The Psychometric Latent Agreement Model (PLAM) for Discrete Latent Variables Measured by Multiple Items

Abstract

The Psychometric Latent Agreement Model (PLAM) is proposed for estimating the subpopulation membership of individuals (e.g., satisfactory performers vs. unsatisfactory performers) at discrete levels of multiple latent trait variables. A binary latent Type variable is introduced to take account of the possibility that, for a given set of observed variables, the latent group memberships of some individuals are indeterminate. The latent Type variable allows for separating individuals who can reliably be assigned to satisfactory versus unsatisfactory performers classes from those individuals whose ratings do not contain the necessary information to make the class assignment possible for a particular set of rating items. Agreements among discrete latent trait variables are also estimated. The PLAM was illustrated with two examples using real data on behavioral rating measures. One example involved ratings of two behavioral constructs by a single rater type, whereas the other involved ratings of one construct by three rater types. Implications were presented for using behavioral ratings to determine the subpopulation membership, such as qualified versus unqualified groupings in hiring decisions and pass versus fail groupings in performance evaluations.