A Nested Logit Model of Commuters' Activity Schedules

Sachin Gangrade
ZS Associates

Ram M. Pendyala*
University of South Florida

Robert G. McCullough
Florida Department of Transportation

ABSTRACT

This paper presents a nested logit model of activity scheduling behavior that can be used to predict a daily activity pattern for commuters. The behavioral paradigm embodied in the model suggests a two-stage decision process in which commuters first plan or identify the nonwork activities that need to be undertaken during the day, and second, schedule these activities in relation to the work activity schedule. Three possible scheduling periods are considered in the model: before work, at work, and after work. Alternative nested logit model structures are estimated on the 1996 San Francisco Bay Area activity survey sample to identify a plausible and statistically acceptable structure. Numerical examples are presented to show how the model, when combined with a Monte Carlo simulation and simple heuristics, can be used to generate daily activity schedules for commuters.

INTRODUCTION

The conceptual deficiencies of the conventional four-step trip-based travel demand modeling procedure, combined with the shift in transportation planning and policy initiatives from transportation infrastructure development to transportation systems management, have led to the emergence of activity-based approaches to modeling individual travel behavior (Jones et al. 1983; Kitamura 1988; Axhausen and Gärling 1992). Activity-based analysis follows the premise that travel demand is a derived demand and the resulting travel demand models are applicable to a wider range of situations than the conventional four-step trip-based procedure (Ettema and Timmermans 1997). The activity-based perspective of travel can also reliably be used to evaluate travel demand management policies, because it explicitly models activity patterns and considers these patterns to be the fundamental influence on individual travel decisions (Golob 1998; Kuppam and Pendyala 2001).

The activity-based approach has seen substantial development in the past few years (Kitamura and Fujii 1998). Bhat and Koppelman (1999) broadly classified these developments into activity time allocation studies and activity episode analysis studies. Activity time allocation studies classify activities into one of the several categories available and then examine the time allocated to these activity types based on socioeconomic and demographic characteristics of individuals (Kitamura 1984). However, these approaches ignore the context in which individuals pursue activities; that is, these approaches do not consider the time of day of the activity performance, the sequence in which activities are performed in a continuous temporal domain, and the location characteristics of activity participation (Kitamura et al. 1997b).

Activity episode analysis is closer to the original theory behind activity-based approaches. This approach analyzes activities and trips and their associated spatial and temporal constraints in a comprehensive model framework. These studies describe in detail the sequence, context, and duration of activity participation, thus leading to more detailed models of activity choice and travel behavior. Many of the earlier activity episode analysis studies focused on participation of individuals in one or more activity episodes, along with one or more accompanying characteristics of the episodes such as duration, location, or time window of activity participation (Damm 1982; Hamed and Mannering 1993; Bhat 1996, 1998; Bhat et al. 1999).

Over the last decade, several researchers have developed models that attempt to microsimulate the daily activity participation and trip schedules of individuals (Chen et al. 1999). Examples include, but are not limited to, STARCHILD (Recker et al. 1986), SCHEDULER (Gärling et al. 1994), and AMOS (Kitamura et al. 1995; Pendyala et al. 1998). The development of such models has been further accelerated by the availability of data that capture household activity scheduling behavior (Doherty and Miller 2000). Development of tour-based model frameworks is another line of research in activity-based modeling, where "tours" are considered to be the basic unit of travel. These approaches use a combination of multinomial logit and nested logit models to simulate activity-travel patterns in the context of tours (Bowman and Ben-Akiva 1997; Wen and Koppelman 1999, 2000).

Activity-based approaches are the foundation of the next generation of travel demand models in the United States and other countries. The objective of this paper is to contribute to the operationalization of the activity-based approach by proposing a simple analysis framework to generate weekday activity engagement and trip scheduling patterns of commuters. Using data from the 1996 San Francisco Bay Area activity survey, nested logit models of activity scheduling behavior were developed and estimated. The proposed nested logit models, though not comprehensive or exhaustive, are practical, provide a plausible behavioral basis, and present activity scheduling and travel behavior of commuters in a simple model system. We believe that the nested logit models of activity scheduling behavior proposed in this paper can be effectively combined with other models of activity behavior (e.g., models of activity frequency and activity duration) and rule-based algorithms (e.g., Pendyala et al. 1998) to develop a full-fledged activity-based model system.

The remainder of this paper is organized as follows. First, we provide a brief description of the survey sample. We then describe the overall modeling approach and nested logit methodology, respectively. Descriptions of the nested logit model specification and estimation results follow. We then present an example of how the nested logit model can be used to predict a commuter's activity pattern. Conclusions are drawn in the final section.

