CHAPTER 2 Literature Review
2.2 Conceptual Framework of the Perceived Physical Ability of the Elderly Passengers
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 are no constraints are placed on the solution (Holland, 1990). Therefore, estimates of such items or persons with perfect scores are not available in the JML estimation. In fact, such measures of items or persons with perfect scores mostly occur on the data of the educational tests but rarely in the psychological exploration. In the psychological exploration, items with perfect scores are regarded as inappropriate items because they provide no information on evaluating construct levels of the respondents; person with perfect scores can be also considered as a ineffective observation for their construct level are not comparable. It is generally suggested to exclude these items or persons from the original data, or to withdraw the data and redesign the whole investigation program.
3.2.3 Reliability and validity statistics in the Rasch model
In latent construct measurement, reliability indices help us to examine whether or not the model is convincing and the material is replicable, and validity indices help us to examine whether or not the properties of our material are consistent with the assumption of the measurement. In Rasch model, indices of reliability and validity are calibrated respectively via person and item aspects (Wright and Master, 1982) to provide the critical proofs on the quality control of data. We would give a brief introduction of these two indices of Rasch measurement in the following paragraphs.
Reliability in latent construct measurement is commonly defined as the consistency of the responses to a set of items or the consistency of scores from the same instrument.
Following such concept, reliability index R in the Rasch model is defined as the degree to which scores are free from measurement errors (Andrich, 1988). As a result, the reliability estimate for persons (R ) is shown (Bond &Fox, 2001) as follows: p
2 2
p p
p SD
R = SA (9)
the total person variability (SD ) represents how much respondents differ on the measure of p2
interest. The adjusted person variability (SA ) represents the reproducible part of this p2 variability (i.e. the amount of variance that can be reproduced by Rasch model). This reproducible variability is divided by the total person variability to obtain the person reliability estimate (R ) with values ranging between 0 and 1, which is consistent to the p concept as Cronbach’s α (Wright, 1996).
On the other hand, reliability for items (RI) is estimated in the same manner as for persons, with item variance being substituted for person variance:
2
where the total item variability (SD ) represents how much items differ on the measure of I2 interest. The adjusted item variability (SA ) also represents the proportion of total item I2 variability that can be reproduced by the Rasch model.
The Rasch model is regarded as a prescriptive rather than a descriptive approach (Bond, 2001). That is, the data must fit the model, or the assumptions of the model must be rejected for a particular data set, i.e., the degree to which the previously described properties hold depends on how closely the data fit the model. With the comparison between the observed and expected patterns, two fit statistics, namely information-weighted fit (“infit”) and outlier-sensitive fit (“outfit”) (Smith, 1991), are generated to evaluate the validity in the Rasch model. An overview of the derivation of fit statistics is summarized in following paragraphs.
Based on the estimated parameters, each observation for person n on item i with K categories (denoted asX , ni X = k if the kni th category is chosen), has its expected response value E : ni
residual Z of each observation ni X are then obtained: ni
These standard residuals are squared and summed to form a chi-square statistic. With divided by total observation numberN , the Mean-square Outfit statistic is then obtained.
∑
=In addition to the Outfit statistic, the Infit statistic weighs the squatted standardized residual Z by their individual variance ni W . It can be calculated as: ni
The main difference of these two fit-statistics is the outfit statistic place more emphasis on unexpected responses far from a person’s or item’s measure, while infit place more emphasis on unexpected responses near a person or item’s measure (Bonds, 2001). The expected values
of these two Mean-square fit statistics are 1, and the guideline for determining unacceptable departures from expectation remains many discussions (Smith et. al, 1995). To achieve a more generalized standards, both the outfit and infit can be further expressed as normalized residuals (Zstd) via a transformation into a t-statistic with an approximate unit normal distribution (Wright & Stone, 1979). Such a Zstd (Z-standardized fit) statistic has an expected value at 0 and a variance as 1, which has previously been used to select items at the 0.05 significance level and according to the ± 2 criteria.
CHAPTER 4
Exploring the Vehicle Dependence behind Mode Choice: Empirical Evidence of Motorcycle Dependence in Taipei
According to the prior discussion, vehicle dependence could be thought of as a latent construct of a traveler that represents the traveler’s reliance on a specific vehicle as a consequence of economic concerns, psychological preference, and habitual behavior. How to gather the necessary information and design a measuring tool to evaluate travelers’ vehicle dependence to make our idea operational is another issue, which we consider below.
4.1 Questionnaire Design for Gathering Vehicle Dependence
Latent constructs are commonly explored by means of questionnaires that include appropriate items that respondents can answer on the basis of their daily life experience. Since there was no available questionnaire to follow, we had to design our own questionnaire for our study. Essentially, people use and depend on vehicles to meet the needs of their daily activities, and the significant relations between travelers’ mode usage and their participation
Latent constructs are commonly explored by means of questionnaires that include appropriate items that respondents can answer on the basis of their daily life experience. Since there was no available questionnaire to follow, we had to design our own questionnaire for our study. Essentially, people use and depend on vehicles to meet the needs of their daily activities, and the significant relations between travelers’ mode usage and their participation