The purpose of this paper is to present a study of partly ordered sets. It includes a rigorous development of relations based on the notion of a relation as a set, lattices, and theorems concerning the lattice of subgroups of a group.

<p> In this thesis we introduce the concept of a dense extension of a partially ordered set and study some of the properties of the resulting class of extensions. In particular we study the dense distributive extensions, dense Boolean extensions and dense meet continuous extensions of distributive, Boolean and meet continuous lattices respectively.</p> / Thesis / Doctor of Philosophy (PhD)

The major results of this work concern perfect ideals of ordered vector spaces, and a representation theory for ordered vector spaces. Perfect ideals are characterized by the property that their annihilators in the order dual are ideals. We obtain a number of conditions for an ordered vector space which are equivalent to the intersection of the set of perfect maximal ideals being 0. We also obtain conditions which permit an ordered vector space to be represented as a subspace of the sections of a vector bundle. This generalizes the representation theory for odered vector spaces with unit. / Thesis / Doctor of Philosophy (PhD)

Using a mixed methodology, the effectiveness of an 8-week modification of Landreth's (1991) 10-week group filial therapy training model was investigated with parents (n = 5) court-ordered for remedial parenting services due to physical abuse and/or neglect of their school-age children. A comparison group (n = 3) concurrently received an 8-week parent education course. Three primary questions were explored. Do filial therapy group participants demonstrate a greater decrease in child physical abuse potential and parenting stress following training when compared to parent education group participants? In addition, do filial therapy group participants show evidence of stronger parent-child relationships following training when compared to participants in the parent education group? Pre- and post-measures were utilized, and anecdotal and qualitative data were also collected. Following the analysis of both the quantitative and qualitative data, it was determined that the group quantitative results detracted from the richness of the qualitative findings, and the former were subsequently dropped. Instead, individual pre- and posttest quantitative scores, along with the anecdotal data, were compiled to create participant profiles that provided additional descriptive information to the emergent focus group themes. Due to the size of the sample (N = 8), findings were only preliminary and merit further study. Participants demonstrated social desirability in their assessment responses; therefore, it is recommended that qualitative or mixed methodology, as well as multiple measures of each construct, be incorporated to combat this phenomenon in future studies with this population. Results of this study further suggested that there are clinical benefits to utilizing a mixed sample of both court- and self-referred participants. In addition, the court-mandated population is heterogeneous and requires multiple treatment options coupled with screening protocol for appropriate treatment assignment. Future filial therapy research with this population should provide greater support to participants in conducting filial therapy sessions, as well as alternative ways of documenting these sessions. In addition, it is proposed that a combination of individual and group filial therapy models that is longer-term would be more effective with this population than the 8-week model used. / Ph. D.

This study identifies the factors influencing adoption of IPM practices and number of pesticide applications in vegetable farmers in Kenya. The sample size for this study includes 263 vegetable farmers. The survey was conducted in four counties of Kenya: Nyeri, Tharka Nithi, Nakuru and Bomet. The vegetables considered in this study are tomato, cabbage and French beans. Different econometric tools are used to analyze adoption of IPM practices and pesticide application for vegetables. It is found that experience in vegetable cultivation and number of livestock owned have a positive impact on the adoption of IPM practices. However, distance to the nearest town has a negative impact on adoption. Moreover, the number of times pesticides are applied to vegetables also declines as distance of the household from the nearest town increases. Farmers whose crops face less stress from insects and disease tend to apply pesticides fewer times as well. Results from this study indicate that being close to town is important for agricultural activities in general. Being farther away not only reduces the probability of IPM adoption but also reduces pesticide application. / Master of Science / This study identifies the factors influencing adoption of IPM practices and number of pesticide applications in vegetable farmers in Kenya. The sample size for this study includes 263 vegetable farmers. The survey was conducted in four counties of Kenya: Nyeri, Tharka Nithi, Nakuru and Bomet. The vegetables considered in this study are tomato, cabbage and French beans. Different econometric tools are used to analyze adoption of IPM practices and pesticide application for vegetables. It is found that experience in vegetable cultivation and number of livestock owned have a positive impact on the adoption of IPM practices. However, distance to the nearest town has a negative impact on adoption. Moreover, the number of times pesticides are applied to vegetables also declines as distance of the household from the nearest town increases. Farmers whose crops face less stress from insects and disease tend to apply pesticides fewer times as well. Results from this study indicate that being close to town is important for agricultural activities in general. Being farther away not only reduces the probability of IPM adoption but also reduces pesticide application.

