PPP {edina} | R Documentation |

## 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 |

`...` |
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

simulate observed responses

`\mathbf Y^{(r)}`

using model parameters from iteration`r`

of the MCMC samplercomputing 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.; andcomputing PPPs for each item pair as the proportion of generated

`OR^{(r)}`

's that exceeded elements of the observed odds ratios.

*edina*version 0.1.1 Index]