No description available.

No description available.

Bus transit driving is an occupation that requires high concentration in driving and is demanding due to work overload, time pressure, and responsibility for lives. In 2006, there were 103 fatal crashes involving transit buses. As the number of distraction-related crashes increases, it is important to conduct a transit distraction study to reduce future crashes. This thesis focused on the analysis of the likelihood of the operator distraction behaviors and the analysis to find a predictive model to classify different distraction categories. An ordinal logistic regression was carried out to evaluate how age, gender, driving experience of the operators, and their driving frequencies accounts for the likelihood of 17 potential distracted driving behaviors. The results of this analysis showed that there were only 5 best models (p-value of model fit less than 0.005 and p-value of parallel line test more than 0.005) that could be constructed, including: listening to the radio/ CD/DVD/MP3 player (D1); picking Up and Holding 2-way Radio (D5); listening to the Dispatch Office broadcast (D6); adjusting switches/controls on dashboard (D15); and utilizing mentor ranger (D16). On the other hand, a discriminant analysis was performed to predict how different transit operator driving behaviors when exposed by 10 different distraction activities and 16 predictors were considered in this analysis. The final results showed that there are 4 predictors that seem to be able to classify distraction groups across all 4 models; those include segment length, average duration of idling time/stop delay at speed interval 0—4 km/hr, frequency of speed transitions that deviate by ± 0 to 4 km/hr from its speed, and frequency of speed transitions that deviate by ± 8 to 12 km/hr from its speed. / Master of Science

Discriminant analysis is a procedure for identifying the relationships between qualitative criterion variables and quantitative predictor variables. Data bases of genetic polymorphisms are currently available that group such polymorphisms by ethnic origin or nationality. Such information could be useful to entities that base financial determinations upon predictions of disease or to medical researchers who wish to target prevention and treatment to population groups. While the use of genetic information to make such determinations is unlawful in states and confidentiality and privacy concerns abound, methods for human “redlining” may occur. Thus, it is necessary to investigate the efficacy of the relationship of certain genetic information to ethnicity to determine if a statistical analysis can provide information concerning such relationship. The use of the statistical technique of discriminant analysis provides a tool for examining such relationship.

The distributional properties of improvement-over-chance, I, effect sizes derived from linear and quadratic predictive discriminant analysis (PDA) and from logistic regression analysis (LRA) for the two-group univariate classification were examined. Data were generated under varying levels of four data conditions: population separation, variance pattern, sample size, and prior probabilities. None of the indices provided acceptable estimates of effect for all the conditions examined. There were only a small number of conditions under which both accuracy and precision were acceptable. The results indicate that the decision of which method to choose is primarily determined by variance pattern and prior probabilities. Under variance homogeneity, any of the methods may be recommended. However, LRA is recommended when priors are equal or extreme and linear PDA is recommended when priors are moderate. Under variance heterogeneity, selecting a recommended method is more complex. In many cases, more than one method could be used appropriately.

Evaluating classifiers in controlled settings is essential for empirical applications, as extensive knowledge on model-behaviour is needed for accurate predictions. This thesis investigates robustness against non-normality of two prominent classifiers, LDA and QDA. Through simulation, errors in leave-one-out cross-validation are compared for data generated by different multivariate distributions, also controlling for covariance structures, class separation and sample sizes. Unexpectedly, the classifiers perform better on data generated by heavy-tailed symmetrical distributions than by the normal distribution. Possible explanations are proposed, but the cause remains unknown. There is need for further studies, investigating more settings as well as mathematical properties to verify and understand these results.

No description available.

