Danny Givon, Jerusalem Transportation Masterplan Team, Israel

Transcription

1 Paper Author (s) Gaurav Vyas (corresponding), Parsons Brinckerhoff Peter Vovsha, PB Americas, Inc. Rajesh Paleti, Parsons Brinckerhoff Danny Givon, Jerusalem Transportation Masterplan Team, Israel Yehoshua Birotker, Jerusalem Transportation Masterplan Team, Israel Paper Title & Number Investigation of Alternative Methods for Modeling Joint Activity Participation [ITM # 9] Abstract Investigation of alternative methods of joint activity participation is a unique research effort to understand how household members interact to participate in a joint activity. The joint activity participation is a less explored step in Activity Based Travel Demand Modeling since enlisting all possible subsets of household members for a large household may result in a large number of alternatives. For example, the number of possible subsets of eligible members out of 0 persons is 0=,0. After exclusion of one empty subset and 0 subsets with a single member we obtain,0 distinct subsets with two or more members for joint activity participation. Even more importantly, a joint choice model formulation is behaviorally unappealing and would require a formulation of a complicated utility function for each possible subset. Additionally, different subsets would have highly differential degree of similarity that would require a sophisticated error structure. The paper analyzed three alternate methods to model joint activity participation which are relatively easier to estimate and implement for households of any size. In all three methods, the travel party is constructed based on individual and pairwise propensities of the household members to be engaged in a joint activity. These propensities were statistically estimated with the survey data in a form of relatively simple binary choice models. Travel party emerges in the process of microsimulation as a result of a reconciliation of decisions of different household members. This approach is an example of using the agent-based modeling paradigm to frame an intra-household decision-making mechanism in addition to econometric models. Statement of Financial Interest The authors do not have any direct financial interest with regard to this work. Statement of Innovation Investigation of alternative methods of joint activity participation is a unique research effort to understand how household members interact to participate in a joint activity. The joint activity participation is a less explored step in Activity Based Travel Demand Modeling since enlisting all possible subsets of household members for a large household may result in a large number of alternatives. For

2 example, the number of possible subsets of eligible members out of 0 persons is 0=,0. After exclusion of one empty subset and 0 subsets with a single member we obtain,0 distinct subsets with two or more members for joint activity participation. Even more importantly, a joint choice model formulation is behaviorally unappealing and would require a formulation of a complicated utility function for each possible subset. Additionally, different subsets would have highly differential degree of similarity that would require a sophisticated error structure. The paper analyzed three alternate methods to model joint activity participation which are relatively easier to estimate and implement for households of any size. In all three methods, the travel party is constructed based on individual and pairwise propensities of the household members to be engaged in a joint activity. These propensities were statistically estimated with the survey data in a form of relatively simple binary choice models. Travel party emerges in the process of microsimulation as a result of a reconciliation of decisions of different household members. This approach is an example of using the agent-based modeling paradigm to frame an intra-household decision-making mechanism in addition to econometric models.

3 Investigation of Alternative Methods for Modeling Joint Activity Participation Gaurav Vyas, Parsons Brinckerhoff Penn Plaza, rd Floor New York, NY 09 Phone: 0 vyasg@pbworld.com Peter Vovsha, Parsons Brinckerhoff Penn Plaza, rd Floor New York, NY 09 Phone: vovsha@pbworld.com Rajesh Paleti, Parsons Brinckerhoff Penn Plaza, rd Floor New York, NY 09 Phone: paletir@pbworld.com Danny Givon, Jerusalem Transportation Masterplan Team (JTMT) Clal Building, First Offices Floor, 9 Jaffa Rd Jerusalem, Israel Phone: danny_g@jtmt.gov.il Yehoshua Birotker Jerusalem Transportation Masterplan Team (JTMT) Clal Building, First Offices Floor, 9 Jaffa Rd Jerusalem, Israel Phone: birotker@jtmt.gov.il Paper size:,9 words + table ( 0) + figure ( 0) =,99 words

