Fitting Statistical Models with Multiphase Mean Structuresfor Longitudinal Data
Institution: | The Ohio State University |
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Department: | |
Year: | 2015 |
Keywords: | Psychology; Education; Statistics; Multiphase Models; Piecewise Models; Longitudinal; Population-Average; Subject-Specific; Full Information Maximum Likelihood; Applied Statistics; Bayesian Multilevel Models |
Posted: | 02/05/2017 |
Record ID: | 2072294 |
Full text PDF: | http://rave.ohiolink.edu/etdc/view?acc_num=osu1430998328 |
When measuring individuals over time, change is frequently curvilinear and residual errors are typically correlated. Two population-average and two subject-specific models with multiphase mean structures are proposed to model change over time and account for error correlations. In the Frequentist tradition, such models fall under the category of nonlinear and nonlinear mixed-effects models, respectively. The latter class becomes increasingly difficult to estimate with full information maximum likelihood (FIML) as the number of random effects increases. However, Bayesian multilevel models care little for the number of individually modeled parameters, as the mechanics of MCMC escape the numerical integration problems encountered by FIML. This thesis illustrates the differences between population-average and subject-specific models, highlights the advantages of multiphase mean structures, comments on issues regarding the estimation of such models, and presents general Bayesian formulations for population-average and subject-specific models with mutliphase mean structures for a real dataset. Advisors/Committee Members: Cudeck, Robert (Advisor).