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

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.

Promover a segurança viária no entorno escolar é uma estratégia que contribui para que sejam construídas cidades seguras, saudáveis e sustentáveis. Nesse sentido, este estudo é dedicado a identificar a influência das características da estrutura urbana na frequência e na severidade dos acidentes no entorno de escolas de educação básica de Porto Alegre. A análise da frequência e da severidade de acidentes foi conduzida através da estimação de modelos econométricos: binomial negativo e logit ordenado, respectivamente. Para esses, foram calculados os efeitos marginais, permitindo a observação da magnitude dos impactos das variáveis explicativas sobre as variáveis dependentes. As variáveis dependentes frequência e severidade foram extraídas dos acidentes registrados em Porto Alegre entre 2012 e 2014. Foram incluídas, simultaneamente, variáveis da estrutura urbana, das escolas, socioeconômicas e dos acidentes (para a severidade). A partir do geoprocessamento dos dados existentes, os entornos escolares puderam ser caracterizados para três diferentes áreas circulares de análise (buffer ring) de raios de 100, 150 e 200 metros, permitindo a comparação do uso das diferentes áreas. O conjunto de estimativas indica que áreas menores produzem modelos de melhor desempenho para ambas as técnicas empregadas. No entanto, áreas maiores permitem a análise de maior quantidade de variáveis relativas à estrutura urbana. Essa relação sugere os benefícios da escolha a partir do trade-off entre ajuste do modelo e sua capacidade de propiciar análises de variáveis. Foi identificado que a frequência e a severidade de acidentes podem estar relacionadas a uma única variável explicativa de formas opostas – a partir de sinais contrários. Essa diferença de resultados para frequência e severidade de acidentes indica que há maiores benefícios em analisá-las em conjunto. Identificou-se ainda que existem benefícios para a segurança viária em áreas de estrutura urbana com quarteirões menores e maior quantidade de interseções de quatro vias, em frequência e severidade, respectivamente. Já as áreas mais arborizadas tendem a apresentar acidentes de menor severidade nos casos de usuários de modos ativos. / Fostering road safety nearby schools is a strategy that contributes to build safe, healthy and sustainable cities. The aim of this study is to identify the influence of the built environment characteristics in the frequency and severity of accidents nearby elementary and secondary schools in Porto Alegre. The frequency and severity of the accidents were analyzed using econometric models: negative binomial and ordered logit, respectively. The evaluation of their marginal effects allowed the magnitude of the impact caused by the explanatory variable on the dependent variables to be observed. The measured variables frequency and severity were extracted from accidents registered in Porto Alegre from 2012 and 2014. Built environment, socioeconomic and school variables were also included, as well as accident data (for severity). Data geoprocessing allowed school surroundings to be characterized for three different buffer rings, measuring 100, 150 and 200 meters of radius. Thereby it was possible to compare the inclusion of different areas in the study. The estimations indicates that models based on smaller areas have better performances for both employed techniques, whereas larger areas allow the study of a bigger quantity of urban infrastructure variables. That indicates the benefits of choosing based on a trade-off between model adjustment and capacity to engender the analysis of variables. It was shown that frequency and severity of accidents could be related to a single explanatory variable in opposite ways – based on contrary signs. This difference in the results found for frequency and severity indicates that there are more benefits when analyzing them together. Moreover, there are benefits for road safety in areas where the city blocks are shorter and where there are more four-way intersections, in frequency and severity of accidents, respectively. Also, areas of more important afforestation tend to decrease the severity of accidents involving users of active modes.