SAMPLE DESCRIPTION

This research paper utilizes activity and trip information collected as part of the 1996 San Francisco Bay Area activity survey. Gangrade et al. (2000) provide a detailed description of the survey and sample characteristics. Only a brief summary is provided here. A two-day activity-based time-use and travel survey was conducted in the nine counties of the San Francisco Bay Area in 1996. Detailed information on both in-home and out-of-home activities and trips undertaken by an individual were recorded.¹ Information was requested for all out-of-home activities and trips but only in-home activities of 30 minutes or more. However, many respondents provided detailed information on all in-home activities regardless of their duration.

The original survey dataset includes a sample of 8,817 individuals residing in 3,919 households who provided detailed activity and trip information over a 48-hour period. After extensive data checking, cleaning, and merging/organizing, the final dataset obtained for use in this study included 7,982 individuals residing in 3,827 households. The dataset identified 4,331 persons as commuters (3,651 persons were noncommuters).

Sample Profile

Table 1 presents the demographic characteristics of households in the sample. The average household size was 2.3 persons per household, while the average number of workers was 1.4 per household. Forty percent of the households were single-worker households, while another 43% were multiple-worker households.

The income variable, which categorized households into low (less than $30,000), medium ($30,000–$75,000), and high (greater than $75,000) income groups, showed as expected that a large percentage of the households in the survey fell into the medium income bracket. Average car ownership in the sample was 1.9 vehicles per household, and 86% of the households in the survey sample have vehicle ownership levels greater than or equal to the total number of commuters in the household. This is indicative of a high level of commuter auto availability.

Person characteristics (provided separately for commuters and noncommuters) of the sample are also shown in table 1. Respondents were categorized into young (29 years or less), middle (30 – 49 years), and old (50 years or more) age groups. More than 50% of the commuter sample fell into the middle age bracket, while over 50% of the noncommuter samples fell into the young age group (the noncommuter group includes children). More than 80% of the commuters were full-time workers. Also, as expected, the percentage of licensed drivers in the commuter sample was substantially higher than that in the noncommuter sample (95% vs. 49%).

Clearly, the noncommuter sample is quite different from the commuter sample. In light of these differences, one would expect noncommuters to have substantially different activity and time-use patterns than commuters. These differences call for the development of separate models of activity scheduling behavior for commuters and noncommuters. In this paper, out-of-home nonwork activity engagement and trip scheduling behavior is modeled only for the commuter sample, and thus the remainder of this paper focuses exclusively on the commuter sample.

Activity Participation and Trip Frequency Analysis

The original dataset had more than 30 categories of activities broadly aggregated into 11 activity types in order to study activity and trip frequencies by purpose. Average frequencies (including both in-home and out-of-home activities) for the commuter sample are presented in table 2. As mentioned earlier, the Bay Area travel survey was conducted over a 48-hour time period. The activity and trip frequencies presented in the table are two-day averages.

The average number of work and work-related activities was 1.6 activity episodes per day for the Bay Area commuter. This value is along expected lines, because many commuters undertake two work activity episodes in a day—one before lunch and one immediately after lunch.

As expected, eating/meal preparation (eat/meal), in-home entertainment, personal care and childcare, and sleep/nap activities averaged one or more activity episodes per day. On the other hand, shopping and personal business, out-of-home entertainment, and out-of-home other activities averaged less than one activity episode per day.

With respect to travel, commuters, on average, took 4.8 trips per day. Table 2 shows trip rates by purpose for both commuter and noncommuter samples in the dataset. Work/work-related and return home trips comprise almost 50% of the trips taken by commuters over a day. The average trip frequency for out-of-home shopping/personal business, entertainment, and maintenance/other related activities was found to be about 0.5 trips per day for each purpose. The average trip frequency associated with childcare was rather low at 0.1 trips per day.

Overall, work activity was shown to be a major part of a commuter's daily activity and travel pattern. In the case of commuters, one may conjecture that other discretionary activities (e.g., shopping, personal business, recreation, and childcare) are scheduled and performed around relatively fixed work schedules. This hypothesis, which is consistent with the literature on activity-based approaches (see, e.g., Damm 1982) forms the basis for the nested logit model of activity scheduling developed in this paper.

FRAMEWORK FOR ACTIVITY SCHEDULING BEHAVIOR

In this paper, nested logit models are formulated with a view to predict activity and trip schedules of commuters over a one-day period. This section provides the behavioral framework underlying the specification of the nested logit models of commuter activity scheduling behavior.

