Selection and Predictive Validity with Latent Variable Structure
Bengt Muthén, Jin‐Wen Yang Hsu · eScholarship (California Digital Library) · 2011
British Jaurnai of Mathematical and Statistical Psychology (1993) 46, 255-271 l' i993 The British Psychological Society Printed in Great Britain Selection and predictive validity with latent variable structuresf Bengt O . MuthenJ a n d Jin-Wen Yang H s u § Graduate School of Education, University of California, Los Angeles, Los Angeles, CA 90024-1521, USA Estimators of the predictive validity of a multifactorial test are considered. These estimators take into account the selectivity of the sample of those who have observations on the criterion measure. It is pointed out that the selectivity problem can be viewed as a missing data situation. The relationships between the classic Pearson Lawley adjustment, regression based on factor scores, and maximum-likelihood estimation under ignorable missingness are described. The estimators are compared in a study of artificial population data. 1. Introduction T h i s paper considers the selection of i n d i v i d u a l s using a m u l t i f a c t o r i a l test a n d the assessment of criterion-related validity of the selection instrument. S u c h selection routinely takes place i n p l a c i n g m i l i t a r y personnel i n v a r i o u s specialties w i t h j o b performance as criterion a n d i n a d m i t t i n g students to v a r i o u s schools w i t h first-year grade point average as criterion. M o s t often a c o m p o s i t e measure related to the total test score or subtests are used i n such selection. W e w i l l argue, however, that the use of a m u l t i p l e factor latent variable m o d e l for the observed variables c o m p r i s i n g the test can m a k e more efficient use of the test i n f o r m a t i o n . T h i s is i n line w i t h arguments for latent variable m o d e l l i n g of b r o a d a n d n a r r o w abilities recently presented by Gustafsson (1988a). E x p l i c i t use of the latent v a r i a b l e m o d e l for selection may also be beneficial. E v e n w h e n the latent v a r i a b l e m o d e l is not used for selection, it can provide more detailed i n f o r m a t i o n i n the v a l i d a t i o n stage. C o r r e c t l y assessing the predictive v a l i d i t y i n t r a d i t i o n a l selection studies, w i t h o u t latent variables, is a difficult task i n v o l v i n g adjustments to c i r c u m v e n t the selective nature of the sample to be used for the v a l i d a t i o n . Adjustment for range restriction is c o m m o n l y carried out by P e a r s o n - L a w l e y corrections. A s we w i l l see, the use o f a latent variable m o d e l produces further c o m p l i c a t i o n s related to selection. T h i s paper w i l l focus o n the technical issues i n v o l v e d i n criterion-related v a l i d i t y assessment fThe research described in the paper was funded by the Graduate Management Admission Council, Los Angeles, USA. The G M A C encourages researchers to formulate and freely express their own opinions, and the opinions expressed here are not necessarily those of the G M A C . JRequests for reprints. §Now at the Foundations of Education, University of Florida.