Dissertations / Theses on the topic 'Multiple Discriminant Analysis (MDA)'

Civil Engineering Project Managers (CEPMs) plan, direct and coordinate a wide variety of construction projects, including buildings of all types of residential, commercial, and industrial structures, roads, bridges, wastewater treatment plants, schools and hospitals. CEPMs may supervise a whole civil engineering project or just part of a project and although CEPMs usually play no direct role in the actual construction of a structure, they typically schedule and coordinate all design and construction processes, including the selection, hiring and oversight of specialty trade contractors. CEPMs therefore, supervise the construction process from the conceptual development stage through to final construction whilst simultaneously meeting time, quality, economic, environmental and health and safety performance criteria as defined by the client. CEPMs evaluate and help determine appropriate construction delivery systems and the most cost-effective plan and schedule for completing the project. They divide all required construction site activities into logical steps, budgeting the time required to meet established deadline. Based upon the massive duties and responsibilities that CEPMs characteristically undertake before and throughout the whole construction cycle, this research has taken place. The predominant aim of this research is to develop a new mathematical model that can be used for classifying the aptitude (capability) of the Civil Engineering Project Manager (CEPM).

Travel and tourism marketers face a highly competitive environment brought on by the changing demographics of the U.S. population, the most significant change being the growth in size of the mature segment of the population. In terms of market size, there are currently 73 million people age 50 and older, comprising nearly one-fourth of the U.S. population (U.S. Census Bureau 2000). That number is expected to rise to 96 million by 2010, representing one-third of the population (Rasmusson 2000). A swelling population is not the only enticement that this age group offers. It is important to note that many mature consumers have deep pockets and a strong desire to spend. In fact, they control more than three-quarters of the wealth and one-half of the discretionary income in the nation. It is also estimated that they lay claim to three-fourths of the country's financial assets and boast more than $1 trillion in annual buying power. When all is said and done, this age group accounts for 40 percent of the total consumer demand in the United States (Swartz, 1999). However, even though recognizing the significance of the mature market in terms of their market size and economic potential, little research has been conducted to identify and understand the mature travelers who use the Internet.The main purpose of this study is to profile mature travelers on the basis of Internet use. More specifically, the intention is to examine the demographic and socio-economic characteristics of mature travelers who use the Internet compared to those who do not use the Internet. In addition, the purpose of the present study is to examine whether or not differences exist between Internet users and Internet non-users among mature travelers with respect to travel behavior. Attention is paid to investigate types of trip selected, the preferred activities participated in during the travel, length of stay, travel-related expenditures, type of lodging, type of transportation, number in the travel party, and type of travel party in explaining the differences between Internet users and Internet non-users of the mature market.Data were collected by utilizing a mailed questionnaire. 433 responses (23.44 percent of the total target population) were coded and used for data analysis. Data were analyzed by employing three types of data analysis: chi-square tests of independence; t-tests; and multiple discriminant analysis.The findings in the present study suggest that there are numerous differences in demographics, socio-economic characteristics, and travel characteristics between Internet users and Internet non-users among mature travelers. As a whole, for example, the results revealed that mature travelers who use the Internet were more likely to be younger, have higher annual household incomes, and have higher levels of education than mature travelers who do not use the Internet. Also, the results indicated that mature travelers who are still working are more likely to use the Internet than those who are not working. By understanding and utilizing information gathered from Internet users' and Internet non-users' demographics, socio-economic characteristics, and travel characteristics, tourism planners and marketers can develop appropriate and effective marketing strategies that appeal to mature travelers.
Master of Science

Session ID: SA-G4-2
Joint 4th International Conference on Soft Computing and Intelligent Systems and 9th International Symposium on advanced Intelligent Systems, September 17-21, 2008, Nagoya University, Nagoya, Japan

