Bayesian Network Inference in Binary Logistic Regression: A Case Study of Salmonella sp Bacterial Contamination on Vannamei Shrimp

Pratnya Paramitha Oktaviana,Kartika Fithriasari

doi:10.3844/jmssp.2017.306.311

Abstract

Recently binary logistic regression has been used to identify four factors or predictor variables that supposedly influence the response variable, which is testing result of Salmonella sp bacterial contamination on vannamei shrimp. Binary logistic regression analysis results that there are two predictor variables which is significantly affect the testing result of Salmonella sp bacterial contamination on vannamei shrimp, those are the testing result of Salmonella sp bacterial contamination on farmers hand swab and the subdistrict of vannamei shrimp ponds. Those significant predictor variables selected have been modelled in binary logit model. This paper proposes to study the statistical associations between the two significant predictor variables and the contamination of Salmonella sp bacterial on vannamei shrimp and to build a numerical simulation of two significant predictor variables parameters using bayesian network inference. Directed Acyclic Graph (DAG) is applied for modelling binary logit model of significant factors in bayesian network inference.

Highlights

According to Hosmer and Lemeshow (2000), if there are p predictor variables, indicated by the vector x = (x1,x2,...,xp) and each of these variables is assumed at least interval scale, so the conditional probability could be indicated by P(Y = 1| x) = π (x)
The highest probability of the presence of Salmonella sp in testing result on vannamei shrimp (0.350) is obtained if the vannamei shrimp is farmed in Subdistrict A and the testing result of Salmonella sp contamination on farmer hand swab show that there is Salmonella sp; while the smallest probability of the presence of Salmonella sp in testing result on vannamei shrimp (0.021) is obtained if the vannamei shrimp is farmed in Subdistrict C and the testing result of Salmonella sp contamination on farmer hand swab show that there is no Salmonella sp
The highest probability of the absence of Salmonella sp in testing result on vannamei shrimp (0.979) is obtained if the vannamei shrimp is farmed in Subdistrict C and the testing result of Salmonella sp contamination on farmer hand swab show that there is no Salmonella sp; while the smallest probability of the absence of Salmonella sp in testing result on vannamei shrimp (0.650) is obtained if the vannamei shrimp is farmed in Subdistrict A and the testing result of Salmonella sp contamination on farmer hand swab show that there is Salmonella sp

Summary

Introduction

The logistic regression model is: π ( If those p predictor variables are discrete or have nominal scale, the method of choice is to use dummy variables. Binary logistic regression has been used by the researchers to identify four factors or predictor variables (X1, X2, X3, X4) that supposedly influence the response variable (Y), which is the testing result of Salmonella sp bacterial contamination on vannamei shrimp. This method obtain that there are two significant predictor variables, i.e., X1 and X2. Chen et al (2015) explains that bayesian network is a set of variables, X and Y, that present joint probability distribution, for i = 1,2,...,n: P( X ,Y ) = ∏ p( xi | pr ( xi )). There are three nodes in DAG as shown as in the Fig. 1: 1. Constant Node: It is used as the icon of random variable, for example: xi ∼ N(μ,σ2)

Logical Node

Conclusion