10.3 The Monte Carlo Approach

The Monte Carlo approach simulates attribute profiles, which are viewed as the true. Based on the simulated profiles, item responses were generated and then calibrated. Estimated attribute profiles are obtained and compared with the true. In particular,

1. Fit a CDM to the data and obtain item parameter estimates \(\mathbf{\delta}\) and proportions of latent classes (i.e.,\(p(\mathbf{\alpha}_c)\) for latent class \(c\))

2. Draw a large number of students with attribute profiles from a categorical distribution with proportion parameter \(p(\mathbf{\alpha}_c)\) for latent class \(c\)

3. Simulate data based on the estimated item parameters and generated attribute profiles

4. With fixed item parameters, the attribute profiles are estimated from the simulated data

5. The generated and estimated attribute vectors are compared to determined how well each individual attribute or attribute profile can be recovered