CHAPTER 1 Introduction
1.4 Research Contributions
The main contributions of this study could be summarized as follows:
(1) The concept of individual’s vehicle dependence in terms of both its socioeconomic and its psychological nature can be conceptualized.
(2) The exploration of vehicle dependence can benefit the related researchers in modifying their formulations of mode choice, and policy makers in enacting more effective policies.
(3) Our concepts and approaches for assessing the level of a single latent construct can serve as a useful example for researchers who have to treat some latent constructs as the influencing variables in their statistical inference.
(4) The realization of the difficulties in the necessary actions or motions that an elderly passenger might encounter when using buses can help to suggest the necessary improvements of facilities and service of bus systems, which provide a safer and friendlier bus service for the elderly travelers.
CHAPTER 2
Literature Review
2.1 Development of the Concept on the Vehicle Dependence
In the Oxford Advanced Learner’s Dictionary, there are two meanings for the word
“dependence”: one is “a state of needing the help and support of somebody/something in order to survive or be successful”, and the other is “the state of being addicted to something”
Economic considerations are the most common and convincing reasons for travelers’
dependence upon specific vehicles (Koppelman, 1981). That is, some travelers are forced to depend on only a specific vehicle because their choice sets are constrained, i.e. they have no other alternative to choose from or their best alternative is out of their acceptable range. The limitations on their choice set may arise from their own abilities (e.g. their ability to operate other vehicles or their ability to afford the cost of using another vehicle) or from environmental conditions (e.g. the lack of a public transportation service). Such travelers are regarded as having structural dependences on a vehicle (Gray et al., 2001), and they are also called “captive riders” (Abe and Sinha, 1973) of that vehicle.
Psychological preferences or considerations also influence travelers’ dependence on the usage of vehicles (Fujii and Garling, 2003; Vredin Johansson et al., 2006). Some people depend on a specific type of vehicle because they can receive direct feedback from the use of such a vehicle. For instance, travelers with an enthusiasm for driving automobiles would depend on automobile usage to achieve most of their daily trips. Special preferences or beliefs could also lead a traveler to depend on a specific type of vehicle. For example, travelers who emphasize the value of privacy and comfort during trips would tend to drive or ride in automobiles, and travelers with a strong awareness of environmental issues might tend to use
vehicles which produce little pollution.
People’s vehicle dependence is also thought to be a result of habitual behavior (Bamberg et al., 2003; Thogersen, 2006). Habitual behavior can be formulated into two processes:
initiation and persistence (Ronis et al., 1989). During the stage of initiation, decisions are still made rationally. However, when the same behavior has been repeated for long enough, decisions that have been made become automatic and habitual as a result of a persistence process. Decision makers then make choices without evaluating any alternatives but just on the basis of their prior experience (Betsch et al., 1998). Chen et al. (2004) showed that travelers’ activity rescheduling behavior is mostly habitual behavior. Travelers who habitually choose one vehicle for routine trips will keep choosing that vehicle until the stimuli (e.g. bad experiences) are strong enough. Travelers’ dependence on such vehicles will thus generate a persistence process.
There have been similar formulations of vehicle dependence (mostly automobile/car dependence) in earlier studies. Dupuy (1999) indicated that the expression “automobile dependence” meant that an individual could not live without a car, just like a smoker who cannot live without cigarettes or a drug addict who is unable to live without drugs. His definition implied that automobile dependence could be an individual’s subjective consideration, somehow beyond full rationality. Goodwin (1995) indicated that the generation of car dependence is a process influenced by travelers’ subjective perception of their daily car usage: if the feedback from their car-driving experience is considered positive, people become more dependent on car usage unawares. His definition is consistent with the argument that vehicle dependence might arise from habitual behavior.