Thesis (MBA)--Stellenbosch University, 2000. / ENGLISH ABSTRACT: The assumption underlying this study is that the regime of the economy imparts certain characteristics to the business cycle indicators and that by using a discriminant analysis it would be possible to gain information from the various indicators as to the state of activity in the economy. A discriminant analysis was developed on an Excel spreadsheet. The Schwartz Information Criterion, SIC, was calculated for the models. This value compares how closely the model follows the true data generating process. The discriminant analysis was performed using all the variables or indicators applicable to the model in question. Using a linear programming algorithm the variables were removed from the model in order to maximise the SIC value for the model. The result was a variable set that maximised the information about the regime of the economy available from the various economic indicators. The models' performance was evaluated for post sample performance in a test data set. Five models were developed. They were: • the coincident logistic model; • the one period ahead logistic CLI (composite leading indicator) model; • the one period ahead logistic component model; • the three period ahead logistic CLI model; and • the three period ahead logistic component model. All the models produced meaningful results in the estimation data set for the United States economy. In the test data set only the coincident logistic model was found to give a clear signal of the regime switch. All models applied to the US data showed activity around all the regime switches. Two of the models did not produce useful results when applied to South African economic data. For this reason the one and two period ahead logistic component models were not used. The remaining three models gave clear signals of regime switches for all regime switches in the estimation and the test data set. The best overall model as far as SIC value was the one period ahead logistic CLI model applied to the South African data. The highest SIC for a model applied to the United States data is the logistic coincident model. The models were also evaluated on the number of wrong classifications. The best model in this regard is the coincident logistic model and one period ahead logistic CLI model applied to the United States data. The most accurate model for the South African data was the one-month ahead logistic CLI model in the estimation data set and the logistic coincident model in the test data set. The models were more decisive in the South African data than in the United States data set having a much lower region of uncertainty. Taking into consideration the greater decisiveness in conjunction with accuracy the models performed better with the South African data. The discriminant analysis generates a probability of expansion, which is used in conjunction with a classification rule based on observed frequencies in the estimation data set. A plot of the probability of expansion calculated by the models versus the true data generating process reveals that the models provide meaningful information as to the regime of the economy. The models tend to lag the true data generating process but do show activity around the regime switches. The models when applied to the United States data show good correlation with the true data generating process over the estimation data set but not as good over the test data set. The models perform better when applied to South African data when evaluated graphically. The models when applied to the South African data give good clear signals over all regime switches in all data sets. Indications of regime switches in the estimation data set were clearer than in the test data set. The use of a discriminant analysis for regime classification has been proven to be effective. This method should be used in conjunction with other methods to evaluate business cycle regimes. Useful information is extracted as regards the state of the economy from the various economic indicators. For this reason discriminant analysis of business cycles can be used as an additional tool for the evaluation of business cycle regimes. / AFRIKAANSE OPSOMMING: Die onderliggende aanname van hierdie studie is dat die ekonomiese stelsel sekere eienskappe aan die sakesiklus verleen, en dat 'n diskriminant ontleding dit moontlik maak om inligting te verkry uit die verskeie aanwysers oor die stand van ekonomiese aktiwiteite. 'n Diskriminant ontleding is op 'n Excel-sigblad ontwerp. Die Schwartz Informasie Kriterium (SIK) is vir die modelle bereken. Hierdie waarde dui aan hoe getrou die model die ware datagenereringsproses volg. Die diskriminant ontleding is gedoen deur gebruik te maak van al die veranderlikes of aanwysers wat van toepassing is op die betrokke model. Die veranderlikes is uit die model verwyder deur die gebruik van 'n lineêre programmerings algoritme, ten einde die SIK-waarde van die model te maksimaliseer. Die resultaat was 'n stel veranderlikes wat inligting via die verskeie ekonomiese aanwysers oor die beskikbare ekonomiese stelsel maksimaliseer het. Die model is vir buite-steekproef prestasie in 'n toetsdatastel evalueer. Die volgende vyf modelle is ontwikkel: • samevallende logistiese model • een periode vooruit logistiese saamgestelde leidende aanwysers (SLA)- model • een periode vooruit logistiese komponentmodel • drie periode vooruit logistiese SLA-model • drie periode vooruit logistiese komponentmodel. Al die modelle het betekenisvolle resultate in die steekproefdata vir die ekonomie van die VSA gelewer. In die toetsdatastel het slegs die samevallende logistiese model 'n duidelike aanduiding van regime-verandering gegee. Alle modelle wat op die VSA data toegepas is, het aktiwiteite rondom al die regime-veranderings aangetoon. Twee van die modelle wat op Suid-Afrikaanse data toegepas is, het nie bruikbare resultate opgelewer nie, en om hierdie rede is die een en twee periodes vooruit logistiese komponentmodelle nie gebruik nie. Die oorblywende drie modelle het duidelike aanduidings van regime-veranderings vir alle regime-veranderings aangetoon in die steekproefdata en die toetsdatastel. Die beste oorkoepelende model in terme van SIK-waarde was die een periode vooruit logistiese SLA-model wat op Suid-Afrikaanse data toegepas is. Die grootste SIK-waarde vir 'n model wat op VSA-data toegepas is, is vir die samevallende logistiese model. Modelle is ook evalueer in terme van die foutiewe klassifikasies. Die beste model in hierdie verband is die samevallende logistiese model en die een periode vooruit logistiese SLA-model wat op VSA-data toegepas is. Die mees akkurate model vir Suid-Afrikaanse data was die een maand vooruit logistiese SLA-model in die steekproef datastel en die samevallende logistiese model in die toetsdatastel. Die modelle was meer beslissend in die Suid-Afrikaanse data as in die VSA-datastel, omdat die Suid-Afrikaanse data 'n baie kleiner onsekerheidsgebied openbaar het. Gegewe die groter beslistheid tesame met akkuraatheid, het die modelle beter presteer met Suid-Afrikaanse data. Die diskriminant ontleding skep 'n opswaaiwaarskynlikheid, wat saam met 'n klassifikasiereël, gebaseer op die waargenome frekwensies in die steekproefdata, gebruik word. 'n Stip van die opswaaiwaarskynlikhede, bereken volgens die modelle versus die ware datagenereringsproses, dui daarop dat die modelle betekenisvolle inligting oor die ekonomiese stelsel bied. Die modelle neig om die ware datagenereringsproses te volg, maar toon tog beweging rondom regime-veranderings. Die modelle het goeie korrelasie met die ware datagenereringsproses oor die steekproefdatastel getoon op die VSA-data, maar nie juis goeie korrelasie oor die toetsdatastel nie. Die modelle presteer beter wanneer dit op Suid-Afrikaanse data toegepas word, en gee goeie, duidelike tekens oor alle regime-veranderings in alle datastelle. Aanduidings van regime-veranderings in die steekproefdatastel was duideliker as in die toetsdatastel. 'n Diskriminant ontleding vir stelselklassifikasie het effektief geblyk te wees. Hierdie metode behoort saam met ander metodes gebruik te word om sakesiklusstelsels te evalueer. Nuttige inligting word uit die verskillende ekonomiese aanwysers verkry oor die stand van die ekonomie. Juis om hierdie rede kan 'n diskriminant ontleding van sakesiklusse as bykomende instrument gebruik word om sakesiklusse te evalueer.

