تأثير تغيير توزيع داده‌ها در آميزه‌اي متناهي از مدل‌هاي خطي تعميم ‌يافته نيم پارامتري

The Negative Binomial Distribution Efficiency in Finite Mixture of Semi-parametric Generalized Linear Models

انتخاب مدل آماري مناسب براي متغير پاسخ يكي از مهم‌ترين مسايل در آميزه­اي متناهي از مدل ­هاي خطي تعميم يافته است. يكي از توزيع­ هايي كه در آميزه­اي متناهي از مدل­ هاي خطي تعميم يافته نيم پارامتري با مشكل رو به ‌رو است، توزيع پواسون است. در اين مقاله، براي غلبه بر بار محاسباتي و بيش پراكندگي، آميزه­اي متناهي از مدل­ هاي خطي تعميم­يافته نيم پارامتري با استفاده از توزيع دوجمله ­اي منفي (GFMMNB) به‌جاي آميزه ­اي متناهي از مدل­ هاي خطي تعميم يافته نيم پارامتري با استفاده از توزيع پواسون (GFMMP) پيشنهاد مي­ شود. كارايي مدل ­هاي آميزه­اي متناهي از مدل‌هاي خطي تعميم يافته نيم پارامتري با استفاده از توزيع دوجمله ­اي منفي نسبت مدل­ هاي آميزه­اي متناهي از مدل­ هاي خطي تعميم يافته نيم پارامتري با استفاده از توزيع پواسون براي داده ­هاي شبيه ­سازي شده و داده­ هاي واقعي و با استفاده از ميانگين وزني توان دوم انحرافات (WGMSE) نشان داده شده است.

Introduction : Selection the appropriate statistical model for the response variable is one of the most important problem in the finite mixture of generalized linear models. One of the distributions which it has a problem in a finite mixture of semi-parametric generalized statistical models, is the Poisson distribution. In this paper, to overcome over dispersion and computational burden, finite mixture of semi-parametric generalized linear models using the negative binomial (GFMMNB) distributions instead of finite mixture of semi-parametric generalized linear models using the Poisson distributions (GFMMP) has been proposed. Efficiency of GFMMNB to GFMMP using weighted generalized mean of square error (WGMSE) for both the simulation data and real data are shown. Material and methods In this scheme, first we have introduced finite mixture of semi-parametric generalized linear models using the Poisson distributions (GFMMP). Then, we have introduced finite mixture of semi-parametric generalized linear models using the negative binomial (GFMMNB) instead of GFMMP. For estimating the parameters in the proposed model, the EM algorithm in two steps computed. We have used the efficiency method using weighted generalized mean of square error (WGMSE) for comparing between GFMMNB and GFMMP model in both the simulation and real data. Results and discussion Results of real example and simulation study between GFMMNB and GFMMP model are shown that the proposed method is very competitive in terms of estimation accuracy and speed of computational estimation methods. The reported results demonstrate that there is a good agreement between simulation study and real data in the GFMMNB model. Also, the numerical results reported in the tables indicate that the accuracy improve by increasing the n for GFMMNB model. Therefore, to get more accurate results, the larger n is recommended. Conclusion The following conclusions were drawn from this research.