There is increasing interest in applying microsimulation approaches to forecast activity-based travel demand (Kitamura et al. 1997a; Pendyala et al. 1998). In microsimulation approaches, the researcher is often attempting to simulate, at the level of the individual traveler, an entire activity schedule and travel itinerary over the course of a day. This involves modeling a series of choices that travelers make, including those related to activity type, duration, timing and scheduling, location and destination, and path. Considering that many of these choices are made under constrained situations, the argument can be made that there are finite spatio-temporal action spaces or space-time prisms within which one can engage in activities and travel (Pendyala et al. 2002).

Space-time prisms provide a means of representing the spatial and temporal constraints that influence activity and travel patterns. For example, from a spatial standpoint, one can conjecture that home and work locations are potential anchors that constrain the potential range of destinations a person can visit. Because of data limitations, this paper does not consider the spatial aspect of commuter activity scheduling behavior.

From a temporal standpoint, several events in time may constrain the range of activity-travel patterns that an individual can pursue. These events and their associated beginning and ending times can play an important role in determining how individuals schedule, sequence, and plan their activities and trips. Six temporal events that might dictate how a commuter schedules and plans activities are identified here.

1. Wake-up time
2. First time of departure from home
3. Work start time
4. Work end time
5. Final time of arrival at home
6. Sleep time

Gangrade et al. (2000) have provided detailed descriptions of these temporal events for the commuter and noncommuter groups in the survey sample. These six events potentially define five temporal prisms² within which commuters schedule their activities. For example, wake-up time and first time of departure from home define an "initial at-home prism." Similarly, work start time and end time define an "at-work prism." In reality, these events may not truly describe the temporal dimension of a prism. The real vertices (or extremities) of a prism are unobserved (e.g., earliest wake-up time, latest possible work arrival time, earliest possible work departure time, latest possible sleep time), and therefore the observed events are used as surrogates to represent the temporal dimensions of prisms.

A commuter can engage in out-of-home activities within prisms that lie between the first time of departure from home and the final time of arrival at home. Only in-home activities can be pursued prior to the first home departure and following the last home arrival. The period between the first home departure and the final home arrival may be further subdivided into:

• Before-work time period: This time period comprises time available between the first departure from home and work start time. During this period, a commuter may pursue activities on the way to work and/or pursue activities and return home prior to departing for work.
• During-work time period: This time period is defined by the work start time and end time. On average, work accounts for approximately 30% of a commuter's day and 50% of the waking hours. As such, this prism is likely to be an important determinant of a commuter's daily activity pattern. Commuters are often temporally constrained by their work schedules. Nonwork activity engagement typically occurs during the lunch break (about one hour for most commuters).
• After-work time period: The time period available to a commuter after work ends and prior to the final time of arrival at home constitutes the after-work time period. During this time period, a commuter may undertake nonwork activities such as shopping, running errands, recreation, etc., either on the way home from work or separately after a temporary stop at home. The latter choice of activity engagement would generate another set of trips before the commuter finally returns home.

Within the framework adopted in this paper, we postulate that commuters choose to engage in out-of-home nonwork activities within one or more of these broad prisms. For example, a commuter may choose to shop before work, during work, or after work, including the possibility of multiple shopping activities in the same or different time prisms. By scheduling out-of-home nonwork activities in various prisms (periods of the day), a commuter's activity schedule can be identified.

For purposes of model development and estimation, we aggregated the various out-of-home nonwork activities undertaken by commuters in the 1996 Bay Area survey sample broadly into eat/meal preparation, shopping/personal business, and entertainment/social recreation. In addition, in an attempt to capture temporary trips home that occur between the first home departure and last home arrival, an additional activity category called "return home" is included in the model formulation. It should be noted, however, that return home really represents in-home activity engagement by commuters in the survey sample. Previous research has clearly shown that there are significant tradeoffs and complementarity between in-home and out-of-home activity engagement (Kitamura 1984; Kuppam and Pendyala 2001). Within the model framework of this paper, relationships between in-home and out-of-home activities and the identification of specific activities pursued during trips home are not explicitly included. Future efforts will involve the integration of such models with the model developed in this paper. However, the inclusion of return trips home as an explicit category in the model framework helps determine the activity sequencing and trip chaining behavior of commuters (e.g., does a commuter shop on the way home from work or after returning home from work?).

In summary, the behavioral framework adopted in this paper takes the form of a two-stage process. In the first stage, commuters choose among activities to be pursued (outside home and work) and in the second stage, they choose when the activity will occur. Such a two-step process may be conveniently represented using nested logit model structures. For example, in one postulated structure, the various out-of-home nonwork activities pursued by individuals, namely eat/meal preparation, shopping/personal business, entertainment/social recreation, and return home comprise the upper level (composite) alternatives. The three time periods available to pursue these activities form the lower level (elemental) alternatives available to an individual. Figure 1 provides a visual depiction of this postulated behavioral structure.