The purpose of this study is to investigate the usefulness of statistical decomposition measures in the prediction of industrial bond rating changes. Further, the predictive ability of decomposition measures is compared with multiple discriminant analysis on the same sample. The problem of this study is twofold. It stems in general from the statistical problems associated with current techniques employed in the study of bond ratings and in particular from the lack of attention to the study of bond rating changes. Two main hypotheses are tested in this study. The first is that bond rating changes can be predicted through the use of financial statement data. The second is that decomposition analysis can achieve the same performance as multiple discriminant analysis in duplicating and predicting industrial bond rating changes. To explain and predict industrial bond rating changes, statistical decomposition measures were computed for each company in the sample. Based on these decomposition measures, the two types of analyses performed were (a) a univariate analysis where each decomposition measure was compared with an industry average decomposition measure, and (b) a multivariate analysis where decomposition measures were used as independent variables in a probability linear model. In addition to statistical decomposition analysis, multiple discriminant analysis was used in duplicating and predicting bond rating changes. Finally, a comparison was made between the predictive abilities of decomposition analysis and discriminant analysis.

Le problème de détection et localisation d’anomalie peut être traité comme le problème du test entre des hypothèses multiples (THM) dans le cadre bayésien. Le test bayésien avec la fonction de perte 0−1 est une solution standard pour ce problème, mais les hypothèses alternatives pourraient avoir une importance tout à fait différente en pratique. La fonction de perte 0−1 ne reflète pas cette réalité tandis que la fonction de perte quadratique est plus appropriée. L’objectif de cette thèse est la conception d’un test bayésien avec la fonction de perte quadratique ainsi que son étude asymptotique. La construction de ce test est effectuée en deux étapes. Dans la première étape, un test bayésien avec la fonction de perte quadratique pour le problème du THM sans l’hypothèse de base est conçu et les bornes inférieures et supérieures des probabilités de classification erronée sont calculées. La deuxième étape construit un test bayésien pour le problème du THM avec l’hypothèse de base. Les bornes inférieures et supérieures des probabilités de fausse alarme, des probabilités de détection manquée, et des probabilités de classification erronée sont calculées. A partir de ces bornes, l’équivalence asymptotique entre le test proposé et le test standard avec la fonction de perte 0−1 est étudiée. Beaucoup d’expériences de simulation et une expérimentation acoustique ont illustré l’efficacité du nouveau test statistique
The anomaly detection and localization problem can be treated as a multiple hypotheses testing (MHT) problem in the Bayesian framework. The Bayesian test with the 0−1 loss function is a standard solution for this problem, but the alternative hypotheses have quite different importance in practice. The 0−1 loss function does not reflect this fact while the quadratic loss function is more appropriate. The objective of the thesis is the design of a Bayesian test with the quadratic loss function and its asymptotic study. The construction of the test is made in two steps. In the first step, a Bayesian test with the quadratic loss function for the MHT problem without the null hypothesis is designed and the lower and upper bounds of the misclassification probabilities are calculated. The second step constructs a Bayesian test for the MHT problem with the null hypothesis. The lower and upper bounds of the false alarm probabilities, the missed detection probabilities as well as the misclassification probabilities are calculated. From these bounds, the asymptotic equivalence between the proposed test and the standard one with the 0-1 loss function is studied. A lot of simulation and an acoustic experiment have illustrated the effectiveness of the new statistical test

Corporate failures pose a problem for banks, investors, customers, employees andinsurers. With a multivariate discrimination method, the study aims to find the specificfinancial ratios that most accurate reveals a company's financial health, which is ofinterest to all of the above parties. The data consist of 1042 Swedish small enterprisesand 30 different financial ratios between the years 2005‐2007. The result shows thatbankrupt firms three years before bankruptcy have a disadvantaged capital structurewith poor solvency and high debt. The year before bankruptcy, profitability and liquiditydeclined for bankruptcy group, and rates vary considerably in comparison with thesurviving companies. Our model can correctly classify 91,2 % of the total sample one yearbefore bankruptcy.

