Correlated ordinal data typically arises from multiple measurements on a collection of subjects. Motivated by an application in credit risk, where multiple credit rating agencies assess the creditworthiness of a firm on an ordinal scale, we consider multivariate ordinal regression models with a latent variable specification and correlated error terms. Two different link functions are employed, by assuming a multivariate normal and a multivariate logistic distribution for the latent variables underlying the ordinal outcomes. Composite likelihood methods, more specifically the pairwise and tripletwise likelihood approach, are applied for estimating the model parameters. Using simulated data sets with varying number of subjects, we investigate the performance of the pairwise likelihood estimates and find them to be robust for both link functions and reasonable sample size. The empirical application consists of an analysis of corporate credit ratings from the big three credit rating agencies (Standard & Poor's, Moody's and Fitch). Firm-level and stock price data for publicly traded US firms as well as an unbalanced panel of issuer credit ratings are collected and analyzed to illustrate the proposed framework.

Correlated ordinal data typically arise from multiple measurements on a collection of subjects. Motivated by an application in credit risk, where multiple credit rating agencies assess the creditworthiness of a firm on an ordinal scale, we consider multivariate ordinal models with a latent variable specification and correlated error terms. Two different link functions are employed, by assuming a multivariate normal and a multivariate logistic distribution for the latent variables underlying the ordinal outcomes. Composite likelihood methods, more specifically the pairwise and tripletwise likelihood approach, are applied for estimating the model parameters. We investigate how sensitive the pairwise likelihood estimates are to the number of subjects and to the presence of observations missing completely at random, and find that these estimates are robust for both link functions and reasonable sample size. The empirical application consists of an analysis of corporate credit ratings from the big three credit rating agencies (Standard & Poor's, Moody's and Fitch). Firm-level and stock price data for publicly traded US companies as well as an incomplete panel of issuer credit ratings are collected and analyzed to illustrate the proposed framework. / Series: Research Report Series / Department of Statistics and Mathematics

Ordered alternatives tests are sometimes used in life-testing experiments and drug-screening studies. An ordered alternative test is sometimes used to gain power if the researcher thinks parameters will be ordered in a certain way if they are different. This research proposal focuses on developing new nonparametric tests for the nondecreasing ordered alternative problem for k (k?3) populations when testing for differences in both location and scale. Six nonparametric tests are proposed for the nondecreasing ordered alternative when testing for a difference in either location or scale. The six tests are various combinations of a well-known ordered alternatives test for location and a test based on the Moses test technique for testing differences in scale. A simulation study is conducted to determine how well the proposed tests maintain their significance levels. Powers are estimated for the proposed tests under a variety of conditions for three, four and five populations. Several types of variable parameters are considered: when the location parameters are different and the scale parameters are equal; when the location parameters are equal and the scale parameters are different; when the location and scale parameters are both different. Equal and unequal samples sizes of 18 and 30 are considered. Subgroup sizes of 3 and 6 are both used when applying the Moses test technique. Recommendations are given for which test should be used for various situations.

The Family Forest Research Center recently conducted a mail survey of about 1,400 Massachusetts landowners. Respondents were given questions about themselves and their land and were then asked to rate three carbon sequestration programs in terms of their likelihood to participate. An ordered logit model is used to estimate probabilities that landowners would participate in various improved forest management programs. There are several estimation issues to consider with the ordered logit model. The relative merits of alternative models, including the multinomial and binomial logit, rank-ordered logit, binary logit and mixed ordered logit are discussed. Results of the ordered logit indicate that older males with less education and who own less than 100 acres are less likely to participate in an improved forest management program. All landowners are less likely to participate in a program that requires a management plan and that has a lengthy time commitment, low revenue stream and early withdrawal penalty. Policy implications and direction for future research are discussed.