It should be noted that the two-stage behavioral paradigm suggested in this paper is not necessarily the only factor motivating the adoption of a nested logit modeling methodology. A nested logit model is usually adopted when there is a potential for shared unobservable attributes across alternatives, if these attributes were to be arranged in a simple multinomial structure. The potential for shared unobserved attributes across alternatives, coupled with the two-stage behavioral paradigm, motivated us to adopt the nested logit methodology in this paper.

Because the behavioral framework adopted in this paper does not include in-home vs. out-of-home activity substitution, and instead uses an aggregate activity-type categorization, it is not comprehensive in its treatment of commuter activity and travel behavior and thus simplifies the behavioral process underlying activity and travel pattern formation. Nevertheless, it provides a practical and convenient way to extract activity schedules and sequences and trip chains of commuters given standard socioeconomic variables.

NESTED LOGIT MODELING METHODOLOGY

The nested logit model is a widely used form of the discrete choice model and has been extensively presented and described in the literature (see e.g., Ben-Akiva and Lerman 1985; Lerman 1984; Train 1986; Ortuzar and Willumsen 1994). There are at least two ways to express the nested logit structure, namely, the Non-Normalized Nested Logit model (NNNL, described by Daly 1987) and the Utility Maximizing Nested Logit model (UMNL, described by McFadden 1978). A detailed discussion of both model structures is beyond the scope of this paper; however, the merits and demerits of the two model structures have recently been discussed in the literature (Koppelman and Wen 1998; Hensher and Greene 2000).

Despite the potentially more appealing nature of the UMNL model, the NNNL model specification is used in this research primarily because of the availability of convenient software to estimate it (e.g., LIMDEP). Also, from a behavioral interpretation standpoint, it was considered sufficient to adopt the NNNL modeling methodology.

The lower level choice in a nested logit model is a multinomial logit choice and can be expressed as

where

P ( k | i ) is the probability of alternative k from subset D i to be chosen on the condition that alternative i on the upper level has been chosen,

D i is the lower level choice set, which is associated with alternative i on the upper level,

V ik is the deterministic portion of the utility associated with choice k in nest i ,

is a vector of model parameters,

x is a vector of exogenous variables.

An inclusive value I i (or logsum) associated with the upper level alternative i is defined as

The upper level choice probability is then expressed as

where

P ( i ) is the probability of choosing alternative i ,

is a vector of model parameters,

z is a vector of exogenous variables.

The parameter is referred to as the inclusive value parameter. The value of this parameter should lie between zero and one. When the parameter equals unity, the structure collapses to a multinomial logit model without a nested structure. The levels are separated and present independent and separate choice situations if the value of the parameter is equal to zero. If <0, an increase in the utility of an alternative in the nest (which should increase the probability of the nest being chosen), actually diminishes the probability of selecting the nest. In virtually all choice modeling situations, this is implausible. If >1, an increase in the utility of an alternative in the nest not only increases its selection probability but also the selection probability of the rest of the alternatives in the nest. That is, improvements in one alternative could increase not only the probability of that alternative being chosen, but some other alternatives would also gain a bigger share (Ortuzar and Willumsen 1994). While this may be plausible under certain limited conditions, it is generally not applicable to a wide variety of choice modeling situations. Therefore, the nesting structure that provides inclusive value parameter estimates between zero and one is generally adopted as long as the structure offers a plausible behavioral framework and interpretation.

NESTED LOGIT MODEL ESTIMATION RESULTS

Several possible alternative nesting structures may describe the activity scheduling behavior of commuters. This section discusses the alternative nested logit model structures that were tested and presents model estimation results for the structure that provided desirable statistical and plausible behavioral indications.

Figure 1 illustrates the nested logit model structure that is most consistent with the behavioral framework postulated earlier in the paper. This structure suggests that a commuter, in formulating an activity schedule, first chooses the out-of-home nonwork activities to be pursued in a day. The choice of the appropriate time period in which to undertake each of the chosen activities comprises the second step in the choice process.

