Computes posterior predictive probabilities (PPPs) based on the odds ratios for each pair of items.
PPP(object, ...) # S3 method for edina PPP(object, alpha = 0.05, ...)
| object | An |
|---|---|
| ... | Not used. |
| alpha | Defining region to indicate the level of extremeness the data must before the model is problematic. |
The PPP value given the specified alpha value.
PPPs that smaller than 0.05 or greater than 0.95 tend to be extreme and evidence of misfit. As a result, this is more of a heuristic metric.
simulate observed responses \(\mathbf Y^{(r)}\) using model parameters from iteration \(r\) of the MCMC sampler
computing the odds ratio for each pair of items at iteration \(r\) as $$OR^{(r)} = n_{11}^{(r)}n_{00}^{(r)}/\left(n_{10}^{(r)}n_{01}^{(r)}\right)$$, where \(n_{11}^{(r)}\) is the frequency of ones on both variables at iteration \(r\), \(n_{10}^{(r)}\) is the frequency of ones on the first item and zeros on the second at iteration \(r\), etc.; and
computing PPPs for each item pair as the proportion of generated \(OR^{(r)}\)'s that exceeded elements of the observed odds ratios.