PPP {edina}

Posterior Predictive Probabilities (PPPs)

Description

Computes posterior predictive probabilities (PPPs) based on the odds ratios for each pair of items.

Usage

PPP(object, ...)

## S3 method for class 'edina'
PPP(object, alpha = 0.05, ...)

Arguments

object

An edina object

...

Not used.

alpha

Defining region to indicate the level of extremeness the data must before the model is problematic.

Details

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.

Value

The PPP value given the specified alpha value.

PPP Computation Procedure

1. simulate observed responses \mathbf Y^{(r)} using model parameters from iteration r of the MCMC sampler

2. 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

3. computing PPPs for each item pair as the proportion of generated OR^{(r)}'s that exceeded elements of the observed odds ratios.