Nested logit model estimation results for this structure are found to offer plausible coefficient estimates, except for those associated with the inclusive value parameters. Because the model did not offer acceptable inclusive value parameter coefficients, it was not adopted, and therefore detailed model estimation results and parameter estimates are not included in the paper. The inclusive value parameter estimate for the nest comprising eat/meal alternatives was 1.45, while that for the nest comprising shopping/personal business alternatives was 1.09 (significantly different from one). These two inclusive value parameter estimates suggest that when the probability of a commuter pursuing either an eat/meal activity or a shopping/personal business activity in one of the three time periods increases, then the probability that the commuter undertakes the same activity in a different time period (on the same day) also increases simultaneously. While this result may hold true for a few commuters, it is not likely to hold true across the sample. The inclusive value parameter estimate for the nest comprising entertainment/social recreation activities was 0.51. This value indicates that a potential tradeoff is involved when pursuing entertainment/social recreation activities during different time periods in a day. This inclusive value is certainly behaviorally intuitive as one would expect commuters to trade off the pursuit of entertainment activities across different time periods.

Because the nested structure shown in figure 1 provided counter-intuitive inclusive value coefficient estimates for two nests, an alternative structure was developed (shown in figure 2). This framework proposes a bottom-up decisionmaking process where a commuter first breaks up the day into various periods (prisms) and then chooses the activity (or activities) to be undertaken in each period. In figure 2, the before-work, at-work, and after-work time periods comprise the three composite alternatives placed at the upper level in the nest structure. The various out-of-home nonwork activities undertaken by individuals (eat/meal, shopping/personal business, and entertainment/social recreation) comprise the elemental alternatives in each nest. However, return home is still retained as an upper level choice as this alternative pertains to the choice to return home temporarily during the day. Because it was considered appropriate to distinguish between out-of-home activity scheduling (in the other three nests) and trip scheduling (for in-home activities), return home was retained in a manner similar to that in the first nesting structure in figure 1.

This model offered plausible coefficient estimates and acceptable goodness-of-fit measures. However, similar to the first structure, the inclusive value coefficient estimates for two nests significantly exceeded one. For the nest comprising activities undertaken before work, the inclusive value coefficient estimate was 1.40, while that for the nest comprising activities pursued after work was 1.29. These inclusive values imply that commuters who are likely to engage in a nonwork activity before work or after work are also likely to simultaneously engage in other activity types during the time period under consideration.

One could posit that these model results are plausible, particularly in the context of the after-work period. During the after-work periods (typically in the evenings), quite a few commuters engage in multiple activities, suggesting that elemental choice alternatives in the after-work nest are not competing but complementary in nature. However, in the presence of household, work, and other institutional and temporal constraints, it is unlikely that this will apply across the entire sample. Also, with respect to the before-work period (typically in the morning), it is very unlikely that commuters treat activities as complementary to one another (with possibly a few exceptions). If this is the case, then, the inclusive value parameter estimate for the before-work nest should be less than one, even if that for the after-work period is acceptable.

In addition, the inclusive value coefficient estimate for the nest comprising activities undertaken while at work was 1.03. This was not significantly different from one at the 95% confidence level, suggesting that activities undertaken while at work are independent of one another (no tradeoffs) and do not belong in a nesting structure. Similarly, the inclusive value for the nest comprising return home trips was also one, suggesting that various return- home trips undertaken by commuters over a day are independent of one another. Again, neither of these findings is consistent with behavioral expectations. Even if the finding that activities undertaken while at work are independent of one another is potentially acceptable, the finding that return-home trips are independent across time periods is behaviorally inconsistent. For a commuter, work and other temporal constraints would undoubtedly result in interdependence (and therefore tradeoffs) among various time periods for undertaking return-home trips. This would call for the nest comprising return-home trips to have an inclusive value coefficient estimate of less than one. The behaviorally inconsistent inclusive value coefficient estimates prompted us to reject this structure and search for a structure that was both behaviorally plausible as well as statistically acceptable.

After an extensive exploratory analysis of commuter activity engagement patterns in the dataset, we found that the most prevalent activity participation behavior included an eat/meal activity pursued while at-work, shopping/personal business pursued (in the evening) after work, and entertainment/social recreation pursued after work. Other types of activity participation behavior before work or while at work occur less frequently in the sample possibly because constraints do not allow the scheduling of activities during those periods for most commuters or simply because those activity patterns are less preferred.

This activity scheduling behavior of commuters may be captured by placing the more prevalent alternatives as separate and independent choices. All of the less-prevalent activity scheduling alternatives may be combined into a single nest to represent their rare nature and the fact that, if a commuter does participate in one of these alternatives, the likelihood of that person participating in another less prevalent alternative (in the same nest) is virtually none. Eat/meal activities while at work, shopping/personal business activities (in the evening) after work, and entertainment/social recreation activities (in the evening) after work are the more prevalent alternatives. They are all treated as separate and independent choice alternatives. Once again, as in the previous case, return-home trips are placed in a separate nest to distinguish between activities and trips. Figure 3 shows the nesting structure for representing the activity scheduling behavior of commuters.