Företagskonkurser är dyrt för samhället och utgör ett problem för bland annat banker,investerare, kunder, anställda, försäkringsbolag och leverantörer. Studien syftar till attfinna de specifika nyckeltal vilka avslöjar ett företags finansiella hälsa, vilket är av intresseför alla ovanstående parter. Med en kvantitativ multivariat analysmetod har 30 olikanyckeltal från sammanlagt 1042 svenska mindre aktiebolag mellan åren 2005 och 2007studerats.Resultatet visar att konkursföretagen tre år innan konkurs har en missgynnandekapitalstruktur med svag soliditet och hög skuldsättning. Året innan konkurs harlönsamheten och likviditeten minskat för konkursgruppen och talen uppvisar storaskillnader i jämförelse med de överlevande företagen. Modellen klassificerar 91,2 % avföretagen korrekt ett år innan konkurs.

Context. Human oracle cost, the cost associated in estimating the correctness of the output for the given test inputs is manually evaluated by humans and this cost is significant and is a concern in the software test data generation field. This study has been designed in the context to assess metrics that might predict human oracle cost. Objectives. The major objective of this study is to address the human oracle cost, for this the study identifies the metrics that are good predictors of human oracle cost and can further help to solve the oracle problem. In this process, the identified suitable metrics from the literature are applied on the test input, to see if they can help in predicting the correctness of the output for the given test input. Methods. Initially a literature review was conducted to find some of the metrics that are relevant to the test data. Besides finding the aforementioned metrics, our literature review also tries to find out some possible code metrics that can be ap- plied on test data. Before conducting the actual experiment two pilot experiments were conducted. To accomplish our research objectives an experiment is conducted in the BTH university with master students as sample population. Further group interviews were conducted to check if the participants perceive any new metrics that might impact the correctness of the output. The data obtained from the experiment and the interviews is analyzed using linear regression model in SPSS suite. Further to analyze the accuracy vs metric data, linear discriminant model using SPSS pro- gram suite was used. Results.Our literature review resulted in 4 metrics that are suitable to our study. As our test input is HTML we took HTML depth, size, compression size, number of tags as our metrics. Also, from the group interviews another 4 metrics are drawn namely number of lines of code and number of <div>, anchor <a> and paragraph <p> tags as each individual metric. The linear regression model which analyses time vs metric data, shows significant results, but with multicollinearity effecting the result, there was no variance among the considered metrics. So, the results of our study are proposed by adjusting the multicollinearity. Besides, the above analysis, linear discriminant model which analyses accuracy vs metric data was conducted to predict the metrics that influences accuracy. The results of our study show that metrics positively correlate with time and accuracy. Conclusions. From the time vs metric data, when multicollinearity is adjusted by applying step-wise regression reduction technique, the program size, compression size and <div> tag are influencing the time taken by sample population. From accuracy vs metrics data number of <div> tags and number of lines of code are influencing the accuracy of the sample population.

Модель, як об’єкт, що штучно сконструйований дослідником, довільної природи (уявний чи матеріально реалізований), замінює або відтворює досліджуваний об’єкт-оригінал так, що розгляд його природної сутності здатний надавати нові дані об’єкта-оригіналу.