This project deals with exploring 1) travel-related health risk perception, and 2) actions taken to mitigate that health risk. Ordered logistic regression models were used to identify factors associated with the perceived risk of contracting influenza at work, school, daycare, stores, restaurants, libraries, hospitals, doctor’s offices, public transportation, and family or friends’ homes. Based on the models, factors influencing risk perception of contracting influenza in public places for discretionary activities (stores, restaurants, and libraries) are consistent but differ from models of discretionary social visits to someone’s home. Mandatory activities (work, school, daycare) seem to have a few unique factors (e.g., age, gender, work exposure), as do different types of health-related visits (hospitals, doctors’ offices). Across all of the models, recent experience with the virus, of either an individual or a household member, was the most consistent set of factors increasing risk perception. Using such factors in examining transportation implications will require tracking virus outbreaks for use in conjunction with other factors. Subsequently, social-health risk mitigation strategies were studied with the objective of understanding how risk perception influences an individual’s protective behavior. For this objective, this study analyzes travel-actions associated with two scenarios during an outbreak of influenza: 1) A sick person avoiding spreading the disease and 2) A healthy person avoiding getting in contact with the disease. Ordered logistic regression models were used to identify factors associated with mitigation behavior in the first scenario: visiting a doctor’s office, avoiding public places, avoiding public transit, staying at home; and in the second scenario: avoiding public places, avoiding public transit, staying at home. Based on the models for Scenario 1, the factors affecting the decision of avoiding public places, avoiding public transit, and staying at home were fairly consistent but differ for visiting a doctor’s office. However, Scenario 2 models were consistent with their counterpart mitigation models in Scenario 1 except for two factors: gender and household characteristics. Across all the models from Scenario 1, gender was the most significant factor, and for Scenario 2, the most significant factor was the ratio of household income to the household size. / Master of Science / Transmission of a communicable disease depends on the social interactions of the members of society. Generally, individuals associate their health-protection behavior to the perception of health risk associated with that activity. Hence, individuals with high health-risk perception are likely to participate in a protective action to reduce the threat of getting infected with influenza. However, in some cases, even if a high health risk is perceived, an individual might have a decreased likelihood to take actions to mitigate that risk. This behavior could be associated with their inability to carry out recommendations, such as vaccination (due to the cost of vaccination) or adopting protective behaviors such as social isolation (switching from public transit to personal vehicle due to the associated cost). This behavior, of either adopting or rejecting protective action, can be explained by protection motivation theory. This theory explains the individual’s perception of the severity of an event (i.e., threat appraisal), and individual’s expectancy of carrying out recommendations (risk mitigation strategies) to reduce threat (i.e., coping appraisal). Both, health risk perception and risk-mitigation strategies are studied for changes in travel decisions.

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Denna uppsats beräknar ett skuggpris för rädslan att gå ensam i mörkret i individens hemmakvarter samt undersöker skillnader mellan män och kvinnors skuggpriser för att vara mindre rädd. Tidigare studier som har använts sig av skuggpris för att beräkna rädsla har studerats och analyserats för att på bästa sätt kunna genomföra denna uppsats. Datamaterialet som använts i uppsatsen kommer från European Social Survey och består av 1791 observationer. Respondenterna fick i undersökningen svara på en skala mellan 1 till 4, där 1 var ’’mycket säker’’ och 4 var ’’mycket osäker’’ angående individens rädsla vid mörker. Skuggpriset motsvarar den summa av hushållets nettoinkomst som individen är villig att offra för att känna sig en enhet mindre rädd. Skuggpriset för att gå ensam i mörkret jämförs med män och kvinnors separata skuggpriser. Skuggpriset för att gå ensam i mörkret beräknades till 15 744 kronor. I uppsatsen skattades männens skuggpris till 12 881 kronor medan kvinnornas skuggpris blev 27 956 kronor. Därmed kan kvinnorna i Sverige tänka sig offra mer av sin månadsinkomst för att vara mindre rädd än männen i Sverige. Skillnaderna mellan män och kvinnors skuggpriser kan bero på att könen har separata psykologiska kostnader samt olika sociala roller i samhället. En kvinna tenderar att känna mer rädsla i vardagen än vad en man gör. Skillnaden mellan män och kvinnors skuggpriser skulle eventuellt kunna förklaras med att samhället kanske inte anser att en man ska känna rädsla och detta skulle kunna leda till att männen är villiga att betala mindre för att minska sin rädsla.

