data_sim_Rasch {DIFtree} | R Documentation |

## Simulated Data Set with Dichotomous Items

### Description

The data set is simulated from a Rasch model
where some items exhibit differential item functioning.
Existing differences in item difficulties are simulated by step-functions.
The true, simulated DIF structure is described in Tutz and Berger (2015), Section 4.2.

### Usage

```
data(data_sim_Rasch)
```

### Format

A data frame containing 500 observations on 5 variables:

**Y** matrix with binary 0/1 response for 20 items

**x1** binary covariate 1

**x2** metric covariate 1

**x3** binary covariate 2

**x4** metric covariate 2

### References

Berger, Moritz and Tutz, Gerhard (2016): Detection of Uniform and Non-Uniform Differential Item Functioning
by Item Focussed TreesJournal of Educational and Behavioral Statistics 41(6), 559-592.

Tutz, Gerhard and Berger, Moritz (2016): Item focussed Trees for the Identification of Items
in Differential Item Functioning, Psychometrika 81(3), 727-750.

### Examples

```
data(data_sim_Rasch)
Y <- data_sim_Rasch[,1]
X <- data_sim_Rasch[,-1]
hist(rowSums(Y), breaks = 0:19 + 0.5)
summary(X)
```

[Package

*DIFtree* version 3.1.6

Index]