Apply a 3PL model (including guessing parameters) to the Law School Admission Test (LSAT) data in the R program ltm. The 2PL model may be fitted with the code

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~ (F[i] ~ dnorm (0,1) dbern (pi [i,m]) model for (i in 1:1000) for (m in 1:5) (y[i,m] logit (pi [i,m]) < lam [m] *F [i] for (m in 1:5) (lam [m] delta [m]}} dexp (1); delta [m] dnorm (0,0.001)}} Suitability of the two models in reproducing the data may be assessed by compar- ing the 10 actual and predicted 22 frequency tables between the five items, with predicted tables based on aggregating subject level replicates yrep [i,m] dbern (pi [i,m]). A posterior predictive check may be based on comparing chi-square statistics using replicate and actual frequency tables.