Variables used in this nested logit model are defined in table 3. They include a series of socioeconomic variables describing the individual and the household. There are two inclusive value parameters for this nesting structure, one associated with the "less frequent" nest and the other associated with the "return home" nest. Model estimation results for the proposed structure are presented in table 4. This model offered plausible and behaviorally sound coefficient estimates for the inclusive value parameters. In addition to this, it offered the same level of goodness-of-fit as the prior two structures we considered and provided coefficient estimates on all other explanatory variables according to expectations. Although several coefficients had low t -statistics from a statistical standpoint, they were retained in the model as they offered behaviorally plausible interpretation and sensitivity. This model structure was finally chosen to represent activity scheduling behavior of commuters in the San Francisco survey sample.

The inclusive value coefficient estimate of the nest comprising the less frequent activities was 0.80, while that for the nest comprised of return home trips was 0.72. Both of these inclusive value parameter estimates were statistically significant at the 99% confidence level and significantly less than one. The inclusive value parameter estimate of 0.80 for the nest comprising rare and less frequent activities indicates that the activities in this nest share unobservable attributes and considerable tradeoffs are involved when pursuing these activities. The inclusive value parameter estimate of 0.72 for the nest comprising return home trips indicates that these trips, typically undertaken over a day, share unobserved attributes. If a commuter returns home temporarily during a certain time period during the day, then the same commuter would show less preference to again return home temporarily at some other time period in the day. This inclusive value is consistent with behavioral expectations that commuters are temporally constrained and are rarely inclined to make multiple return trips home during the day.

With respect to socioeconomic variables, the model offers very consistent coefficient estimates. In general, males in the sample were more likely to engage in the eat/meal activity while at work. On the other hand, females were more likely to engage in shopping/personal business activities after work. However, more males pursued entertainment and other social recreation activities after work compared with their female counterparts. These findings are consistent with traditional gender-based differences in household roles and obligations. Strangely, males also exhibited a greater tendency to return home while at work, which clearly shows the importance of integrating models of in-home activity engagement with models of out-of-home activity engagement. Furthermore, the reasons for males' return-home trips while at work merits further investigation.

Younger commuters in the sample were more likely to eat while at work and undertake entertainment/recreation activities after work. It appears that they were more likely to undertake their after work activities after a temporary trip home as indicated by the positive coefficient associated with the return home after work alternative. Licensed individuals, who presumably have access to an automobile, were more likely to pursue shopping/personal business activities during the day and more likely to return home in the middle of the workday. As expected, commuters employed full time were less inclined to return home during the day, but were more inclined to engage in an eat/meal activity while at work. Students were more likely to participate in activities in the period prior to work (they are more often part-time workers who have the flexibility to undertake before-work activities).

Single people showed a greater propensity to engage in entertainment/social recreation activities in the after-work period than other household types. Single parents were more likely to return home during the day, presumably because of childcare or other household obligations. Commuters in households with children showed a negative propensity to engage in recreation and other out-of-home nonwork activities during the day. This is presumably because they devote much time in-home to childcare activities and other household obligations. As expected, high income commuters and commuters in households with high car availability were more prone to participate in entertainment activities in the after-work period (while these coefficients were not statistically significant at the 95% confidence level, they were retained because of their behaviorally intuitive interpretation). Those who drive to work appeared to have the flexibility and therefore positive propensity to return home during the day (while at work) and undertake shopping/personal business activities after work (possibly on the way home from work).

In summary, the final adopted model structure provides model parameter estimates consistent with behavioral and empirical expectations. Most of the model coefficients are statistically significant at the 95% confidence interval. The inclusive value parameter estimates are also behaviorally plausible. Therefore, we may conjecture that this nesting structure provides a reasonable representation of activity scheduling for commuters. However, we draw this conclusion with caution, because this nested logit structure generated consistent inclusive value parameter estimates in the context of the 1996 San Francisco Bay Area survey sample. Alternate nesting structures estimated on several different sample datasets should be examined and tested before drawing conclusions about the behavioral paradigm underlying commuter activity scheduling behavior.

NESTED LOGIT MODEL APPLICATION

The previous section described a nested logit model structure intended to represent commuters' activity scheduling behavior. In this section, a sample numerical simulation is provided to show how the model can be used to predict activity scheduling patterns of commuters.