O fenómeno do e-commerce tem vindo a crescer em Portugal e jáa faz parte do dia-a-dia dos portugueses, complementarmente e/ou em alternativa ao comercio tradicional. Por isso, cada vez mais as empresas procuram compreender as tendências que moldam o comportamento do consumidor online e podem influenciar as suas praticas de consumo. Nesse sentido, este estudo tem como objetivo geral caracterizar os hábitos de e-commerce dos portugueses com 18 ou mais anos. Para o efeito foi elaborado um questionário e recolhida uma amostra pelo processo de amostragem em bola de neve. No processo de analise de dados, foram utilizadas as técnicas Analise de Correspondências Multiplas, função de Fisher resultante da Analise Discriminante e Regressão Logística, também com o objectivo de compreender a coerência entre os resultados e a complementariedade entre elas. Participaram no estudo 400 indivíduos, sendo a maioria mulheres (58%), residentes em diversos distritos de Portugal, com idades compreendidas entre os 18 e os 71 anos, tendo a maior parte um grau de instrução universitária. Os resultados permitiram concluir quais os produtos e serviços com maior compra/adesão online para cada um dos sexos, assim como inferir sobre as principais vantagens e desvantagens associadas a compra online, para ambos os sexos e para compradores e nao compradores. No que diz respeito a perceção de segurança nas compras online, este estudo revelou que metade dos participantes consideram este modo de compra seguro, sendo os fatores mais importantes para a percepcão de segurança a credibilidade da empresa/marca do produto e a variedade de meios de pagamento disponíveis; Abstract: CHARACTERIZATION OF E-COMMERCE BEHAVIOR The phenomenon of e-commerce has been growing in Portugal and is already part of the day to day life of the Portuguese, complementary and/or alternatively to traditional trade. Therefore, more and more companies seek to understand the trends shaping the online consumer behavior that can influence their consumption practices. In this sense, this study has the general objective to characterize the e-commerce habits of the Portuguese with 18 or more years. For this purpose, a questionnaire was prepared and a sample was collected with a snowball sampling process. In the process of data analysis, we used the following techniques: Multiple Correspondence Analysis, Fisher function resulting from the Discriminant Analysis and Logistic Regression. This study also has the aim of understanding the consistency between the results and the complementarity among these techniques. In this study, participated 400 individuals, the majority being women (58%), resident in several districts of Portugal, aged between 18 and 71 years, with most having a degree of university education. The results allowed to know the goods and services with higher purchase/online adherence by gender, as well as to inference about the main advantages and disadvantages associated with online shopping, for both sexes and for both buyers and no buyers. With regard to the security perception in online shopping, this study revealed that half of the participants consider online buying safe, and that the most important factors for the security perception are the credibility of the company / brand of the product and the variety of media available payment.

Dans ce travail, l'approche non-paramétrique par noyaux associés mixtes multivariés est présentée pour les fonctions de densités, de masse de probabilité et de régressions à supports partiellement ou totalement discrets et continus. Pour cela, quelques aspects essentiels des notions d'estimation par noyaux continus (dits classiques) multivariés et par noyaux associés univariés (discrets et continus) sont d'abord rappelés. Les problèmes de supports sont alors révisés ainsi qu'une résolution des effets de bords dans les cas des noyaux associés univariés. Le noyau associé multivarié est ensuite défini et une méthode de leur construction dite mode-dispersion multivarié est proposée. Il s'ensuit une illustration dans le cas continu utilisant le noyau bêta bivarié avec ou sans structure de corrélation de type Sarmanov. Les propriétés des estimateurs telles que les biais, les variances et les erreurs quadratiques moyennes sont également étudiées. Un algorithme de réduction du biais est alors proposé et illustré sur ce même noyau avec structure de corrélation. Des études par simulations et applications avec le noyau bêta bivarié avec structure de corrélation sont aussi présentées. Trois formes de matrices des fenêtres, à savoir, pleine, Scott et diagonale, y sont utilisées puis leurs performances relatives sont discutées. De plus, des noyaux associés multiples ont été efficaces dans le cadre de l'analyse discriminante. Pour cela, on a utilisé les noyaux univariés binomial, catégoriel, triangulaire discret, gamma et bêta. Par la suite, les noyaux associés avec ou sans structure de corrélation ont été étudiés dans le cadre de la régression multiple. En plus des noyaux univariés ci-dessus, les noyaux bivariés avec ou sans structure de corrélation ont été aussi pris en compte. Les études par simulations montrent l'importance et les bonnes performances du choix des noyaux associés multivariés à matrice de lissage pleine ou diagonale. Puis, les noyaux associés continus et discrets sont combinés pour définir les noyaux associés mixtes univariés. Les travaux ont aussi donné lieu à la création d'un package R pour l'estimation de fonctions univariés de densités, de masse de probabilité et de régression. Plusieurs méthodes de sélections de fenêtres optimales y sont implémentées avec une interface facile d'utilisation. Tout au long de ce travail, la sélection des matrices de lissage se fait généralement par validation croisée et parfois par les méthodes bayésiennes. Enfin, des compléments sur les constantes de normalisations des estimateurs à noyaux associés des fonctions de densité et de masse de probabilité sont présentés
This work is about nonparametric approach using multivariate mixed associated kernels for densities, probability mass functions and regressions estimation having supports partially or totally discrete and continuous. Some key aspects of kernel estimation using multivariate continuous (classical) and (discrete and continuous) univariate associated kernels are recalled. Problem of supports are also revised as well as a resolution of boundary effects for univariate associated kernels. The multivariate associated kernel is then defined and a construction by multivariate mode-dispersion method is provided. This leads to an illustration on the bivariate beta kernel with Sarmanov's correlation structure in continuous case. Properties of these estimators are studied, such as the bias, variances and mean squared errors. An algorithm for reducing the bias is proposed and illustrated on this bivariate beta kernel. Simulations studies and applications are then performed with bivariate beta kernel. Three types of bandwidth matrices, namely, full, Scott and diagonal are used. Furthermore, appropriated multiple associated kernels are used in a practical discriminant analysis task. These are the binomial, categorical, discrete triangular, gamma and beta. Thereafter, associated kernels with or without correlation structure are used in multiple regression. In addition to the previous univariate associated kernels, bivariate beta kernels with or without correlation structure are taken into account. Simulations studies show the performance of the choice of associated kernels with full or diagonal bandwidth matrices. Then, (discrete and continuous) associated kernels are combined to define mixed univariate associated kernels. Using the tools of unification of discrete and continuous analysis, the properties of the mixed associated kernel estimators are shown. This is followed by an R package, created in univariate case, for densities, probability mass functions and regressions estimations. Several smoothing parameter selections are implemented via an easy-to-use interface. Throughout the paper, bandwidth matrix selections are generally obtained using cross-validation and sometimes Bayesian methods. Finally, some additionnal informations on normalizing constants of associated kernel estimators are presented for densities or probability mass functions

