Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Date of Graduation

Spring 2015

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Graduate Psychology

Advisor(s)

Christine E. DeMars

Abstract

The purpose of this study was to review the challenges that exist in the estimation of complex (multidimensional) models applied to complex (multilevel) data and to examine the performance of the recently developed Metropolis-Hastings Robbins-Monro (MH-RM) algorithm (Cai, 2010a, 2010b), designed to overcome these challenges and implemented in both commercial and open-source software programs. Unlike other methods, which either rely on high-dimensional numerical integration or approximation of the entire multidimensional response surface, MH-RM makes use of Fisher’s Identity to employ stochastic imputation (i.e., data augmentation) via the Metropolis-Hastings sampler and then apply the stochastic approximation method of Robbins and Monro to approximate the observed data likelihood, which decreases estimation time tremendously. Thus, the algorithm shows great promise in the estimation of complex models applied to complex data.

To put this promise to the test, the accuracy and efficiency of MH-RM in recovering item parameters, latent variances and covariances, as well as ability estimates within and between groups (e.g., schools) was examined in a simulation study, varying the number of dimensions, the intraclass correlation coefficient, the number of clusters, and cluster size, for a total of 24 conditions. Overall, MH-RM performed well in recovering the item, person, and group-level parameters of the model. More replications are needed to better determine the accuracy of analytical standard errors for some of the parameters. Limitations of the study, implications for educational measurement practice, and directions for future research are offered.

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.