4 Objectives, Motivations and Innovation In recent years, many researchers and practitioners have put an increased focus on modeling joint activities. Most of these efforts have limited their study to either two primary adults in the household (Cherchyne et al., 0) or on a small set of non-mandatory trip purposes (Wang and Li, 009). Such an approach provides a starting point in the study of joint travel, but it cannot capture the intra-household interaction mechanism in its entirety. One of the more advanced modeling of joint activity participation is done by Bhat et al, 0. They use Multiple Discrete Continuous Extreme Value (MDCEV) as a time allocation model and allocate out-of-home activity time among different combinations of individual and joint activities for different household members. While this approach is more consistent, it does not take into account the possibility of multiple episodes of the same joint activity purpose. Moreover, the number of alternatives explodes with an increase in household size. The analysis presented in this paper is implemented on, households surveyed in the GPS-assisted Household Travel Survey (HTS) in the Jerusalem Metropolitan Region completed in 00. The survey includes population sectors: ) Secular Jewish population (%), ) Orthodox Jewish population (%), and ) Arab population (%). The average household size for both the Orthodox Jewish and Arab population is more than and for Secular Jewish population is more than. which emphasizes the importance of intra-household interactions. This paper investigates alternate methods to model joint activity participation which can be estimated statistically and applied in the framework of microsimulation ABM, including large households that represent a problem for some other methods that explode with the growing household size. This is a unique effort to understand how household members interact with each other to participate in joint activities. Each of the compared models below is applied to the household sample in a microsimulation fashion and its performance is evaluated against the observed participation in joint activities Methodology In the current research, we focus on joint non-mandatory activities implemented by household members. In most cases, these joint activities are associated with fully-joint travel. In the Coordinated Travel and Regional Activity Modeling Platform (CT-RAMP) that served as the ABM design framework for this research, joint non-mandatory activities are modeled in two steps. First, these activities are generated at the household level. Secondly, the joint participation sub-model comes after the joint activity generation step in order to identify the exact subset of household members participating in each activity. The joint activity generation step explicitly models the number of joint activities by nonmandatory purposes (Shopping, Maintenance, Eating-out, Visiting relatives or friends, and other Discretionary) and by party types (Adults only, Children only, and Mixed party). This step in itself is relatively straightforward and it has been presented in the previous publications and included in many applied ABMs in practice (CT-RAMP and others). Number of alternatives household activity generation in MDCEV structure for a household with N members and P purpose is ( N ) P.

5 9 0 The person participation model applied at the second step is in the focus of the current study. This model is less straightforward compared to the activity generation step since enlisting all possible subsets of household members for a large household may result in a large number of alternatives. For example, the number of possible subsets of eligible members out of 0 persons is 0 =,0. After exclusion of one empty subset and 0 subsets with a single member we obtain,0 distinct subsets with two or more members for joint activity participation. Even more importantly, a joint choice model formulation is behaviorally unappealing and would require a formulation of a complicated utility function for each possible subset. Additionally, different subsets would have highly differential degree of similarity that would require a sophisticated error structure. In this paper, three different methods to construct a travel party for joint activity are analyzed that obviate an explicit enumeration of all possible subsets. In all three methods, the travel party is constructed based on individual and pair-wise propensities of the household members to be engaged in a joint activity. These propensities were statistically estimated with the survey data in a form of relatively simple binary choice models. Travel party emerges in the process of microsimulation as a result of a reconciliating intra-household mechanism. The three methods analyzed in this paper are shown in Figure and described in the following sub-sections.

6 Figure : Model structures of Three Models analyzed in this paper

7 Individual Sequential Person Participation Model This method has been adopted as the standard method for modeling joint participation in CT-RAMP applications to date. The model structure is illustrated as Model in Figure. The participation model represents a set of simple binary choice models developed for each person type. Then the model is applied sequentially for each relevant household member in micro-simulation setup. Each person may join the party or not based on his/her individual propensity estimated as a function of the person characteristics (worker status, student status, age, gender, etc) as well as household characteristics (income, car ownership, size etc). In a case when the model fails to form a party with at least household members, the simulation procedure is restarted and repeated until a valid travel party has been formed. This model is simple and captures some basic propensities of each individual to participate in a certain joint activity. However, it lacks an explicit interaction among different household members and it does not take into account the pair-wise preferences among different household members. For instance, a full-time worker might be more likely to have a joint activity with non-workers than with other full-time workers in the household because of the difficulty to consolidate schedules between two full-time workers. This inability of this model to capture the affinities among different household member motivates for a pair-wise approach explained in the next section.. Non-Ordered Pair-wise Propensities Model To capture the affinities among different household members with respect to participation in joint activity, a binary choice model for each non-ordered pair of persons in the household to perform a joint activity together was estimated. The model structure is explained with an example as Model in Figure. As an example, consider a household with household members and one joint activity. Let s say Person and Person are participating in the joint activity, as shown in the Figure. So, the chosen alternative for the pair (P,P) is yes whereas for pair (P,P) and (P,P) the chosen alternative is not participating in the joint activity. Thus, this model has an inherent advantage over the sequential model because it captures the interactions between different household members by considering all pair-wise subsets of the household members. The variables used to explain these interactions are various personlevel variables such as age difference for the pair, gender composition, work status etc. A simulation algorithm is used to apply this model which includes the following steps:. Simulate choice X[i][j] = X[j][i] = 0, (0=not to participate, =participate) for each pair of household members [i,j] independently using propensity P[i,j] given by the binary choice model.. Calculate marginal participation index for each person Y[i] = max{x[i][j]}. This index is equal to if the person participates in at least one pair with somebody.. Identify all household members k that chose to participate with at least one other household member Y[k]=. If k=null, no party is formed.. Check consistency (transitivity) of the simulated choices across all participating household members X*k+*k+ =. If true, the party is formed with k participants. If not, go to.