This thesis is concerned with the development of two generalized set covering models. The first model is formulated for the total set covering problem where cost is minimized subject to the constraint that each customer must be served by at least one facility. The second model is constructed for the partial set covering problem in which customer coverage is maximized subject to a budget constraint. The conventional formulations of both the total set covering and partial set covering problems are shown to be special cases of the two generalized models that arc developed. Appropriate solution strategies arc discussed for each generalized model. A specialized algorithm for a particular case of the partial covering problem is constructed and computational results are presented. / M.S.

This dissertation consists of two chapters related to inference about locally ordered and common breaks in multiple regressions and one chapter pertains to modeling exchange rate volatility with random level shifts. The first chapter considers inference about locally ordered breaks in a system of equations. These apply when break dates in different equations are not separated by a positive fraction of the sample size. We extend the results of Qu and Perron (2007) in several directions allowing: a) the covariates to be any mix of trends, stationary or integrated regressors; b) breaks in the variance-covariance matrix of errors; c) an arbitrary number of breaks occurring in a subset of equations. We show that the limit distributions derived provide good approximations to the finite sample distributions and forming confidence intervals in a joint fashion allows more precision. The second chapter considers testing for common breaks and estimating locally ordered breaks in a multiple system with joined segmented trends. To test for common breaks, we consider a likelihood ratio type test. The null hypothesis is that some subsets of coefficients for slope shifts share some common breaks, while the alternative hypothesis is that the breaks dates are different and possibly locally ordered. To estimate locally ordered breaks, we use a quasi-maximum likelihood estimation method. We show consistency and derive rate of convergence and asymptotic distributions of test statistics and estimates of the break dates. Simulation results show that the asymptotic results provide useful approximations in finite samples. In the third chapter, we estimate a random level shifts model for the log-absolute returns of the Dollar-Mark and Dollar-Yen exchange rates, in order to assess whether random level shifts can explain the long memory property. The results show that there are few level shifts, but once they are taken into account, the long memory property disappears. We also provide out-of-sample forecasting comparisons, which show that the random level shifts model outperforms standard fractionally integrated models.

<p>Betting under ordered forms has been around for a long time, but the recent increase in Internet betting and the large sums of money that are now involved makes it even more important for betting companies to have correct odds.</p><p> </p><p>The purpose of the essay is to calculate probabilities for outcomes of football games using a statistical model and to see if you can find better odds than a betting company.</p><p>The data contains the 380 games from the 2004/2005 season and the variables form, head-to-heads, league position, points, home/away, average attendance, promoted team, distance and final league position from previous season.</p><p> </p><p>After performing an ordered probit regression we only find the variable “form of the away team” to be significant at the 5 % level. We suspect the presence of multicollinearity and perform a VIF-test which confirms this. To fix this problem we perform a second ordered probit regression where a number of variables are combined to index variables. In the second regression we once again find only one significant variable. This time it is the variable “difference between home and away teams’ final league position”. A reason for the lack of significant variables could be the size of the data. A new model with five variables is examined and it results in four significant variables.</p><p> </p><p>The calculated odds pick the correct result in 200, 203 and 198 out of 380 games respectively, compared to 197 out of 380 for Unibet. Betting one krona on the lowest calculated odds from the second model will result in a positive yield for season 2004/2005 when using Unibet’s odds.</p> / <p>Vadslagning under ordnade former har funnits under en längre tid, men de senaste årens explosionsartade ökning av Internetspel och de stora summor som då omsätts har gjort det allt viktigare för spelbolagen att sätta korrekta odds.</p><p> </p><p>Syftet med uppsatsen är att med hjälp av en statistisk modell räkna ut sannolikheter för utfall i fotbollsmatcher och att undersöka om man kan hitta bättre odds än ett spelbolag.</p><p>Datamaterialet innefattar de 380 matcherna som spelades säsongen 2004/2005 samt de oberoende variablerna form, inbördes möten, tabellplacering, poängskörd, hemmaplan/bortaplan, publiksnitt, uppflyttat lag, avstånd och slutplacering.</p><p> </p><p>Efter utförd ordered probit regression erhåller vi endast en signifikant variabel vid en signifikansnivå på 5 %, nämligen ”bortalagets form”. Vi misstänker att det kan förekomma multikollinearitet och utför därför ett VIF-test som bekräftar detta. För att råda bot på detta problem genomför vi en andra ordered probit regression där flera variabler slås ihop till indexvariabler. I den andra regressionen får vi åter igen en enda signifikant variabel, men i detta fall är det variabeln ”differensen mellan hemma- och bortalagets slutplaceringar”. Ett skäl till att det inte blir fler signifikanta variabler misstänks vara storleken på datamaterialet. En ny modell med fem variabler undersöks och då blir fyra variabler signifikanta.</p><p> </p><p>De beräknade oddsen väljer rätt utfall i 200, 203 respektive 198 av 380 matcher för de tre modellerna mot Unibets 197 av 380 matcher. I modell 2 ger en spelad krona på utfallet med lägst beräknat odds positiv avkastning under säsongen vid spel hos Unibet.</p>