Promover a segurança viária no entorno escolar é uma estratégia que contribui para que sejam construídas cidades seguras, saudáveis e sustentáveis. Nesse sentido, este estudo é dedicado a identificar a influência das características da estrutura urbana na frequência e na severidade dos acidentes no entorno de escolas de educação básica de Porto Alegre. A análise da frequência e da severidade de acidentes foi conduzida através da estimação de modelos econométricos: binomial negativo e logit ordenado, respectivamente. Para esses, foram calculados os efeitos marginais, permitindo a observação da magnitude dos impactos das variáveis explicativas sobre as variáveis dependentes. As variáveis dependentes frequência e severidade foram extraídas dos acidentes registrados em Porto Alegre entre 2012 e 2014. Foram incluídas, simultaneamente, variáveis da estrutura urbana, das escolas, socioeconômicas e dos acidentes (para a severidade). A partir do geoprocessamento dos dados existentes, os entornos escolares puderam ser caracterizados para três diferentes áreas circulares de análise (buffer ring) de raios de 100, 150 e 200 metros, permitindo a comparação do uso das diferentes áreas. O conjunto de estimativas indica que áreas menores produzem modelos de melhor desempenho para ambas as técnicas empregadas. No entanto, áreas maiores permitem a análise de maior quantidade de variáveis relativas à estrutura urbana. Essa relação sugere os benefícios da escolha a partir do trade-off entre ajuste do modelo e sua capacidade de propiciar análises de variáveis. Foi identificado que a frequência e a severidade de acidentes podem estar relacionadas a uma única variável explicativa de formas opostas – a partir de sinais contrários. Essa diferença de resultados para frequência e severidade de acidentes indica que há maiores benefícios em analisá-las em conjunto. Identificou-se ainda que existem benefícios para a segurança viária em áreas de estrutura urbana com quarteirões menores e maior quantidade de interseções de quatro vias, em frequência e severidade, respectivamente. Já as áreas mais arborizadas tendem a apresentar acidentes de menor severidade nos casos de usuários de modos ativos. / Fostering road safety nearby schools is a strategy that contributes to build safe, healthy and sustainable cities. The aim of this study is to identify the influence of the built environment characteristics in the frequency and severity of accidents nearby elementary and secondary schools in Porto Alegre. The frequency and severity of the accidents were analyzed using econometric models: negative binomial and ordered logit, respectively. The evaluation of their marginal effects allowed the magnitude of the impact caused by the explanatory variable on the dependent variables to be observed. The measured variables frequency and severity were extracted from accidents registered in Porto Alegre from 2012 and 2014. Built environment, socioeconomic and school variables were also included, as well as accident data (for severity). Data geoprocessing allowed school surroundings to be characterized for three different buffer rings, measuring 100, 150 and 200 meters of radius. Thereby it was possible to compare the inclusion of different areas in the study. The estimations indicates that models based on smaller areas have better performances for both employed techniques, whereas larger areas allow the study of a bigger quantity of urban infrastructure variables. That indicates the benefits of choosing based on a trade-off between model adjustment and capacity to engender the analysis of variables. It was shown that frequency and severity of accidents could be related to a single explanatory variable in opposite ways – based on contrary signs. This difference in the results found for frequency and severity indicates that there are more benefits when analyzing them together. Moreover, there are benefits for road safety in areas where the city blocks are shorter and where there are more four-way intersections, in frequency and severity of accidents, respectively. Also, areas of more important afforestation tend to decrease the severity of accidents involving users of active modes.

Emerging automotive and transportation technologies, such as autonomous vehicles (AVs) have created revolutionary possibilities in the way we might travel in the future. Major car manufacturers and technology giants have demonstrated significant progress in advancing and testing AV technologies in real-life traffic conditions. Results from multi-population surveys indicate that despite enjoying moderate familiarity with AVs, more than 40% of the respondents were likely to use them when they become available. Simply looking at the demographic differences without paying any regard to the perceptions might suggest that the demographic differences are the primary causal factors behind the differences observed in the intended adoption of AVs. This study investigates the role of demographics and other factors (current travel characteristics, crash history and familiarity with AVs) on consumers’ perceptions and intended adoption of AVs with a view of disentangling one factor from the other. Results show that the observed demographic differences in intended adoption rates are due to demographic differences in the perceptions on the benefits and concerns of AVs. The study outcomes suggest that it may be beneficial to first address consumers’ perceptions on the benefits and concerns regarding AVs. The results from this study can be used to inform modeling decisions and policy discussions relevant to future market penetration of AV technology.