The problem undertaken in this paper is to determine what the algebraic structure of the class of C-sets is, when the notion of sum is to be the "set sum. " While the preliminary work done by Appling took place in the space of additive and bounded real valued functions, the results here are found in the more general setting of a complete lattice ordered group. As a conseque n c e , G . Birkhof f' s book, Lattice Theory, is used as the standard reference for most of the terminology used in the paper. The direction taken is prompted by a paper by W. D. L. Appling, "A Generalization of Absolute Continuity and of an Analogue of the Lebesgue Decomposition Theorem. " Since some of the results obtained provide another approach to a problem originally studied by Nakano, and improved upon by Bernau, reference is made to their work to provide other terminology and examples of alternative approaches to the problem of lateral completion. Thus Chapter I contains a brief history of the notion of C-sets and their relationship to lattice ordered groups, along with a summary of the properties of lattice ordered groups needed for later developments. In addition, several results in the general theory of lattice ordered groups are cited to provide insight into the comparability of the assumptions that will ultimately be made about the groups. Chapter II begins with the axiomatization of the collection of nearest point functions" for the closed A-ideals of the cone of a complete lattice ordered group. The basic results in the chapter establish that the functions defined do indeed characterize the complete A-ideals, and that the maps have a 'nearest point property." The maps are then extended to the entire group and shown to correspond to the "nearest point maps" for a C-set in PAB' Chapter III is devoted to exploring the algebraic structures found in the collection of all closed A-ideal maps, denoted J. J is shown to be a lattice ordered monoid, abelian and complete, containing a maximal group cone P*. It is further shown that the original group cone P is isomorphic to a subset of P*. Chapter IV looks into a rather interesting characterization of P*, one that, in the terminology of Bernau, implies that P* is the cone of the group that is the lateral completion of the original group. A final result is a demonstration that the members of j each have a representation as the sum of an element of P* and an additive element of j.

Charles University in Prague Faculty of Social Sciences Institute of Economic Studies MASTER THESIS The determinants of access to finance. Evidence for transition economies Author: Alina Cazachevici Supervisor: Roman Horvath, Ph.D. Academic Year: 2012/2013 Abstract The thesis provides an empirical analysis of impact of country-level and firm-level determinants on access to finance in transition economies. Generalized Ordered Logit model is applied on survey data for transition countries, combined with financial market indicators. The results show that higher concentration in banking sector, as well as higher financial deepening have a positive impact on access to finance, while volatile macroeconomic environment, higher implication of foreign-owned and state- owned banks seems to be perceived as increasing obstacles in accessing external financing. Combining indexes for liberalization in banking sector and liberalization of securities markets proved that before liberalization process firms had better access to finance. One of the possible explanations is that before liberalization state banks were forced by politicians to issue more loans, while after reforms the political pressure was removed, imposing stricter conditions for loan granting. Inclusion of corruption variable yields expectable results that...

by Chi-keung Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Includes bibliographical references. / Introduction --- p.1 / Chapter Chapter 0. --- Preliminary --- p.4 / Chapter 0.1 --- Topological vector spaces / Chapter 0.2 --- Ordered vector spaces / Chapter 0.3 --- Ordered normed spaces / Chapter 0.4 --- Ordered topological vector spaces / Chapter 0.5 --- Ordered bornological vector spaces / Chapter Chapter 1. --- Results on Ordered Normed Spaces --- p.23 / Chapter 1.1 --- Results on e∞-spaces and e1-spaces / Chapter 1.2 --- Complemented subspaces of ordered normed spaces / Chapter 1.3 --- Half injections and Half surjections / Chapter 1.4 --- Strict quotients and strict subspaces / Chapter Chapter 2. --- Helley's Selection Theorem and Local Reflexivity Theorem of order type --- p.55 / Chapter 2.1 --- Helley's selection theorem of order type / Chapter 2.2 --- Local reflexivity theorem of order type / Chapter Chapter 3. --- Operator Modules and Ideal Cones --- p.68 / Chapter 3.1 --- Operator modules and ideal cones / Chapter 3.2 --- Space cones and space modules / Chapter 3.3 --- Injectivity and surjectivity / Chapter 3. 4 --- Dual and pre-dual / Chapter Chapter 4. --- Topologies and Bornologies Defined by Operator Modules and Ideal Cones --- p.95 / Chapter 4.1 --- Generalized polars / Chapter 4.2 --- Topologies and bornologies defined by β and ε / Chapter 4. 3 --- Injectivity and generating topologies / Chapter 4.4 --- Surjectivity and generating bornologies / Chapter 4.5 --- The solid property and the generating topologies / Chapter 4.6 --- The solid property and the generating bornologies / Chapter Chapter 5. --- Semi-norms and Bounded disks defined by Operator Modules and Ideal Cones --- p.129 / Chapter 5.1 --- Results on semi-norms / Chapter 5.2 --- Results on bounded disks / References --- p.146 / Notations --- p.149