The Transport Studies Unit (1995) at Oxford University conducted research on car
dependence and indicated that car dependence may contain two elements: the absolute need for a car in order to maintain mobility without any other available option, and the perception of reliance on a car without actively considering the alternatives. This viewpoint is similar to our concept that the vehicle dependence of travelers arises from three types of reasons:
economic considerations, psychological preferences, and habitual behavior. Overall, vehicle dependence could be interpreted as a level of reliance on a specific vehicle usage which is gradually developed as a consequence of travelers’ economic concerns, psychological preference, and habitual behavior. Although vehicle dependence has been discussed in previous studies, however, no quantitative method to evaluate it among people with various personal characteristics has been tried. This might be the reason why the idea of vehicle dependence has not been applied to provide any useful information in the area of the description and prediction of mode choice.
2.2 Conceptual Framework of the Perceived Physical Ability of the Elderly Passengers When Using Buses
Even though the elderly bus passengers need not deal directly with the complicated traffic;
they still have to maintain some physical abilities in order to travel by bus. In other words, if driving an automobile on the road is considered as a tough test for elderly travelers to coordinate the vehicle and traffic conditions with their human factors, then taking buses might be regarded as a relative easy test for them in terms of the necessary actions or motions in approaching the stations, traveling on the routes, and approaching the destination. Based on the required actions or motions on a bus trip, 18 items are conceptually collected and shown in Fig 2-1 for discussions as follows.
Fig 2-1. A conceptual framework for the required actions or motions when using buses
As shown in Fig 2-1, items in the process of bus taking can be simply divided into three stages. At the stage of approaching the station, four items need to be achieved: “walking independently to the station”, “reading the information posted at the station”, “discerning the approaching buses”, and “beckoning the bus”. Items at this stage would mainly demand elderly passengers’ physical strength and their visual abilities. Previous studies have shown that elderly people are proved to have about 12–15% less muscle strength than young people (Blocker, 1992). Arthritis also commonly occurs in the elderly population (Yee, 1985). The muscle strength will influence the elderly people’s ability to walk independently to the station.
Older people also tend to have a smaller useful field of vision than younger people (Sekuler
and Ball, 1986), and the gradual degradation of eye muscle over time will influence their ability to focus on the objects at a distance or under a poor lighting condition. As a result, their poor visual ability is expected to worsen the elderly passengers’ ability to read the information at the station and discern the approaching buses, more than that, it might deter them from signaling to the approaching bus drivers.
At the stage of traveling on the route, the elderly travelers might encounter the following ten items to be dealt with: “stepping onto the bus”, “purchasing the ticket”, “moving to the seat on the bus when it starts to move”, “keeping balance on the seat of the moving bus”,
“keeping a standing balance on the moving bus”, “keeping a standing balance when the bus is accelerating or decelerating”, “realizing the location and direction along the route”, “being aware of the approaching destination stations”, “informing the driver and preparing to leave the bus”, and “stepping down from the bus”. These ten items will demand the elderly passengers’ physical strength, cognitive abilities, and sense of direction. It has been proved, that the speed of contraction and muscle coordination for elderly people are significantly slower than those of young people (Blocker, 1992), which may influence elderly people’s motion in stepping up and down from the vehicles. Joint flexibility declines by nearly 25% in older adults (Smith and Sethi, 1975), which may decrease their ability to retain their balance on the moving buses. It was found that the general cognitive ability of an elderly person would worsen (Kelsey, 1989), reaction time would become longer (Retchin et al., 1988), and the ability to navigate would probably be reduced by the loss of cognitive abilities (Manton, 1989).
At the stage of approaching the destination, another four possible items need to be achieved: “realizing the way to the destination”, “realizing the bus service information for the return trip”, “walking independently to the destination”, and “finding the location of the
station for the return journey”. These four items will demand elderly passengers’ physical abilities to achieve the final access to the destination and to prepare the necessary information for the return journey. Such physical abilities are also much related to the visual abilities, cognitive abilities, and physical strength that we have already discussed.
CHAPTER 3
Methods for Measuring a Latent Trait
From the illustration of conceptual frameworks, vehicle dependence and perceived physical ability of elderly bus passengers can be respectively conceptualized as two specific latent constructs of the related travelers. In this chapter, we would introduce the psychological viewpoints on measuring a latent construct. The item response theory (IRT), which is a model-based measurement in which trait level estimates depend on both persons’ responses and on the properties of the item that were administered, has become the mainstream of the psychological measurement (Hambleton and Swaminathan, 1991). Among the various models of IRT, the Rasch model is the one which is widely applied for exploring the psychological construct. The review of IRT and Rasch model will be illustrated in the following parts of this chapter.
