irt.responses {psych} | R Documentation

## Plot probability of multiple choice responses as a function of a latent trait

### Description

When analyzing ability tests, it is important to consider how the distractor alternatives vary as a function of the latent trait. The simple graphical solution is to plot response endorsement frequencies against the values of the latent trait found from multiple items. A good item is one in which the probability of the distractors decrease and the keyed answer increases as the latent trait increases.

### Usage

    irt.responses(theta,items, breaks = 11,show.missing=FALSE, show.legend=TRUE,
    legend.location="topleft", colors=NULL,...)

### Arguments

`theta` | The estimated latent trait (found, for example by using `score.irt`).
`items` | A matrix or data frame of the multiple choice item responses.
`breaks` | The number of levels of the theta to use to form the probability estimates. May be increased if there are enough cases.
`show.legend` | Show the legend
`show.missing` | For some SAPA data sets, there are a very large number of missing responses. In general, we do not want to show their frequency.
`legend.location` | Choose among c("bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right", "center","none"). The default is "topleft".
`colors` | if NULL, then use the default colors, otherwise, specify the color choices. The basic color palette is c("black", "blue", "red", "darkgreen", "gold2", "gray50", "cornflowerblue", "mediumorchid2").
`...` | Other parameters for plots and points

### Details

This function is a convenient way to analyze the quality of item alternatives in a multiple choice ability test. The typical use is to first score the test (using, e.g., `score.multiple.choice` according to some scoring key and to then find the `score.irt` based scores. Response frequencies for each alternative are then plotted against total score. An ideal item is one in which just one alternative (the correct one) has a monotonically increasing response probability.

Because of the similar pattern of results for IRT based or simple sum based item scoring, the function can be run on scores calculated either by `score.irt` or by `score.multiple.choice`. In the latter case, the number of breaks should not exceed the number of possible score alternatives.

### Value

Graphic output

### Author(s)

William Revelle

### References

Revelle, W. An introduction to psychometric theory with applications in R (in prep) Springer. Draft chapters available at https://personality-project.org/r/book/

### See Also

`score.multiple.choice`, `score.irt`

### Examples

    data(iqitems)
    iq.keys <- c(4,4,4, 6,6,3,4,4,  5,2,2,4,  3,2,6,7)
    scores <- score.multiple.choice(iq.keys,iqitems,score=TRUE,short=FALSE)
    #note that for speed we can just do this on simple item counts rather
    # than IRT based scores.
    op <- par(mfrow=c(2,2))  #set this to see the output for multiple items
    irt.responses(scores$scores,iqitems[1:4],breaks=11)
    op <-  par(op)

[Package psych version 1.8.4 Index]