predicted.validity function

Find the predicted validities of a set of scales based on item statistics

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)

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

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.

Returns

• 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

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://osf.io/preprints/psyarxiv/2y3w9 Preprint available from PsyArxiv

Author(s)

William Revelle

See Also

reliability, scoreItems, scoreFast

Examples

pred.bfi <- predicted.validity(bfi[,1:25], bfi[,26:28], bfi.keys)
pred.bfi