Estimating Optimal Weights for Compound Scores: A Multidimensional IRT Approach
| Autor: | Cees A. W. Glas, Liseth Siemons, Hendrika G. van Lier, Mart A.F.J. van der Laar |
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| Přispěvatelé: | Psychology, Health & Technology |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Bayesian probability Experimental and Cognitive Psychology Latent variable 01 natural sciences 010104 statistics & probability symbols.namesake 0504 sociology Arts and Humanities (miscellaneous) Item response theory Humans 0101 mathematics Latent variable model Mathematics Bayes estimator Likelihood Functions 05 social sciences 050401 social sciences methods item response theory multidimensional item response theory Markov chain Monte Carlo Bayes Theorem General Medicine Variance (accounting) Bayesian estimation Markov Chains Statistics::Computation marginal maximum likelihood symbols Algorithm full-information factor analysis Monte Carlo Method Gibbs sampling |
| Zdroj: | Multivariate behavioral research, 53(6), 914-924. Psychology Press Ltd |
| ISSN: | 1532-7906 0027-3171 |
| Popis: | A method is proposed for constructing indices as linear functions of variables such that the reliability of the compound score is maximized. Reliability is defined in the framework of latent variable modeling [i.e., item response theory (IRT)] and optimal weights of the components of the index are found by maximizing the posterior variance relative to the total latent variable variance. Three methods for estimating the weights are proposed. The first is a likelihood-based approach, that is, marginal maximum likelihood (MML). The other two are Bayesian approaches based on Markov chain Monte Carlo (MCMC) computational methods. One is based on an augmented Gibbs sampler specifically targeted at IRT, and the other is based on a general purpose Gibbs sampler such as implemented in OpenBugs and Jags. Simulation studies are presented to demonstrate the procedure and to compare the three methods. Results are very similar, so practitioners may be suggested the use of the easily accessible latter method. A real-data set pertaining to the 28-joint Disease Activity Score is used to show how the methods can be applied in a complex measurement situation with multiple time points and mixed data formats. |
| Databáze: | OpenAIRE |
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