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

Becker's discrimination theory predicted that the discrimination by employers on competitive markets should cease to exist. However, in past decades, it was shown that discrimination on the labour market is a prevalent phenomenon. In this thesis I analyse what is the impact of agency problem on the theory of discrimination. I show that when an agent (in the thesis called 'agent employer') is deciding whether to employ or not to employ a worker, his motivation is different compared to principal's. The outcome of the analysis is such that under certain assumptions, the agent employer with non-zero taste for discrimination will always choose to discriminate.

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.

The purpose of this thesis was to evaluate the impact of dynamic message signs (DMS) on the Orlando-Orange County Expressway Authority (OOCEA) toll road network using the Post-Deployment DMS Survey analysis. DMS are electronic traffic signs used on roadways to give travelers information about travel times, traffic congestion, accidents, disabled vehicles, AMBER alerts, and special events. The particular DMS referred to in this study are large rectangular signs installed over the travel lanes and these are not the portable trailer mount signs. The OOCEA has added twenty-nine fixed DMS to their toll road network from 2006-2008. At the time of the post-deployment survey, a total of twenty-nine DMS were up and running on the OOCEA toll road network. Since most of the travelers on the OOCEA toll roads were from Orange, Osceola, and Seminole counties, this study was limited to these counties. This thesis documents the results for the post-deployment survey analysis. The instrument used to analyze the travelers' perception of DMS was a survey that utilized computer aided telephone interview. The post-deployment survey was conducted during the month of May, 2008. Questions pertaining to the acknowledgement of DMS on the OOCEA toll roads, satisfaction with travel information provided on the network, formatting of the messages, satisfaction with different types of messages, diversion questions (Revealed and Stated preferences), and classification/socioeconomic questions (such as age, education, most traveled toll road, county of residence, and length of residency) were asked to the respondents. This thesis is using results of the multinomial logit model for diversion of traffic. This model takes into account the different diversion decisions from the post development survey (stay vs. divert all the way vs. divert and come back vs. abandon trip) and explains the differences in the diversion behavior. Drivers that use SunPass or Epass tend to stay on the toll road during unexpected congestion. Frequent SR 408 users are more likely to divert and stay off the toll road and frequent SR 417 users are more likely to divert and get back on the toll road. Drivers whose stated preference was to divert off the toll road were more likely to do the same in the real world. However, not too many of the respondents were likely to abandon their trips in the real world even if they said they would in a hypothetical congestion scenario. Users of 511 were more likely to divert and get back on the toll road or abandon their trips due to unexpected congestion. OOCEA can use this study to concentrate on keeping their toll roads more attractive during unexpected congestion to keep drivers from diverting all the way or abandoning their trips. For example, better incident management in clearing accidents more efficiently (thereby decreasing delay) and encouraging the use of SunPass or EPass could help drivers stay than divert or abandon their trip. This thesis also used ordered logit model for satisfaction. This model explains the levels of magnitude of satisfaction with traveler information on OOCEA toll roads. Drivers who acquired traveler information from DMS were less likely to be dissatisfied with traveler information provided on toll roads than other respondents. Drivers who were satisfied with accuracy and information on hazard warnings on DMS were more likely to be satisfied with information provided on toll roads than other respondents. This thesis provides a microscopic insight on the driver behavior on toll roads. This thesis expands the diversion and satisfaction models from previous studies in a way that OOCEA can identify specific groups of drivers related to a given response behavior (i.e., diverts off toll roads or dissatisfied with traveler information). Such analysis can be conducted in the future in the same study area or replicated in other areas to quantify the effects of individual and choice related attributes on choice behavior.

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