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Conducting Bayesian Analysis Online Using BUGS
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Built-in models:2PL
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!Model Let \(y_{ij}, i=1,\ldots,N, j=1,\ldots,T\) denote the response for person \(i\) on item \(j\) that takes value 0 or 1. The 2PL model can be written as {{%% \[ y_{ij} \sim B(p_{ij}) \] \[ \log\frac{p_{ij} }{1-p_{ij} } = \alpha_j(\theta_i - \beta_j) \] \[ \theta_i \sim N(0,1) \] %%}} where \(\theta_i\) is the latent trait for person \(i\), \(\beta_j\) is the item difficulty parameter and \(\alpha_j\) is the item discrimination parameter for item \(j\). !BUGS code {{ model{ for (i in 1:N){ for (j in 1:T){ #Change logit to probit for ogive model logit(p[i,j])<-alpha[j]*(theta[i]-beta[j]) y[i,j]~dbern(p[i,j]) } theta[i]~dnorm(0,1) } for (j in 1:T){ alpha[j]~dnorm(0,.0001) beta[j]~dnorm(0, .0001) } } }}
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. Last changed: 2014/11/12 02:49
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WebBUGS