Kesikli seçim modelleri ve İstanbul'daki deniz yolları için araba sahipliği modeli

Abstract

Bu çalışma iki bölümden oluşmaktadır. İlk bölümde Kesikli Seçim modellerinin geniş bir tanıtımı yapılmaktadır. İkinci bölümde ise İstanbul'da eviyle işi arasında şehrhatları gemileri ve denizotobüsleri ile günlük yolculuk yapan deniz yolcularının araba sahipliği davranışları incelenmektedir. Kesikli Seçim Modeli, bağımlı değişkeninin kesikli değerler alması nedeniyle Genel Doğrusal Regresyon modelinin özel bir durumu olduğu kabul edilir. Kesikli bağımlı değişkenin aldığı değerler karar vericiye sunulan seçeneklerdir. Modelin açıklayıcı değişkenleri ise karar vericiyi ve seçtiği seçeneği tanımlayan değişkenlerdir. Kesikli Seçim Modelleri, En Yüksek Olabilirlik yöntemi ile tahmin edilebilirler. Örneklem yeterince büyük ise tahminler sapmasız ve etkindir. Öte yandan tahmin edilen modelleri karşılaştırmak için uyum iyiliği ölçütleri tanımlanmıştır. Uygulama bölümünde İstanbul'da şehirhatlan gemilerinde ve denizotobüslerinde günlük yolculuk yapan deniz yolcuları için araba sahipliği modeli geliştirilmiştir. Modelin bağımlı değişkeni araba sahipleri için 1 ve araba sahibi olmayanlar için 0 değerlerini alan kesikli değişkendir. Açıklayıcı değişkenler ise bireyin aylık geliri, yaşı, cinsiyeti ve üniversite mezunu olup olmadığı ile eviyle işi arasındaki yol mesafesidir. Modelin tahmini için gerekli veri kümesi, Temel Mühendislik A.Ş. tarafından yapılan İstanbul Büyükşehir Ulaşım Nazım Planı çerçevesinde gerçekleştirilen anket çalışmasından elde edilmiştir. Üç ayrı model çalışması yapılmıştır. İlk model şehirhatlan yolcularının, ikinci model denizotobüsleri yolcularının ve üçüncü model ise toplam veri kümesinin araba sahipliği modelidir. Ancak değerlendirmeler ilk iki model için yapılmaktadır.

