For a graph G = (V, E), a set S ⊆ V is a dominating set if every vertex in V - S is adjacent to at least one vertex in S. A dominating set S ⊆ V is a paired-dominating set if the induced subgraph 〈S〉 has a perfect matching. We introduce a variant of paired-domination where an additional restriction is placed on the induced subgraph 〈S〉. A paired-dominating set S is an induced-paired dominating set if the edges of the matching are the induced edges of 〈S〉, that is, 〈S〉 is a set of independent edges. The minimum cardinality of an induced-paired dominating set of G is the induced-paired domination number γip(G). Every graph without isolates has a paired-dominating set, but not all these graphs have an induced-paired dominating set. We show that the decision problem associated with induced-paired domination is NP-complete even when restricted to bipartite graphs and give bounds on γip(G). A characterization of those triples (a, b, c) of positive integers a ≤ b ≤ c for which a graph has domination number a, paired-domination number b, and induced-paired domination c is given. In addition, we characterize the cycles and trees that have induced-paired dominating sets.

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The Thurstone-Mosteller and Bradley-Terry Models are commonly used to rank items from paired comparisons experiments in which one item in each pair "wins," and to assess the importance of time-independent explanatory variables on such rankings. The first part of this thesis clarifies the use of probit and logistic regression models for such designs, including the incorporation of time-dependent explanatory variables and the analysis of unbalanced designs. In addition, likelihood inference, using the EM Algorithm, is proposed for Thurstone's Case HI Model allowing the estimation of variance parameters to account for variable item performances. The second half of this thesis presents an extension of the model to permitting the "performances" or "worths" of each competitor to be serially correlated. As an example, the performance of a basketball team in its current game is allowed to be correlated with its performance from the previous game. The Thurstone-Mosteller Model is sometimes motivated through the use of an underlying, normally-distributed performance distribution for each item or competitor, with a competitor winning a trial if a draw from its performance distribution exceeds that from its competitor's. The observed outcome is solely the win or loss for each team, but regression models, using either time-dependent or time-independent explanatory variables, may be specified for the performance means. The extension in this thesis comes from supposing the error structure for the performance distribution for each team is normal with first-order autocorrelation. The EM Algorithm is used, treating the underlying draws from the performance distributions as "missing data." This provides approximate maximum likelihood estimates; the approximation is due to the use of Monte Carlo integration in the E-step of the algorithm. Unfortunately, the heavy computational requirement and the inability to calculate the maximized likelihood function or the information matrix, make the approach unattractive for practical use. Two approximations are presented, however, which can be carried out with standard routines and some minor programming. Keywords: auto-regressive model, Bradley-Terry Model, EM Algorithm, generalized linear model, logistic regression, MCEM Algorithm, probit regression, serial correlation, Thurstone-Mosteller Model. / Graduation date: 1996

Thesis (B.A.(Hons.))--University of Queensland, 2002. / Includes bibliographical references.

Thesis (B.A. Hons.))--University of Adelaide, Dept. of Psychology, 1969.

Thesis (M.S.)--University of Wisconsin--Madison, 1972. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1961. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison, 1975. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison, 1972. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison, 1969. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.