Thesis (PhD)--Stellenbosch University, 1997. / One copy microfiche. / ENGLISH ABSTRACT: Discriminani analysis and logistic regression are techniques that can be used to classify entities of unknown origin into one of a number of groups. However, the underlying models and assumptions for application of the two techniques differ. In this study, the two techniques are compared with respect to classification of entities. Firstly, the two techniques were compared in situations where no data dependent variable selection took place. Several underlying distributions were studied: the normal distribution, the double exponential distribution and the lognormal distribution. The number of variables, sample sizes from the different groups and the correlation structure between the variables were varied to' obtain a large number of different configurations. .The cases of two and three groups were studied. The most important conclusions are: "for normal and double' exponential data linear discriminant analysis outperforms logistic regression, especially in cases where the ratio of the number of variables to the total sample size is large. For lognormal data, logistic regression should be preferred, except in cases where the ratio of the number of variables to the total sample size is large. " Variable selection is frequently the first step in statistical analyses. A large number of potenti8.Ily important variables are observed, and an optimal subset has to be selected for use in further analyses. Despite the fact that variable selection is often used, the influence of a selection step on further analyses of the same data, is often completely ignored. An important aim of this study was to develop new selection techniques for use in discriminant analysis and logistic regression. New estimators of the postselection error rate were also developed. A new selection technique, cross model validation (CMV) that can be applied both in discriminant analysis and logistic regression, was developed. ."This technique combines the selection of variables and the estimation of the post-selection error rate. It provides a method to determine the optimal model dimension, to select the variables for the final model and to estimate the post-selection error rate of the discriminant rule. An extensive Monte Carlo simulation study comparing the CMV technique to existing procedures in the literature, was undertaken. In general, this technique outperformed the other methods, especially with respect to the accuracy of estimating the post-selection error rate. Finally, pre-test type variable selection was considered. A pre-test estimation procedure was adapted for use as selection technique in linear discriminant analysis. In a simulation study, this technique was compared to CMV, and was found to perform well, especially with respect to correct selection. However, this technique is only valid for uncorrelated normal variables, and its applicability is therefore limited. A numerically intensive approach was used throughout the study, since the problems that were investigated are not amenable to an analytical approach. / AFRIKAANSE OPSOMMING: Lineere diskriminantanaliseen logistiese regressie is tegnieke wat gebruik kan word vir die Idassifikasie van items van onbekende oorsprong in een van 'n aantal groepe. Die agterliggende modelle en aannames vir die gebruik van die twee tegnieke is egter verskillend. In die studie is die twee tegnieke vergelyk ten opsigte van k1assifikasievan items. Eerstens is die twee tegnieke vergelyk in 'n apset waar daar geen data-afhanklike seleksie van veranderlikes plaasvind me. Verskeie onderliggende verdelings is bestudeer: die normaalverdeling, die dubbeleksponensiaal-verdeling,en die lognormaal verdeling. Die aantal veranderlikes, steekproefgroottes uit die onderskeie groepe en die korrelasiestruktuur tussen die veranderlikes is gevarieer om 'n groot aantal konfigurasies te verkry. Die geval van twee en drie groepe is bestudeer. Die belangrikste gevolgtrekkings wat op grond van die studie gemaak kan word is: vir normaal en dubbeleksponensiaal data vaar lineere diskriminantanalise beter as logistiese regressie, veral in gevalle waar die. verhouding van die aantal veranderlikes tot die totale steekproefgrootte groot is. In die geval van data uit 'n lognormaalverdeling, hehoort logistiese regressie die metode van keuse te wees, tensy die verhouding van die aantal veranderlikes tot die totale steekproefgrootte groot is. Veranderlike seleksie is dikwels die eerste stap in statistiese ontledings. 'n Groot aantal potensieel belangrike veranderlikes word waargeneem, en 'n subversamelingwat optimaal is, word gekies om in die verdere ontledings te gebruik. Ten spyte van die feit dat veranderlike seleksie dikwels gebruik word, word die invloed wat 'n seleksie-stap op verdere ontledings van dieselfde data. het, dikwels heeltemal geYgnoreer.'n Belangrike doelwit van die studie was om nuwe seleksietegniekete ontwikkel wat gebruik kan word in diskriminantanalise en logistiese regressie. Verder is ook aandag gegee aan ontwikkeling van beramers van die foutkoers van 'n diskriminantfunksie wat met geselekteerde veranderlikes gevorm word. 'n Nuwe seleksietegniek, kruis-model validasie (KMV) wat gebruik kan word vir die seleksie van veranderlikes in beide diskriminantanalise en logistiese regressie is ontwikkel. Hierdie tegniek hanteer die seleksie van veranderlikes en die beraming van die na-seleksie foutkoers in een stap, en verskaf 'n metode om die optimale modeldimensiete bepaal, die veranderlikes wat in die model bevat moet word te kies, en ook die na-seleksie foutkoers van die diskriminantfunksie te beraam. 'n Uitgebreide simulasiestudie waarin die voorgestelde KMV-tegniek met ander prosedures in die Iiteratuur. vergelyk is, is vir beide diskriminantanaliseen logistiese regressie ondemeem. In die algemeen het hierdie tegniek beter gevaar as die ander metodes wat beskou is, veral ten opsigte van die akkuraatheid waarmee die na-seleksie foutkoers beraam word. Ten slotte is daar ook aandag gegee aan voor-toets tipeseleksie. 'n Tegniek is ontwikkel wat gebruik maak van 'nvoor-toets berarningsmetode om veranderlikes vir insluiting in 'n lineere diskriminantfunksie te selekteer. Die tegniek ISin 'n simulasiestudie met die KMV-tegniek vergelyk, en vaar baie goed, veral t.o.v. korrekte seleksie. Hierdie tegniek is egter slegs geldig vir ongekorreleerde normaalveranderlikes, wat die gebruik darvan beperk. 'n Numeries intensiewe benadering is deurgaans in die studie gebruik. Dit is genoodsaak deur die feit dat die probleme wat ondersoek is, nie deur middel van 'n analitiese benadering hanteer kan word nie.

