ANALISIS BAYESIAN UNTUK REGRESI BINARI KUANTIL TERPENALTI DENGAN MENGGUNAKAN ALGORITMA GIBBS SAMPLING; BAYESIAN ANALYSIS FOR PENALIZED BINARY QUANTILE REGRESSION USING GIBBS SAMPLING ALGORITHM

Rahayu, Devi Noviyanti, Gunardi

2015 | Skripsi | FMIPA UGM

Penalized binary quantile regression is an extension of quantile regression where the dependent variable scale is binary/dichotomous. This regression is used to analyze the data containing outliers and heterocedastisity. Binary quantile regression with LASSO (Least Absolute Shrinkage and Selection Operator) penalty will produce estimation of parameters that more resistant (robust) with data containing outliers, can shrink the error, and can identify which variables are important for the different quantile of the response variables. Binary quantile regression with LASSO penalty can be estimated using Bayesian methods. Bayesian method is a method of analysis that is based on information derived from the sample and prior information. This combined information is called the posterior. To find the posterior distribution is often produce calculations that can not be solved analytically so used Gibbs sampling approach. Estimation of the parameters of the model is the mean of the posterior distribution obtained from the Gibbs sampling. In this thesis discussed penalized binary quantile regression using Asymmetric Laplace Distribution of Bayesian viewpoint. The case study in this thesis, Penalized Bayesian binary quantile regression was applied to analyze the factors that affect water quality in Bantul. Penalized Bayesian binary quantile regression estimation results will be compared with the logistic regression and probit regression. With a model based on the accuracy of the methods are used, it is concluded that the Penalized Bayesian binary quantile regression estimation better than logistic and probit regression estimation, because it produces more precise models.

Kata Kunci : binary quantile regression, Lasso Penalty; Bayesian; Gibbs sampling; Asymmetric Laplace Distribution