This study is a treatise on empirical microeconomics. It describes the econometric theory of discrete choice models and the empirical practise of modelling carownership. Accordingly, the study has two parts. The first part gives a detailed survey of discrete choice models with the emphasis on binary case. The second part concentrates on the carownership of commuters across the bosphorus on both ferries and seabuses in Istanbul. Discrete choice models have proved to be a very convenient apparatus to study human behaviour. Since the connection between human behaviour and the factors affecting it cannot be tested directly, discrete choice models are resorted to investigate this complex phenomena. Discrete choice models are characterized by a dependent dummy variable that indicates which alternative is chosen among a finite set of alternatives. Therefore the dependent variable has a nominal character, and its value is a label without numerical content. Discrete choice models arise from two situations, either naturally because the dependent variable is of qualitative rather than quantitative nature, or by categorization of an originally continuous dependent variable. Examples of naturally qualitative variables are labour force participation, occupation, the choice of transportation and travel mode, brand choice etc. Examples for categorized variables which are originally continuous are trip timing, location, household consumption etc. vn The discrete choice model has the form of; Pr( behaviour = b / B ) = f( b / B, x, 8 ) where b is an alternative in a finite choice set B, x is a vector of attributes defining choice set and decision maker, 6 is a vector of unknown parameters to be estimated and P gives the conditional probability that, given x, b will be selected among the finite choice set B. Thus the formulation of f( b / B, x, 9 ) consistent with the rational choice behaviour and inference on the parameters 8 from observations of the choice made by samples of decision makers are the concerns of the first part of the study. According to the number of alternatives within the dependent variable, discrete choice models are investigated as binary choice and multinomial choice models. In the former, there are only two alternatives available to decision makers, and in the latter more than two alternatives are presented to them. In binary choice models, the dependent variable takes two values 0 and 1. The most commonly used forms of probability function f are Linear Probability Model (LPM), Probit and Logit models, and these models are originally cumulative uniform, normal and logistic distribution functions respectively. Since a discrete choice model consistent with rational choice behaviour has to be non-linear with its explanatory variables and lie between 0 and 1, LPM is found not to satisfy these conditions. Therefore Probit and Logit models are only extended to multinomial case. Since logistic distribution is a very good approximation to normal distribution, these two models are very similar to one another, and it does not matter much whether one uses a probit model or logit model, except in cases where data are heavily concentrated in the tails. If the decision maker is faced on three or more alternatives multinomial models are used to analyze the problem. Li this case, the dependent variable takes m+1 values 0,l,2,...,m. viii Although there are several multinomial models available, the Multinomial Probit and Logit models are the commonly used ones. However, if the assumption of independence of alternatives is not satisfied in Multinomial Logit model, which turns out to be true in most situations, this model is no longer consistent with rational choice. On the other hand, the Multinomial Probit model happens to be uncontrollable to estimate if there are especially more than four alternatives. In either multinomial or binary choice model, it is assumed that the decision maker always chooses the alternative that maximizes his or her utility. This is, of course, the general definition of utility maximisation concept Both types of models are very well estimated by the use of maximum likelihood method, and the estimates are proved to be BLUE in large samples only. Though there are several goodness of fit measures available to the researcher, none of them is universally accepted. Thus, two or more measures should be used at the same time to find out the best model. In the application, it is aimed at developing a model of carownership of commuters across the bosphorus on both of the ferries and seabuses in Istanbul. The model is a binary choice model with a dependent variable which takes the values 1 for carowners and 0 for non-carowners. The explanatory part of the model consists of two distinct parts. The first part gives information about the individual's socio-economic characteristics such as monthly income, age, sex, university education. The first two explanatory variables are continuous and the second two are discrete. These variables other than sex are all presumed to have positive effect on the carownership, which is proved to be true by previous carownership studies. For the sex variable we have no expectation. The second part is the distance between origin and destination of the commuter if he is to drive to his destination. To the contrary of previous studies, this ix variable is presumed to be negatively affecting the carownership. This may be acknowledged to some conditions of Istanbul only, such as the availability of public transport services, relatively higher prices of gasoline, the difficulty in finding parking area etc. The data to calibrate the model are from a survey sample carried out by Temel Mühendislik A.S. within the Istanbul Master Plan Transport study. After leaving out the observations of the commuters who do not have regular income such as students, housewives, unemployeds etc., there is left 423 and 293 observations of ferries and seabuses, respectively. Thus, we attempt to construct three distinct carownership models. The first two models are of the commuters of ferries and seabuses, respectively, and the third model is of the total number of commuters obtained by adding up the observations of the two marine vechiles. By the previous studies, we are convinced that the Logit model is theoretically correct specification of carownership behaviour. The variable selection is made in a stepwise manner. Only the variables significantly increasing the loglikelihood value of the model are kept in at the end of each step, and this procedure ends where the inclusion of a new variable no longer increases the loglikelihood value significantly. Thus the final forms of the models are obtained as follows; For the commuters of ferries; f = f ( Monthly income, Age, Distance ) For the commuters of seabuses; f = f ( Monthly income, Graduation, Distance ) x For the total number of commuters; f = f ( Monthly income, Graduation, Age, Distance ) However, it is found that Logit model specification does not fit well the observations of the total number of commuters according to the goodness of fit measure of interest Therefore, the last model is given up at this stage and inferences are drawn for the first two models only. The LOGIT (2.0) package is used to estimate the models. The signs of estimated coefficients turn out to confirm our expectations. All the coefficients are found to be statistically significantly different from zero either individually or simultaneously. The monthly income and distance variables take place in both models. In the ferries' model, the absolute values of the coefficients of these two variables are greater than the ones in the seabuses' model. Since the coefficient of any variable gives the percent change of the log odds ratio for unit change of the variable, it is observed that the ferries model is more sensitive to the possible changes of these variables than the seabuses model. Thus, it can be concluded that the carownership of the ferries' commuters is more affected by the changes in their incomes and distances of their travels between origin and destination than the carownership of seabuses' commuters. On the other hand, the negative sign of distance coefficient arises very important conclusion. Since, as the distance of a travel increases, the cost and the time of the travel increase proportionally. Therefore, it can be concluded that, the commuters of both marine vechiles tend to keep their travel costs low at the expense of their travel time.