In the last twelve years there has been considerable research interest in mathematical programming approaches to the statistical classification problem, primarily because they are not based on the assumptions of the parametric methods (Fisher's linear discriminant function, Smith's quadratic discriminant function) for optimality. This dissertation focuses on the development of mathematical programming models for the three-group classification problem and examines the computational efficiency and classificatory performance of proposed and existing models. The classificatory performance of these models is compared with that of Fisher's linear discriminant function and Smith's quadratic discriminant function. Additionally, this dissertation investigates theoretical characteristics of mathematical programming models for the classification problem with three or more groups. A computationally efficient model for the three-group classification problem is developed. This model minimizes directly the number of misclassifications in the training sample. Furthermore, the classificatory performance of the proposed model is enhanced by the introduction of a two-phase algorithm. The same algorithm can be used to improve the classificatory performance of any interval-based mathematical programming model for the classification problem with three or more groups. A modification to improve the computational efficiency of an existing model is also proposed. In addition, a multiple-group extension of a mathematical programming model for the two-group classification problem is introduced. A simulation study on classificatory performance reveals that the proposed models yield lower misclassification rates than Fisher's linear discriminant function and Smith's quadratic discriminant function under certain data configurations. Data configurations, where the parametric methods outperform the proposed models, are also identified. A number of theoretical characteristics of mathematical programming models for the classification problem are identified. These include conditions for the existence of feasible solutions, as well as conditions for the avoidance of degenerate solutions. Additionally, conditions are identified that guarantee the classificatory non-inferiority of one model over another in the training sample.