Abstract
The dissertation revolves around three aims. The first aim is the construction of a conceptually and computationally simple Bayes factor for Type I constrained-model selection (dimensionality determination) that is determinate under usage of improper priors and the subsequent utilization of this Bayes factor in a Bayesian exploratory factor analysis (EFA)
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concerned with the selection of an optimal dimensionality for the latent factors. Chapter 2 deals with this aim. It connects the candidate estimator for marginal likelihood computation with the usage of training sample priors so that, pending certain conditions, a simulation consistent MCMC implementation of well-known default Bayes factors is obtained. This automated candidate estimator allows for noninformative prior usage in EFA, such that the problem of interference of informative prior information with the determination of the intrinsic dimensionality of the factor solution may be avoided. Subsequently, an appropriate stopping rule for factor analytic data compression is proposed. The second aim of this dissertation is to construct a conceptually and computationally simple Bayes factor for Type II constrained-model selection (the determination of appropriate inequality restrictions on the parameter space) that is geared towards inequalities on regression-type parameters and the subsequent embedding of this Bayes factor within a strategy that allows one to express factor analytic structure using inequality constraints. This aim has been given attention in Chapters 3 and 4. Chapter 3 gives a set of conditions for global rotational identification of the factor model. The condition set enables the formulation of an unrestricted confirmatory factor model (UCFM). An UCFM is a factor analysis model that places only minimal restrictions on the factor model for achieving global rotational uniqueness of the factor solution, with the restrictions chosen such that they convey preconceived theoretical meaning and thus render unnecessary post-hoc rotation of the solution for interpretation purposes. In Chapter 4 a Bayes factor for Type II constrained-model selection is given. Computation of this Bayes factor is relatively simple as its expressions of model fit and model complexity are explicitly connected to, respectively, the posterior and prior probability mass satisfying the constraints defining the constrained model. This implies that one only needs to evaluate the number of times an appropriate MCMC sampler visits the permissable space. This Bayes factor is then used in rendering a take on confirmatory factor analysis (CFA) in which factor structure is expressed using inequalities. The strategy consists of choosing as a base model an UCFM and to subsequently express factor structure using inequalities on and between the free parameters in the loadings matrix. The third and final aim is to let the provisions from Aims 1 and 2 conjoin in order to develop an integrative factor analytic strategy that proposes a bridge crossing the divide between EFA and CFA and to bring this strategy to bear on substantive fields of study outside the direct realm that brought about the FA model. Chapter 5 applies the integrative strategy to epidemiological data on the metabolic syndrome. Chapter 6 utilizes this strategy to analyze political sciences data on decision acceptance and ethical leadership
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