An EM Algorithm for Maximum Likelihood Estimation of Process Factor Analysis Models Public Deposited

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  • October 10, 2018
  • Lee, Taehun
    • Affiliation: College of Arts and Sciences, Department of Psychology and Neuroscience
  • In this dissertation, an Expectation-Maximization (EM) algorithm is developed and implemented to obtain maximum likelihood estimates of the parameters and the associated standard error estimates characterizing temporal flows for the latent variable time series following stationary vector ARMA processes, as well as the parameters defining the relationship between the latent stochastic vector and the observed scores taking measurement errors into account. Such models have been known as Process Factor Analysis (PFA) models (Browne & Nesselroade, 2005). In the E-step, the complete-data expected log-likelihood, the so-called Q-function, which is the joint likelihood of the manifest variables and the latent time series process variables, is constructed by supposing the latent process variables are observed. In the M-step, the Newton-Raphson algorithm is employed in order to update the parameter estimates. The closed form expressions for the gradient vector and the Hessian matrix of the target function are derived for implementing the M-step of the EM algorithm. Methods for obtaining the associated standard error estimates are developed and implemented. The proposed EM algorithm employs the covariance structure derived by du Toit & Browne (2007) where the influence of the time series prior to the first observation has remained stable and unchanged when the first observations are made. Thus, unlike other conventional structural equation modeling (SEM) software, model implied covariance matrices satisfy the stability condition and are Block-Toeplitz matrices. The proposed algorithm is applied to simulated data in order to ascertain its viability. Specifically, the recovery of the population parameter values of the proposed EM algorithm is studied with simulated data, which is generated so as to follow a PFA model. The performance of the developing method for standard error estimation is evaluated in the simulation study. The results of the simulation study show that the proposed methods for obtaining parameter estimates and the associated standard error estimates for PFA models can be effectively employed to both single-subject time-series analysis and repeated time-series analysis. Remaining methodological issues for future research are discussed.
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  • In Copyright
  • "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Psychology (Quantitative)."
  • MacCallum, Robert C.
Degree granting institution
  • University of North Carolina at Chapel Hill
Place of publication
  • Chapel Hill, NC
  • Open access

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