tif {birtr} | R Documentation |

## Test Information Function

### Description

Plots a test information function from a set of item parameters under the one-, two-, or three-parameter logistic model.

### Usage

```
tif(b, a, c)
```

### Arguments

`b` |
a numeric vector representing the values of item difficulty. |

`a` |
a numeric vector representing the values of item discrimination. |

`c` |
a numeric vector representing the values of lower asymptote. |

### Details

While the theoretical range of ability is from negative infinity to positive
infinity, practical considerations usually limit the range of values
from -3 to +3.
The length of `b`

should be the same as that of `a`

and `c`

.
Each parameter `c`

has a theoretical range from 0 to 1, but in practice
values above .35 are not considered acceptable, hence use the range from 0
to .35 for each `c`

.
Under the one-parameter logistic model, `a = rep(1, length(b))`

and
`c = rep(0, length(b))`

.
Under the two-parameter logistic model, `c = rep(0, length(b))`

.
In case `b`

to be a single number, then the plot contains the item
informaiton function.
Note that the maximum of the information value on the vertical axis of
the graph is arbitrarily set to 10.

### References

Baker, F. B., & Kim, S.-H. (2017).
*The basics of item response theory using R.*
New York, NY: Springer.
ISBN-13: 978-3-319-54204-1

### Examples

```
b <- c(-1.0, -0.5, 0.0, 0.5, 1.0)
a <- c(2.0, 1.5, 1.5, 1.5, 2.0)
c <- c(.2, .2, .2, .2, .2)
tif(b, a, c)
tif(a = a, b = b, c = c)
tif(b) # tif(b, a = rep(1, length(b)), c = rep(0, length(b)))
tif(b, a) # tif(b, a, c = rep(0, length(b)))
```

*birtr*version 1.0.0 Index]