by Pun Kam Wai, Peter.
Thesis (M.B.A.)--Chinese University of Hong Kong, 1990.
Bibliography: leaves 45-47.
ABSTRACT --- p.ii
TABLE OF CONTENTS --- p.iv
LIST OF TABLES --- p.v
ACKNOWLEDGEMENT --- p.vi
Chapter I. --- INTRODUCTION --- p.1
Chapter II. --- LITERATURE REVIEW --- p.3
Chapter III. --- RESEARCH METHODOLOGY --- p.9
Selection of Target Companies --- p.9
Selection of Control Companies --- p.10
Time Span of Study and Data Collection --- p.10
Computation of Financial Ratios --- p.12
Empirical Methods --- p.12
Multiple Discriminant Analysis --- p.16
Factor Analysis --- p.18
Splitting Data by Year --- p.19
Chapter IV. --- RESULTS OF EMPIRICAL STUDY --- p.21
Discriminant Analysis on Whole Data Set --- p.21
Factorization and Further Analysis on Whole Data Set --- p.23
Discriminant Analysis on Split Data Set --- p.27
Chapter V. --- ANALYSIS AND DISCUSSION --- p.36
Chapter VI. --- CONCLUSION --- p.40
Conclusion of Study --- p.40
Limitations of Study and Recommendations for Further Study --- p.40
APPENDIX --- p.44
BIBLIOGRAPHY --- p.45

This thesis provides a comprehensive ranking of 11 Czech statistical and 4 foreign credit scoring models. The ranking is based on the predictive performance of individual models, as measured by the area under curve, evaluated on a randomly sampled set of 250 training and validation samples. After establishing a baseline comparison, 3 avenues of estimation setup optimization are explored, namely missing value treatment, estimation method and the use of additional non-financial variables. After being optimized, the models are once again ranked based on their predictive performance. Statistical inference is drawn using ANOVA and the Friedman test, along with the corresponding Tukey and Nemeyi pos-hoc tests. In their baseline form, the Czech credit scoring models are found to be outperformed by the foreign benchmark model. Treating the missing values by OLS imputation and estimating the models by probit, significantly is found to significantly improve their predictive performance. In their optimized form, the difference in predictive performance between Czech and foreign credit scoring model is found to be only marginal. JEL Classification G28, G32, G33, G38 Keywords credit scoring, multiple discriminant analysis, logit analysis, probit analysis Author's e-mail 71247263@fsv.cuni.cz Supervisor's e-mail...