Betting under ordered forms has been around for a long time, but the recent increase in Internet betting and the large sums of money that are now involved makes it even more important for betting companies to have correct odds.   The purpose of the essay is to calculate probabilities for outcomes of football games using a statistical model and to see if you can find better odds than a betting company. The data contains the 380 games from the 2004/2005 season and the variables form, head-to-heads, league position, points, home/away, average attendance, promoted team, distance and final league position from previous season.   After performing an ordered probit regression we only find the variable “form of the away team” to be significant at the 5 % level. We suspect the presence of multicollinearity and perform a VIF-test which confirms this. To fix this problem we perform a second ordered probit regression where a number of variables are combined to index variables. In the second regression we once again find only one significant variable. This time it is the variable “difference between home and away teams’ final league position”. A reason for the lack of significant variables could be the size of the data. A new model with five variables is examined and it results in four significant variables.   The calculated odds pick the correct result in 200, 203 and 198 out of 380 games respectively, compared to 197 out of 380 for Unibet. Betting one krona on the lowest calculated odds from the second model will result in a positive yield for season 2004/2005 when using Unibet’s odds. / Vadslagning under ordnade former har funnits under en längre tid, men de senaste årens explosionsartade ökning av Internetspel och de stora summor som då omsätts har gjort det allt viktigare för spelbolagen att sätta korrekta odds.   Syftet med uppsatsen är att med hjälp av en statistisk modell räkna ut sannolikheter för utfall i fotbollsmatcher och att undersöka om man kan hitta bättre odds än ett spelbolag. Datamaterialet innefattar de 380 matcherna som spelades säsongen 2004/2005 samt de oberoende variablerna form, inbördes möten, tabellplacering, poängskörd, hemmaplan/bortaplan, publiksnitt, uppflyttat lag, avstånd och slutplacering.   Efter utförd ordered probit regression erhåller vi endast en signifikant variabel vid en signifikansnivå på 5 %, nämligen ”bortalagets form”. Vi misstänker att det kan förekomma multikollinearitet och utför därför ett VIF-test som bekräftar detta. För att råda bot på detta problem genomför vi en andra ordered probit regression där flera variabler slås ihop till indexvariabler. I den andra regressionen får vi åter igen en enda signifikant variabel, men i detta fall är det variabeln ”differensen mellan hemma- och bortalagets slutplaceringar”. Ett skäl till att det inte blir fler signifikanta variabler misstänks vara storleken på datamaterialet. En ny modell med fem variabler undersöks och då blir fyra variabler signifikanta.   De beräknade oddsen väljer rätt utfall i 200, 203 respektive 198 av 380 matcher för de tre modellerna mot Unibets 197 av 380 matcher. I modell 2 ger en spelad krona på utfallet med lägst beräknat odds positiv avkastning under säsongen vid spel hos Unibet.

Interaction and marginal effects are often an important concern, especially when variables are allowed to interact in a nonlinear model. In a linear model, the interaction term, representing the interaction effect, is the impact of a variable on the marginal effect of another variable. In a nonlinear model, however, the marginal effect of the interaction term is different from the interaction effect. This report provides a general derivation of both effects in a nonlinear model and a linear model to clearly illustrate the difference. These differences are then demonstrated with empirical data. The empirical study shows that the corrected interaction effect in an ordered logit or probit model is substantially different from the incorrect interaction effect produced by the margins command in Stata. Based on the correct formulas, this report verifies that the interaction effect is not the same as the marginal effect of the interaction term. Moreover, we must be careful when interpreting the nonlinear models with interaction terms in Stata or any other statistical software package. / text