Data simulation with Markov Chain Monte Carlo, Gibbs sampling, and Bayes (beta-binomial) methods as the parameter estimations of spatial bivariate probit regression model.

Autor: Saputro, Dewi Retno Sari, Wardani, Yuanita Kusuma, Pratiwi, Nafisa Berliana Indah, Widyaningsih, Purnami, Indriati, Diari, Kusmayadi, Tri Atmojo, Sutrima, Sutrima, Utomo, Putranto Hadi
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Zdroj: AIP Conference Proceedings; 2020, Vol. 2326 Issue 1, p1-8, 8p
Abstrakt: A probit regression model is a regression with categorical dependent variable in dichotomy or binary form. The dependent variable value of the probit regression states the probability of certain issue. In some cases, the application of this model considers the influence of area (spatial effect). The dependency tendency to the close regions is known as autocorrelation in spatial data. Due to this matter, the parameter estimations of ordinary least square (OLS) method can not be used thus it is substituted by the simulation technique, which is a method in randomly raising data. The method includes direct and indirect simulations. The latter has Markov Chain Monte Carlo (MCMC) method with Gibbs Sampling algorithm, which is the order in conducting certain distributed random data sampling by understanding the required distribution. In this case, the beta binomial distribution is applied. A data simulation with Gibbs Sampling algorithm can be conducted by knowing the required distributions of each variable used for R software beforehand. This research purposes to define the parameter estimation value of spatial probit regression by applying MCMC and Gibbs sampling methods with R software. The results show that the parameter estimations of spatial bivariate probit regression model by simulating through Gibbs sampling algorithm (R software), in which β̂ is the independent variable parameter and ρ̂ is the spatial lag autoregressive coefficient. The simulation with the first-value determination rise result data β = (0, 1, -1), ρ = 0.7 deciding n = 400, 10, and k = 6 show the estimations for β̂ = (0.01205, 0.98709, -0.9675) and β̂ = 0.68523. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index