Genelleştirilmiş Doğrusal Modeller Kullanılarak Satış Geçmişine Dayalı Talep Tahminlemesi

Ticari işletmeler için mevcut satış verilerini kullanarak talebi net olarak tahmin etmek önemlidir. Şirketlerin karlılığı artırmak için karar destek sistemlerinin bir parçası olarak tahmin analitiği yapabiliyor olması gerekir.

Anahtar Kelimeler:

Satış talep tahminlemesi, Gama dağılımı, Genelleştirilmiş doğrusal modeller, Kategorizasyon

Sales History-based Demand Prediction using Generalized Linear Models

It's vital for commercial enterprises to accurately predict demand by utilizing the existing sales data. Such predictive analytics is a crucial part of their decision support systems to increase the profitability of the company.In predictive data analytics, the branch of regression modeling is used to predict a numerical response variable like sale amount. In this category, linear models are simple and easy to interpret yet they permit generalization to very powerful and flexible families of models which are called Generalized linear models (GLM). The generalization potential over simple linear regression can be explained twofold: First, GLM relax the assumption of normally distributed error terms. Moreover, the relationship of the set of predictor variables and the response variable could be represented by a set of link functions rather than the sole choice of the identity function.This work models the sales amount prediction problem through the use of GLM. Unique company sales data are explored and the response variable, sale amount is fitted to the Gamma distribution. Then, inverse link function, which is the canonical one in the case of gamma-distributed response variable is used. The experimental results are compared with the other regression models and the classification algorithms. The model selection is performed via the use of MSE and AIC metrics respectively. The results show that GLM is better than the linear regression. As for the classification algorithms, Random Forest and GLM are the top performers. Moreover, categorization on the predictor variables improves model fitting results significantly.

Keywords:

Sales demand prediction, Gamma distribution, Generalized linear models, Categorization,

PDF

___

[1] Nelder, J.A., Wedderburn, R.W.M. 1972. Generalized linear models. Journal of the Royal Statistical Society, Series A, General, 135, 370-384.
[2] Razzaghi, M. 2013. The Probit Link Function in Generalized Linear Models for Data Mining Applications. Journal of Modern Applied Statistical Methods, 12(19), 164-169.
[3] Tauras, J.A. 2005. An Empirical Analysis of Adult Cigarette Demand. Eastern Economic Journal, 31(3), 361-375.
[4] The Odum Institute, 2015. Logistic Regression and the American National Election Study 2012: Vote Choice in the 2012 US Presidential Election. The Odum Institute.
[5] Kutner, M.H., Nachtsheim, C., Neter, J. 2004. Applied linear regression models. McGraw-Hill/Irwin.
[6] Johnson, P. 2006. GLM with Gamma-Distributed Dependent Variables (Access Date: 28.05.2018.
[7] Friedman, J., Hastie, T., Tibshirani, R. 2010. Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, Articles, 33(1), 1-22.
[8] Schapire, R.E., Freund, Y. 2012. Boosting: Foundations and Algorithms. MIT Press.
[9] Pearson, K. 1900. X. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine, 50(302), 157-175.
[10] Jolliffe, I.T. 1982. A Note on the Use of Principal Components in Regression. Journal of the Royal StatisticalSociety. Series C (Applied Statistics), 31(3), 300-303.
[11] Cortes, C., Vapnik, V. 1995. Support-Vector Networks. Mach. Learn., 20(3), 273-297.
[12] Breiman, L. 2001. Random Forests. Mach. Learn., 45(1), 5-32.
[13] Hothorn, T., Hornik, K., Zeileis, A. 2006. Unbiased Recursive Partitioning: A Conditional Inference Framework. Journal of Computational and Graphical Statistics, 15(3), 651-674.
[14] Zhou, Z. 2012. Ensemble Methods: Foundations and Algorithms. 1st. MIT Press. Chapman & Hall/CRC.
[15] Cohen, P.R. 1995. Empirical Methods for Artificial Intelligence. MIT Press, Cambridge, MA, USA.
[16] Bensoussan, A., Bertrand, P., Brouste, A. 2014. A generalized linear model approach to seasonal aspects of wind speed modeling. Journal of Applied Statistics, 41(8), 1694-1707.