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Conducting Bayesian Analysis Online Using BUGS
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Built-in models:Logistic regression
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!Model The logistic regression model with binary dependent variable \(y\) and independent variables \(\mathbf{x}=(x_{1},\ldots,x_{p})\) using a logit link, {{%% \[y_{i} \sim Bernoulli(p_{i})\] \[logit(p_{i})=\log\left(\frac{p_{i} }{1-p_{i} }\right) = \beta_{0}+\beta_{1}x_{1i}+\ldots+\beta_{p}x_{pi}\] %%}} In this model, the dependent variable can only take two values, 1 and 0. For example, in an experiment, 1 can represent success and 0 can represent failure. \(p_{i}\) is the probability that \(y_{i}=1\). Thus, \(p_{i}/(1-p_{i})\) is the odds that \(y_{i}=1\). Essentially, the predictors are predicting the log-odds. !Code {{ model{ for (i in 1:N){ y[i]~dbern(p[i]) logit(p[i])<-beta0+beta1*(x1[i]-mean(x1[]))+beta2*(x2[i]-mean(x2[])) } beta0~dnorm(0,1.0E-6) beta1~dnorm(0,1.0E-6) beta2~dnorm(0,1.0E-6) exp1<-exp(beta1) exp2<-exp(beta2) } }}
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. Last changed: 2014/11/12 02:44
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