture of Berkson and Classical Errors”. Journal of the Royal Statistical Society, 69, 859-878.
II. Czado, C, (2007). “Linear Models with Random Effects”. Lecture notes, web paper.
III Hardle, W., (1994), “Applied Nonparametric Regression”. Humboldt – University, Berlin, Germany.
IV Heather, T., (2008). “Introduction to Generalized Linear Models”. ESRC National Centre for Research Methods, University of Warwick, UK.
V Jiang, J. (2007).” Linear and Generalized Linear Mixed Models and Their Applications”. Springer, New York.
VI McCullagh, P., and Nelder, J. A‖ Generalized Linear Models‖, (1989). 2nd ed. London: Chapman& Hall.
VII Nelder, J., Wedderburn.W., (1972).” Generalized Linear Models‖, Journal of the Royal Statistical Society. Series A (General), 135(3), 370-384.
VIII Racine J, Li, Q., (2004). “Nonparametric Estimation of Regression Functions with both Categorical and Continuous Data.” Journal of Econometrics, 119(1), 99–130.
IX Racine JS, Li Q, Zhu X (2004). “Kernel Estimation of Multivariate Conditional Distributions.”. Annals of Economics and Finance, 5(2), 211–235.
X – Wand M, Ripley, B., (2008).” Kern Smooth Functions for Kernel Smoothing R package”, version 2.22-22, URL http://CRAN.R-project.org/package=KernSmooth.
XI – Watson, G., (1964). “Smooth Regression Analysis.” Sankhya, 26(15), 359–372.
XII- Yin, Z., Liu, F.& Xie, Y., (2016). “Nonparametric Regression Estimation with Mixed Measurement Errors “. Applied Mathematics, (7), 2269-2284.