Li, Jie
(2015)
THE INFLUENCE OF MISSPECIFICATION OF BETWEEN-SUBJECT AND WITHIN-SUBJECT COVARIANCE STRUCTURES IN HIERARCHICAL GROWTH MODELS.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Hierarchical growth models are widely used in longitudinal studies to investigate individual changes over time since the model can handle unbalanced design and missing data. Between-subject and within-subject covariance structures can also be flexibly modeled. However, the current methods for selecting the optimal covariance structure are inefficient. It is common that covariance structures are misspecified. This dissertation is to examine the influences on fixed and random effects due to the misspecification of between-subject and within-subject covariance structures in a two-level hierarchical quadratic growth model with one continuous level-two predictor via two simulations. In addition, whether the Standardized Root Mean square Residual (SRMR) can be used in selecting the optimal covariance is examined.
The results indicate that the estimates of fixed effects are unbiased. The estimates of random effects and standard errors of fixed effects are biased due to the misspecification of the covariance structures. The over-specification of the covariance structure at one-level cannot compensate due to the under-specification of the covariance structure at the other level. When the within-subject covariance is under-specified and the between-subject covariance is over-specified, the relative biases of standard errors of fixed effects are smaller than those when the within-subject covariance structure is over-specified and the between-subject covariance structure is under-specified. When random slopes of a quadratic change cannot be modeled, we recommend to use an unspecified R matrix so that the fixed effects and their standard errors can be estimated bias-free. However, the over-specified between-subject covariance has little impact on fixed effects and their standard errors. There are biased estimations of random effects due to the misspecification of within-subject and between-subject covariance structures. If the random effects are of interest, different R matrices and G matrices should be examined. If there are large differences among the results when using different R matrices, the results should be interpreted carefully. The results suggest that BIC is the best method in detecting the optimal covariance structure under the designed factors no matter whether the within-subject and between-subject covariances are over- or under-specified. SRMR performs poorly in the covariance selection under the misspecification of covariance structures.
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| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
18 May 2015 |
| Date Type: |
Publication |
| Defense Date: |
3 April 2015 |
| Approval Date: |
18 May 2015 |
| Submission Date: |
3 May 2015 |
| Access Restriction: |
2 year -- Restrict access to University of Pittsburgh for a period of 2 years. |
| Number of Pages: |
217 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
School of Education > Psychology in Education |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Hierarchical growth models, misspecification of covariance structures, fixed effects, random effects |
| Date Deposited: |
18 May 2015 17:45 |
| Last Modified: |
18 May 2017 05:15 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/25108 |
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