acase@tulane.edu

The comparison of latent class models with differing numbers of classes faces the so-called boundary problem. This problem is common in finite mixture models of which latent class models are a special case. The difficulty arises because one of the latent probabilities is set to zero to fit the model with the reduced number of classes under the null hypothesis. In turn, this violates one of the regularity conditions necessary for the difference test statistic, generally the likelihood ratio, to converge to a chi-square distribution. Thus, its distribution is unknown. The parametric bootstrap has been proposed to cope with this situation A simulation study was carried out to assess the Type I Error of test statistics commonly used in improvement tests of latent class models. Conditions varied were: sample size, and 10 one-class models. The statistics investigated were: the Pearson's chi-square, the likelihood ratio, the Cressie-Read (lambda = 2/3), and the Freeman-Tukey. These statistics, when regularity conditions are met, converge to a chi-square distribution with the same degrees of freedom Results indicate that the actual Type I Error rate may be about double the nominal level when testing a one-class model versus a two-class model at the 0.1 level. Likewise, there is strong evidence in favor of the parametric bootstrap as all four statistics maintain the nominal desired level under this procedure. For a few conditions associated with small sample sizes the bootstrapped statistics were conservative / acase@tulane.edu

In the received histories F. H. Bradley's philosophy is credited with being the watershed between the old-fashioned metaphysical philosophy and contemporary philosophical practice. It is often contended that his main claims are outdated or soundly refuted However, this view is inaccurate due to the prejudices arising from influential misinterpretations of his philosophy. A prominent area in Bradley's philosophy which has been neglected owing to this traditional misinterpretation is his philosophy of the self. He is not usually credited with a theory of the self since it is usually pointed out that he claimed that the self is unreal. Although that claim is Bradley's, the usual interpretation of it is inadequate In this dissertation, Bradley's conception of philosophy is explained and defended against this traditional misinterpretation. His general critics are discussed and answered. His philosophy of the self is developed from its expression from the Ethical Studies through Appearance and Reality to the Essays on Truth and Reality The central portion of the dissertation develops and defends Bradley's theory of the self which claims that the self is a dialectic within Reality which is generated by the tensions found within experience. The self lies chiefly in the tension between self-knowledge and self-ignorance. As the self is able to balance the tensions which generate it, it gains integrity and Individuality. Bradley's claim that the self is the highest appearance is thereby explained The dissertation also contrasts Bradley's theory of the self with contemporary views and finds them to come short of Bradley's theory due to their tendency towards solipsism and to their neglect of the problem of self-ignorance. Finally, the dissertation describes Bradley's continuing influence upon contemporary philosophy, including his contribution to logic, Process philosophy, and contemporary Idealism / acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

We investigate the structure of C*-algebras with a finite bound on the dimensions of their irreducible representations, sometimes called 'subhomogenous' In the first chapter we develop the theory of C*-semigroup bundles. These are C*-bundles over semigroups together with a 'structure map' which links the semigroup structure of the base space to the bundle. Under suitable conditions we prove the existence of 'enough' bounded sections, which are 'compatible' with the C*-semigroup bundle structure. Then we establish a complete duality between a certain class of C*-semigroup bundles and subhomogenous C*-algebras, namely the algebra of compatible sections of such a C*-semigroup bundle is subhomogenous and conversely, every subhomogenous C*-algebra is isomorphic to the algebra of compatible sections of such a C*-semigroup bundle. In this way we are able to even represent C*-algebras with non-Hausdorff spectrum as sections in bundles The second chapter is devoted to developing methods for the computation of the functor (PI)H(,R)('1), which classifies certain C*- bundles with varying finite dimensional fibres. (PI)H(,R)('1) is the C*- bundle analog of Cech-cohomology for bundles with one fibre type. The difficulty here is, that homotopy classes of cocycles of bundle imbeddings have to be computed, while only homotopies that satisfy a corresponding cocycle condition can be considered. We define a functor MH(,R)('1) which describes the multiplicities of the imbeddings of the fibres into the bundle and assignment of multiplicity matrices to cocycles yields a natural transformation: (PI)H(,R)('1) (--->) MH(,R)('1) Chapter three finally gives some applications. We calculate (PI)H(,R)('1) for C*-bundles over a two disk for an assignment of different finite dimensional fibres. The result is stated in terms of MH(,R)('1) and quotients of homotopy groups of bundle imbeddings. It provides a new way to describe the group C*-algebra of an interesting group called p4gm, which has been computed by I. Raeburn, and furthermore, our description yields complete invariants--in fact these are given by MH(,R)('1) A last example involving bundles over a three ball with 3 different fibres shows the fact that MH(,R)('1) does not always provide complete invariants and at the same time illustrates the limits of our methods / acase@tulane.edu