3.1 Review of Item Response Theory
Psychological constructs are usually conceptualized as latent variables that underlie behavior. Latent variables are assumed as unobservable entities that influence the manifest variables (e.g. test scores or item responses). Thus the observation on these manifest variables can only serve as indicators of a person’s standing on the latent variable. As a result, measurements of psychological constructs are usually indirect, that is, latent variables are measured by observing behavior on relevant tasks or items. A measurement theory in psychology must provide a rationale that both persons and items on a psychological dimension should be inferred from behavior. Based on such a rationale, the item response theory has been elaborated to serve as a methodology in developing or executing a psychological test.
The item response theory is a measurement method which was developed to estimate the values of latent variables on an interval scale from item scores on an ordinal scale. In the original response data, the sum of scores across items for each person is referred to as the person raw score, and the sum of the scores across people for each item is called the item raw score. Discussions of item response theory are based on the Guttman scale (Guttman, 1950).
A Guttman scale means that item raw scores are monotonic with item difficulties, and person’s raw scores are monotonic with the person’s abilities. If the raw scores form a unidimensional ordinal scale, then when the data are displayed with the items ordered according to item raw scores, and with the persons ordered according to person raw scores, such a data matrix will conform to a Guttman scale. For a data matrix which fits Guttman scale perfectly, the abilities of people are ranked by the person raw scores and the difficulty of the items are ranked by the item raw scores; the ranking of people will be the same for each item and the ranking of items will be the same for each person. In reality, however, such a rigid rule is hard to achieve because of some unexplored randomness. Thus, in applying item response theory, some violations of Guttman scales are allowed, but the overall statistical pattern of responses should agree with these expectations. The more closely the data fit a Guttman scale, the more likely that the raw scores represent an ordinal scale.
Item response theory begins with a definition of the latent variable,θ , which is supposed to be measured. This variable θn must be an attribute of the respondent and will have a unique value for each respondent n. In item response theory, each item is supposed to require a specific value (threshold) of θ to elicit a particular response from the respondent 50% of the time. Such a response threshold for item i , b , is assumed in the same unit as i θ . The probability that respondent n will give a particular response to item i , P
( )
θni , can be modeled in a logistic form as Eq (1):( )
( ) 1968). In earlier educational applications, the parameter c usually refers to the chance performance, d usually refers to a possible careless response error, and a is the i discriminability of item i . In this study in our applications on self-rated responses, there is no“right” or “wrong” answer; thus we assume that c is equal to 0 and d is equal to 1 in Eq(1). In Birnbaum’s formulations, the parameter of discriminability, a , is designed to i absorb the variability and to create the illusion of precise estimation of person and item values.
As previously illustrated, a perfect Guttman scale is hard to achieve, and minor violations are allowed in practice. Measurement noise can be due to instability in person abilities, in item difficulties, or in both. It can also be attributed to variables that are not being studied. In our case, we define a=1 to keep an invariance across the items, which enables our items to be interpreted as measurements of a single variable.
The simplified item response model (d= 1, c = 0, and a = 1) in our case is identical to i the probabilistic measurement model developed by Georg Rasch (Rasch, 1960). He deduced his model from the item response theory (Andersen, 1995), and proved that the person and item parameters (θn and b ) are separable, and that item and person raw scores are sufficient i statistics to estimate the values of the item and person parameters. Since the 1980s, Rasch models have been intensively used to estimate values on an interval scale from raw scores in psychometric studies.
3.2 Brief Introduction of the Rasch Model
3.2.1 Formulation of the Rasch model
The Rasch model has been intensively used to estimate values on an interval scale from raw ordinal responses in psychometric studies (Fisher et al., 1995; Massof and Fletcher, 2001).
To simplify our introduction of the Rasch model, we shall consider only the dichotomous responses to begin with.
