psych (version 2.1.9)

# predicted.validity: Find the predicted validities of a set of scales based on item statistics

## Description

The validity of a scale varies as a function of the number of items in the scale, their average intercorrelation, and their average validity. The asymptotic limit of a scales validity for any particular criterion is just the average validity divided by the square root of the average within scale item correlation. `predicted.validity` will find the predicted validity for a set of scales (defined by a keys.list) and the average item validity for various criteria.

The function will find (and report) scale reliabilities (using `reliability`) and average item validities (using `item.validity`)

## Usage

```predicted.validity(x, criteria, keys, scale.rel = NULL, item.val = NULL)
item.validity(x,criteria,keys)```

## Arguments

x

A data set

criteria

Variables to predict from the scales

keys

A keys.list that defines the scales

scale.rel

If not specified, these will be found. Otherwise, this is the output from `reliability`.

item.val

If not specified, the average item validities for each scale will be found. Otherwise use the output from `item.validity`

## Value

predicted

The predicted validities given the scales specified

item.validities

The average item validities for each scale with each criterion

scale.reliabilities

The various statistics reported by the `reliability` function

asymptotic

A matrix of the asymptotic validities

## Details

When predicting criteria from a set of items formed into scales, the validity of the scale (that is, the correlations of the scale with each criteria) is a function of the average item validity (r_y), the average intercorrelation of the items in the scale (r_x), and the number of items in the scale (n). The limit of validity is r_y/sqrt(r_x).

Criteria will differ in their predictability from a set of scales. These asymptotic values may be used to help the decision on which scales to develop further.

## References

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

Revelle, W. and Condon, D.M. (2019) Reliability from alpha to omega: A tutorial. Psychological Assessment, 31, 12, 1395-1411. https://doi.org/10.1037/pas0000754. https://psyarxiv.com/2y3w9/ Preprint available from PsyArxiv

`reliability`, `scoreItems`, `scoreFast`

## Examples

Run this code
``````# NOT RUN {
pred.bfi <- predicted.validity(psychTools::bfi[,1:25], psychTools::bfi[,26:28],
psychTools::bfi.keys)
pred.bfi
# }
``````

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