This thesis uses data of more than 180 banks from CEE region to identify the main determinants of long term credit ratings assigned to these banks in period between 2010 - 2012. This is done by employing two frequently used classification methods - Multiple Discriminant Analysis and Ordered Logit Model. The main contribution lies in including explanatory variables from various areas which have impact on financial health of examined banks. Apart from standard spheres of banks' performance such as capital adequacy, asset quality or profitability we investigate relevance of macroeconomic and qualitative factors as well. Although our results suggest that all mentioned areas are relevant for credit risk and hence rating assignment process the bank specific variables, both quantitative and qualitative, still play the key role.

When we develop and use species distribution models to predict species' current or potential distributions, we are faced with the trade-offs between model generality, precision, and realism. It is important to know how to improve and validate model generality while maintaining good model precision and realism. However, it is difficult for ecologists to evaluate species distribution models using field-sampled data alone because the true species response function to environmental or ecological factors is unknown. Species distribution models should be able to approximate the true characteristics and distributions of species if ecologists want to use them as reliable tools. Simulated data provide the advantage of being able to know the true species-environment relationships and control the causal factors of interest to obtain insights into the effects of these factors on model performance. I used a case study on Bythotrephes longimanus distributions from several hundred Ontario lakes and a simulation study to explore the effects on model performance caused by several factors: the choice of predictor variables, the model evaluation methods, the quantity and quality of the data used for developing models, and the strengths and weaknesses of different species distribution models. Linear discriminant analysis, multiple logistic regression, random forests, and artificial neural networks were compared in both studies. Results based on field data sampled from lakes indicated that the predictive performance of the four models was more variable when developed on abiotic (physical and chemical) conditions alone, whereas the generality of these models improved when including biotic (relevant species) information. When using simulated data, although the overall performance of random forests and artificial neural networks was better than linear discriminant analysis and multiple logistic regression, linear discriminant analysis and multiple logistic regression had relatively good and stable model sensitivity at different sample size and detection limit levels, which may be useful for predicting species presences when data are limited. Random forests performed consistently well at different sample size levels, but was more sensitive to high detection limit. The performance of artificial neural networks was affected by both sample size and detection limit, and it was more sensitive to small sample size.

The research was undertaken to analyse and evaluate the nature and quality of interactions in multicultural primary school classrooms. Special attention was focused on the influence 25 independent variables had on the dependent variable, namely group membership. Literature indicates that warm and nurturant relationships within the family help the child to achieve independence and promote social adjustment outside the home. Literature also reveals that self-acceptance and acceptance of others are dependent on the self-concept, and that acceptability in peer groups is enhanced by characteristics such as friendliness, cooperation, emotional stability and intellectual ability. It is essential to mention that some researchers claim that within multicultural classrooms, pupils often interact in racially and culturally segregated patterns. Others maintain that no racial and cultural discrimination is evident in the choice of friends in multicultural classrooms. The empirical research was undertal<.en by administering four measuring instruments, namely own designed questionnaire, the sociogram, the self-concept scale for primary school pupils and the children's personality questionnaire to 121 standard five pupils in multicultural primary schools. The administering of these instruments was aimed at determining the influence of the independent variables on the dependent variable. The stepwise discriminant analysis method revealed that of the 25 independent variables, only six, namely family background, friendship skills, gender, scholastic achievement and personality factors E (submissive versus dominant) and Q3 (undisciplined versus controlled) contributed to the variance in group membership. The multiple discriminant function was used to determine how close the individual scores of children were, in a given friendship group. The general pattern obtained, indicated that children choose each other on the basis of similar characteristics. A point that clearly came to light, is that race and language/culture do not contribute to the variance in group membership. Children formed various friendship groups across racial and cultural lines. In view of the aforementioned findings, the researcher made recommendations on ways in which parents and teachers can create suitable teaching and learning environments for children from diverse cultural milieus.
Psychology of Education
D.Ed. (Psychology of Education)