Taking the elderly bus passengers’ ability as an example, the questions are assumed to be the type of “Can you easily achieve the following necessary action or motion?” The response is either “yes” or “no”. A score of 1 is assigned to an item to which the traveler responds “yes, I can”; otherwise, a score of 0 is assigned. The probability that an elderly passenger n will respond with “yes, I can” for item i is expressed as
and the probability that an elderly passenger n will respond with “no, I can’t” for item i is then expressed as
therefore, the odds ratio that an elderly passenger n can achieve item i is
( )
and the logarithm of the odds ratio, known as the “logit”, is
( )
which isolates the parameters of interest.
The person and item parameters in the case of dichotomous responses can be estimated from the response odds ratios in the data set using the formulation of Eq. (5). In addition to dichotomous responses, the Rasch model has been modified to be applicable to polytomous rating-scale instruments, such as the five-point Likert scale (Andrich, 1978; Masters, 1982).
The modified Rasch model decomposes a polytomous response into several dichotomous responses and formulates one multinomial-choice problem into several binary-choice problems. That is, it assigns b as the value of the item parameter for the rating category ik k to item i , and assumes that Eq. (2) refers to the probability of subject n responding with rating category k rather than k −1 to item i . In other words, we can model the log odds of the probability that a person responds in category k for item i , compared with category
−1
k , as a linear function of the person parameter θn and the relative parameter of category k, namely b , for item i ik
Following Andrich’s modification of the Rasch model for a polytomous response, two types of formulation are widely applied in assessing the values of item and person parameters, namely the “rating scale model” and the “partial-credit model”. The rating scale model is used only for instruments in which the definition of the rating scale is the same for all items, while the partial-credit model is used when the definition of the rating scale differs from one item to
another. Specifically, the partial-credit model is similar to the rating scale model except that each item i has its own threshold parametersF for each category ik k (Wright, 1977). This is achieved by a reparameterization of Eq. (6)
ik i
ik b F
b = + (7)
and the partial-credit model becomes
ik
The partial-credit model (Masters, 1982) is used for items where: (1) credits are given for partially correct answers, (2) there is a hierarchy of cognitive demand on the respondents for each item, (3) each item requires a sequence of tasks to be completed, or (4) there is a batch of ordered response items with individual thresholds for each item. In exploring the latent constructs, it is not necessary to assume that the rating scales of the items are the same, and thus the partial-credit model would be suggested for the proposed empirical studies.
3.2.2 Parameter estimation of the Rasch model
Based on different statistical assumptions, there are several approaches for estimating the parameters of Rasch model. Among them, the joint maximum likelihood (JML) estimation is a relative simple and effective way, which is also the core technique of the related computer programs: the WINSTEPS and FACETS (Linacre and Wright, 1997). A simple introduction of the JML estimation is given as follows.
In JML estimation, unknown construct levels are handled by using provisional trait level estimates as known values. The provisional trait level estimates themselves are
improved by using subsequently estimated item parameters, which are successively improved.
In other words, JML estimation is an iterative procedure which typically involves sequential estimates of person and item parameters. In the initial stage, person parameters are estimated.
The first iteration of the two-stage procedure involves specifying starting values for the item parameters so that the maximum likelihood estimates of person parameters can be obtained.
Then the item parameters are estimated using the first person-parameter estimates. In the following iterations, person and item parameters are iteratively estimated using the improved person or item parameters respectively. The iterations continue until the item parameters change very little between the successive iterations (the convergence status).
JML has been extensively applied in the estimation of many IRT models. It has several advantages in applications. First, this algorithm is easily programmable. Second, JML is applicable to many IRT model. Both the 1PL IRT (e.g. the Rasch model) and 2PL IRT (e.g.
the Multi-Facet Rasch Model) can be estimated with JML. Third, JML is efficient on computation. One thing has to be noted in applying the JML estimation that there is a strong limitation of in applying JML algorithm. In JML estimation, the items or persons with perfect scores (all passed or all failed) provides no information about the parameters because there
the Multi-Facet Rasch Model) can be estimated with JML. Third, JML is efficient on computation. One thing has to be noted in applying the JML estimation that there is a strong limitation of in applying JML algorithm. In JML estimation, the items or persons with perfect scores (all passed or all failed) provides no information about the parameters because there