# Person Separation Reliability

### Description

This function calculates the proportion of person variance that is not due to error.
The concept of person separation reliability is very similar to reliability indices such as Cronbach's *α*.

### Usage

1 2 3 4 5 6 7 |

### Arguments

`pobject` |
Object of class |

`x` |
Object of class |

`object` |
Object of class |

`...` |
Further arguments. |

### Details

Returns the person separation reliability *(SSD-MSE)/SSD* where SSD is the squared standard deviation and MSE the mean squared error.

#### Caveats

Please note that the concept of *reliability* and associated problems are fundamentally different between IRT and CTT (Classical Test Theory).
Separation reliability is more like a workaround to make the “change” from CTT to IRT easier for users by providing something “familiar.”
Hence, we recommend not to put too much emphasis on this particular measure and use it with caution.

#### Varying results in different programs

If you compare the separation reliability obtained using eRm with values by other software, you will find that they are most likely not equal. This has a couple of reasons, one of the most important is the employed estimation method.

eRm uses a conditional maximum likelihood (CML) framework and handles missing values as separate groups during the estimation of item parameters. Person parameters are computed in a second step using unconditional or joint maximum likelihood (UML or JML) estimation with item parameters assumed to be known from the first step. Other programs might do JML to estimate item and person parameters at the same time, or employ marginal maximum likelihood MML to estimate item parameters, assuming a certain distribution for person parameters. In the latter case person parameters might be obtained by various methods like EAP, MAP, .... Even CML-based programs yield different values, for example, if they use Warm's weighted maximum likelihood estimation WLE to compute person parameters in the second step.

The bottom line is that, since there is not “definite” solution for this problem, you will end up with different values under different circumstances. This is another reason to take results and implications with a grain of salt.

### Value

`SepRel`

returns a list object of class `eRm_SepRel`

containing:

`sep.rel` |
the person separation reliability, |

`SSD.PS` |
the squared standard deviation (i.e., total person variability), |

`MSE` |
the mean square measurement error (i.e., model error variance). |

### Author(s)

Original code by Adrian Brügger (Adrian.Bruegger@imu.unibe.ch), adapted by Marco J. Maier

### References

Wright, B.D., and Stone, M.H. (1999). *Measurement essentials.* Wide Range Inc., Wilmington. (http://www.rasch.org/measess/me-all.pdf 28Mb).

### Examples

1 2 3 4 5 | ```
# Compute Separation Reliability for a Rasch Model:
pers <- person.parameter(RM(raschdat1))
res <- SepRel(pers)
res
summary(res)
``` |