|
Parameter estimation in latent variable models for binary and ordinal data pose multiple challenges. Firstly, a model needs to be specified that accounts for multiple sources of measurement error. Secondly, direct evaluation of the maximum likelihood estimators is often computationally burdensome. For example, a stochastic EM algorithm can be used, but calculations incur a long run time.
We present the development of a composite likelihood approach based on paired observations. Direct maximization of the composite likelihood only requires evaluation of bivariate normal CDFs, and is expected to use less computational resources. Then, in a simulation study, we implement the new method and compare it to two existing methods for models of this type. All methods assume that both the latent traits and measurement error components are mutually independent and normally distributed. The simulation study compares methods both in terms of efficiency (RMSE) and calculation time.
Finally, application of the three methods is also illustrated using real data from a set of personality assessments with test and retest information.
|