For the purpose of this exercise, six hypothetical individuals are considered. Their characteristics in relation to the socioeconomic variables included in the nested logit model are shown in table 5. In general, the six hypothetical individuals cover a range of socioeconomic characteristics thus providing a means of examining whether the model is truly sensitive to differences among individuals. Prior to the application of the nested logit model of activity scheduling behavior, the total number of out-of-home nonwork activities (including temporary return trips home) pursued by each commuter was predicted using Poisson- and negative-binomial regression-based activity frequency models similar to those developed by Ma and Goulias (1999). These activity frequency models provided a basis for determining the number of activities that need to be drawn and included in the commuters' activity schedules. The predicted activity frequency for each individual is shown in the last column of table 5.

The nested logit model includes a total of 12 different alternatives as shown in the first column of table 6. In this table, predicted probabilities associated with each alternative are shown for person number 4 from table 5. This person is a young, high-income female single parent. The predicted probabilities for the 12 alternatives are shown in the second column of table 6. In order to determine the activities that need to be included in this person's schedule, a simple Monte Carlo simulation method was adopted. Using a random number generation process, random numbers between 0 and 1 were repeatedly drawn to determine the choices according to the predicted probability distribution of the alternatives for each individual. The number of draws is equal to the predicted activity frequency as provided by the Poisson- or negative-binomial regression-based activity frequency model.

For this individual, the activities that were drawn in the simulation included return home before work, shop/personal business before work, entertainment after work, eat/meal at work, eat/meal after work, and shop/personal business after work. In order to develop the pattern, we started at the beginning of the day and assumed that the person is at home (initial location). According to the model, this person undertakes shop/personal business before work. During the aggregation of activity types, serve-child activities were combined with shopping and personal business activities. Because this person is a single parent, we conjectured that this must be a serve-child activity. Also, the person returns home before work. Then, it appears that this person drops off a child and then returns home prior to work. So far, the pattern is as follows: home → child drop → (return) home.

Next the individual goes to work. While at work, the individual undertakes an eat/meal activity. No other activities are undertaken while at work. The individual presumably returns to work after the eat/meal activity. The pattern thus far has become: home → child drop → return home → work → eat/meal → work.

There are a total of three activities undertaken in the after-work period. They are shopping/personal business (presumably serve or pickup child), entertainment, and eat/meal. There is no temporary return home trip in the after-work period. Thus, it appears that this individual undertakes all of these activities after work prior to returning home. The question then becomes: how are these three activities sequenced? Many factors influence the sequencing of activities and one would need richer preference data and possibly rule-based heuristics to determine activity sequencing (Pendyala et al. 1998). At this point in the model development, we adopted a simplified heuristic rule to determine the activity sequence. Using the values of predicted probabilities in table 6 as an ordering mechanism, the individual would first proceed to an entertainment activity, then turn to an eat/meal activity, and finally pick up the child (shop/personal business after work) prior to returning home. The final pattern then becomes: home → child drop → return home → work → eat/meal → work → entertainment → eat/meal → child pickup → home.

Figure 4 shows the activity scheduling patterns generated for the six hypothetical individuals considered in table 5. The model offers very plausible and reasonable activity schedules. For example, person number 2 is a high-income single male. Consistent with expectations, this person undertakes several after-work activities including eating out, shopping/personal business, and entertainment/recreation. On the other hand, person number 1, who is a low-income single male, undertakes fewer activities and does not engage in out-of-home entertainment. Person number 3 is very similar to person number 4, except she is a low-income individual. The difference between their activity patterns reflects their income difference: whereas person number 4 eats out and pursues entertainment after work, person number 3 does not.

The model may predict activity scheduling patterns that are not possible due to situational or institutional constraints (Kitamura et al. 2000). For example, an individual may be constrained to pick up a child prior to engaging in other after-work activities. These aspects of activity pattern generation need to be incorporated by combining this model with other models of activity behavior, including rule-based, econometric, or behavioral decision approaches. By combining this model with models of activity sequencing and prioritization, activity duration, departure time choice, prism constraints, etc., realistic and plausible activity patterns (with detailed time-of-day information) that do not violate various constraints can be generated.

CONCLUSIONS AND FUTURE RESEARCH

This paper presents a simple and practical nested logit model that can be used to predict the daily activity schedule of a commuter. The model schedules nonwork activities in relation to the work activity, thus explicitly recognizing the limited spatial and temporal flexibility associated with the work schedule. The model schedules various nonwork out-of-home activities in three possible time periods (or prisms), namely, before work, at work, and after work. In addition to scheduling out-of-home non-work activities, the model includes the capability of scheduling temporary return-home trips, thus facilitating the identification of both home-based and work-based trip chains for commuters.