The prediction of a company's financial health is of critical importance to a variety of stakeholders ranging from auditors, creditors, customers, employees, financial institutions and investors through to management. There has been considerable research in this field, ranging from the univariate dichotomous approach of Beaver (1966) to the multivariate multi-state approaches of Lau (1987) and Ward (1994). All of the South African studies namely, Strebel and Andrews (1977), Daya (1977), De La Rey (1981), Clarke et al (1991) and Court et al (1999), and even, Lukhwareni's (2005) four separate models, were dichotomous in nature providing either a "Healthy" or a "Failed" state; or a "Winner" or "Loser" as in the latter case. Notwithstanding, all of these models would be classified as first stage, initial screening models. This study has focused on following a two stage approach to identifying (first stage) and analysing (second stage) the States of Health in a company. It has not adopted the rigid "Healthy" or "Failed" dichotomous methodology. For the first stage, three-state models were developed classifying a company as Healthy, Intermittent or Distressed. Both three year and five year Profit after Tax (PAT) averages for Real Earnings Growth (REG) calculations were used to determine the superior definition for the Intermittent state; with the latter coming out as superior. Models were developed for the current year (Yn), one (Yn-1), two (Yn-2) and three years (Yn-3) forward using a Test sample of twenty companies and their predictive accuracy determined by using a Holdout sample of twenty-two companies and all their data points or years of information. The statistical methods employed were a Naïve model using the simple Shareholder Value Added (SVA) ratio, CHAID and MDA, with the latter providing very disappointing results - for the Yn year (five year average), the Test sample results were 100%, 95% and 95%, respectively; with the Holdout sample results being 81.3%, 83.8% and 52.5%, respectively. The Yn-1 to Yn-3 models produced very good results for the Test sample but somewhat disappointing Holdout sample results. The best two Yn models namely, the Naïve and the CHAID models, were modified so as to enable a comparison with the notable, dichotomous De La Rey (1981) model. As such, three different approaches were adopted and in all cases, both the modified Naïve (100%, 81.3%, 100%) and the modified CHAID (100%, 85.9%, 98%) produced superior results to the De La Rey model (84.8%, 62.6%, 75.3%). For the second stage, a Financial Risk Analysis Model (FRAM) using ratios in the categories of Growth, Performance Analysis, Investment Analysis and Financial Status were used to provide underlying information or clues, independent of the first stage model, so as to enable the stakeholder to establish a more meaningful picture of the company. This would pave the way for the appropriate strategy and course of action to be followed, to take the company to the next level; whether it be taking the company out of a Distressed State (D) or further improving on its Healthy status (H).
Business Management
D. BL.

O negócio bancário está exposto a diferentes fontes de risco, cujos efeitos podem ser adversos tanto ao nível do capital próprio como da sua rendibilidade. O principal risco inerente à actividade bancária é denominado de ‘risco de crédito’, que se identifica com a probabilidade de um devedor não cumprir com as obrigações contratuais acordadas. A incidência de risco de crédito permite quantificar o valor da perda esperada associada a um crédito individual. Para o efeito, devem ser calculados diferentes parâmetros: a probabilidade de incumprimento (PD), a perda em caso de incumprimento (EAD) e a exposição a incumprimento (LGD). O presente estudo aplica quatro métodos econométricos para a estimação da probabilidade de incumprimento, designadamente os modelos de probabilidade linear, logit, probit e a análise discriminante múltipla. A amostra utilizada incide sobre 200 contratos de empréstimo para aquisição de habitação, originados entre os anos de 2000 e 2010, incluindo contratos afectados por evento de default durante o ano de 2011, e contratos sem ocorrência de default no mesmo período.
Banks are exposed to different sources of risk which may affect its equity levels and profitability. The main risk approached is called ‘credit risk’, defined by the probability of a debtor to default with the agreed contractual terms. This risk allows us to quantify the expected loss regarding an individual credit, which depends on three different parameters: the probability of default (PD), the exposure at default (EAD) and the loss given default (LGD). The following study applies four econometric techniques to estimate the probability of default, namely, linear probability model, logit, probit and multiple discriminant analysis. The sample collected covers 200 mortgage residential loans, originated between 2000 and 2010, including contracts affected by a default event during 2011 and contracts free of default event during the same year.