WebBUGS
Conducting Bayesian Analysis Online Using BUGS
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Built-in models_3PL
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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 {{%% \[ y_{ij} \sim B(p_{ij}) \] \[ p_{ij} = c_j + \frac{1-c_j}{1+\exp[-\alpha_j(\theta_i - \beta_j)]} \] \[ \theta_i \sim N(0,1) \] %%}} where \(\theta_i\) is the latent trait for person \(i\), \(\beta_j\) is the item difficulty parameter, \(\alpha_j\) is the item discrimination parameter and \(c_j\) is a guessing parameter for item \(j\). !BUGS code {{ model{ for (i in 1:N){ for (j in 1:T){ p[i,j]<-c[j]+(1-c[j])/(1+exp(-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) c[j]~dnorm(0,.001) } } }}
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. Last changed: 2014/07/30 19:57
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WebBUGS