The behavioral paradigm suggested in this paper is that individuals first plan the nonwork activities that they need to accomplish in a day and then schedule these activities in relation to their work activity. Several alternative nested logit structures were estimated on the 1996 San Francisco Bay Area activity survey sample dataset in an attempt to operationalize the behavioral paradigm. The two-stage decision process embodied in the behavioral paradigm was supported by the estimation results, albeit with some modifications to account for the fact that some activity scheduling patterns are far more prevalent than others.

The paper includes a numerical example to illustrate how the model can be used to predict a daily activity schedule for commuters. The model includes the capability of scheduling return trips home that may occur during the day, thus facilitating the identification of home-based trip chains (in addition to work-based trip chains). Six hypothetical individuals with different socioeconomic characteristics were considered and their activity schedules simulated using the nested logit model. This was done by combining the application of the nested logit model with a Monte Carlo simulation method and simple heuristics that facilitated the identification and sequencing of activities in the schedule. A quick check in which predicted schedules were compared against actual observed schedules of very similar (but not always identical) individuals in the dataset showed that the model predictions were virtually identical to observed schedules.

The model presented in this paper is only a small piece of an overall activity-based model system. The model needs to be combined with other models of activity behavior including activity sequencing, activity frequency, activity duration, activity timing, and in-home vs. out-of-home activity substitution/complementarity to fully identify and describe an individual's activity-travel pattern. In addition, appropriate rule-based heuristics need to be incorporated to ensure that the predicted pattern is plausible, feasible, and satisfies all constraints.

The nested logit model presented in this paper may itself be improved in several ways both from an empirical as well as a methodological standpoint. In this effort, several activity purposes were aggregated into composite categories (e.g., shopping/personal business/serve child). However, it would be preferable to retain the differentiation among activity categories so that their unique characteristics may be better reflected in the model and the identification of specific activities in the pattern is easier. The inclusion of accessibility variables would be another important enhancement to the model, because activity generation and time-of-day scheduling are highly influenced by spatio-temporal activity accessibility. In addition, it would be helpful to test and estimate alternative structures on different datasets to see whether a more robust and unified theory of activity scheduling behavior can be developed.

The assumptions implicit in the nested logit model (for example, that the Independence from Irrelevant Alternatives (IIA) assumption holds at each level of the nested structure) should be tested to ensure that the nested logit modeling methodology and the nested structure adopted are appropriate for modeling activity scheduling behavior. Also, the nested logit model structure proposed in this paper does not accommodate multiple episodes of the same activity type in one time period. Some individuals will pursue multiple episodes of the same activity (say, shopping) in one time period (this was found to be extremely rare in the San Francisco Bay Area dataset, but nevertheless worthy of accommodation in the model structure). Finally, another issue that merits improvement concerns the use of the nested logit model in the presence of interrelated choice alternatives.

From an application standpoint, the model should be enhanced to incorporate the capability of responding to a range of transportation policy scenarios. A major benefit of the activity-based approach is that it offers a behaviorally robust framework in which the impacts of transportation policies on individual travel behavior can be assessed (Pendyala et al. 1997). Increases in congestion, travel demand management strategies, transportation control measures, or new transportation investments (highway or transit expansion) may lead to adjustments in daily activity schedules. In its current form, the model is not wholly sensitive to such variables. Either the model needs to incorporate such variables so that it is sensitive to the changes brought about by alternative transportation policies or it needs to be combined with another model capturing such sensitivities (e.g., a stated preference model). The development of such models would, however, also place greater demands on data requirements.

ACKNOWLEDGMENT

The authors thank the Florida Department of Transportation for providing funding for the research described in this paper. The authors also thank Ken Vaughn and Chuck Purvis of the San Francisco Bay Area Metropolitan Transportation Commission for providing the data used in this study and taking the time to answer many questions. The contents of this paper reflect the views of the authors who are responsible for the facts and the accuracy of the information presented here. The contents do not necessarily reflect the official views or policies of the Florida Department of Transportation.

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Address for Correspondence and End Notes

Ram M. Pendyala, University of South Florida, ENB 118, Department of Civil and Environmental Engineering, 4202 East Fowler Avenue, Tampa, FL 33620-5350. Email: pendyala@eng.usf.edu.

1. The survey also collected data on Bay Bridge usage in connection with a peak-period toll study; however, variables in the dataset related to this aspect of the study are not used in this paper.

2. The term prisms, in the context of activity-based travel behavior, has been widely used to represent the limited time and spatial accessibility travelers typically have.