8 So, the party for a joint tour is formed by pair-wise participations. Unlike the individual sequential model, the party type emerges from microsimulation. Also, checking consistency among different pairs indirectly incorporates simultaneity (across the entire household) in the model application although it was estimated treating each pair as a separate observation.. Combinatorial Algorithm Based on Individual Marginal and Ordered Pair-Wise Conditional Propensities The third model was developed as a predetermined sequence of binary choice models. The algorithm is based on marginal and ordered conditional pair-wise probabilities to participate in a joint activity. This model consists of a set of three binary choice models: ) Marginal individual participation model (P[i]), ) Conditional pair-wise propensities model with a pivot on the members participating in joint activity (P[j i] that is probability of person [j] to participate in joint activity if person [i] participates), and ) Conditional pair-wise propensities model with a pivot on the members not participating in joint activity (Q[j i] that is probability of person [j] not to participate in joint activity if person [i] does not participate). The model structure is illustrated as Model in Figure. As shown in the Figure, this model captures the willingness of the household members to join each other person in the household for a joint activity. For example, consider the same -person household as was described for the non-ordered pair-wise propensities model. For the marginal model, P and P will have the chosen alternative as Yes i.e. participating in the joint activity. For the participation P[j i] model, the pairs are pivoted on the participating members i.e. Person and Person. So, there are pairs for P[j i] model as shown in the Figure. As an illustration, (P,P) pair captures the willingness of Person to join Person in the joint activity. For the non-participation Q[j i] model, the pivot is Person and thus there are possible pairs. So, (P,P) pair captures the tendency of Person to not participate in the joint activity when Person is not participating. In a certain sense, thus, this model is behaviorally richer compared to the two other models since it captures intra-household interactions in a more comprehensive way, incorporating the willingness of household members to participate or not to participate in a joint activity together. The combinatorial algorithm is adopted to apply this model which includes the subsequent steps:. Apply marginal model for each household member and make a preliminary choice (making sure to preserve the observed marginal probabilities to participate by person type).. Loop over all ordered pairs of household members sequentially, redefining their participation and non-participation choices.. If the st person participates, apply P[j i] model for nd person (in order to preserve pair-wise conditional probabilities for joint participation).. If the st person does not participate, apply Q[j i] model for nd person (in order to preserve pair-wise conditional probabilities for no participation).. If or more persons participate, form a party, else go to step and simulate again until a valid party is formed.

9 For the conditional models, a random sequence of household members is applied to reduce any possible systematic bias in prediction. Also, similar to the non-ordered pair-wise propensities model, the party type for the joint activity is an outcome of this model Major Results The three models illustrated in the previous section share a similar and quite rich set of explanatory variables. The estimated results are not discussed here due to the space constraint but they are included in the full paper and presentation. The focus of the brief paper is on the assessment of three model mechanisms and their ability to capture the observed dimensions of joint activity participation. The three models were implemented in micro-simulation fashion for the surveyed sample of households to assess their ability to replicate the observed characteristics of the party for joint activities. The results for such important characteristic as party size are shown in Table.

10 Table : Validation of alternative methods for modeling joint activity participation Prediction by individual sequential method Sector + + Arab % 0% 0% % 0% 0% 0% Orthodox 0 0 % % 9% % % 0% 0% Secular % % % % 0% 0% 0% Arab 0 % 0% % % % 0% 0% Orthodox 9 9 % % % 9% % % % Secular % 9% % % % 0% 0% Prediction by non-ordered pair-wise propensities method Sector + + Arab % 0% 0% % 0% 0% 0% Orthodox 0 0 % % 9% % % 0% 0% Secular % % % % 0% 0% 0% Arab 0 0 % % % 0% 0% 0% 0% Orthodox % % % % 0% 0% % Secular 0 % % % 0% 0% 0% 0% Prediction by non-ordered pair-wise propensities method (calibrated) Sector + + Arab % 0% 0% % 0% 0% 0% Orthodox 0 0 % % 9% % % 0% 0% Secular % % % % 0% 0% 0% Arab 0 % % % % 0% % % Orthodox 9 % % % % % % % Secular 0 9% % % % % 0% 0% Prediction by individual marginal and ordered pair-wise conditional propensities method Sector + + Arab % 0% 0% % 0% 0% 0% Orthodox 0 0 % % 9% % % 0% 0% Secular % % % % 0% 0% 0% Arab % % % % 0% 0% 0% Orthodox 0 % 9% % % % % 0% Secular 0 0 % % 0% % % 0% 0%

11 9 0 As can be seen in Table, the individual sequential method doesn t replicate the observed party size distribution well and it is biased toward bigger party sizes. On the other hand, the non-ordered pairwise model is somewhat biased towards smaller party sizes but the distribution is not as skewed as for the individual sequential method. The indirect simultaneous application through consistency checks inherent to the non-ordered pair-wise method, helped in replicating the party size distribution better. In the non-ordered pair-wise model, the party size emerges out of the pair-wise participation and thus the model could be calibrated, to some extent, by increasing the pair-wise affinity among different household members. The calibrated results show a good replication of party size distribution. Finally, the prediction by ordered pair-wise model seems to be biased towards bigger party sizes but the results are far better than the individual sequential method Implication for the science and/or practice of travel modeling Modeling intra-household interaction is a very important and complex component of ABMs. Methods applied in ABMs in practice are unable to capture this behavior with the necessary level of details. For Jerusalem, where the average household size is very high, there is no yet an adequate model structure in practice or research to capture the joint activity participation mechanism. With that motivation, this paper investigated three alternate methods to model joint activity participation. These models were applied to the sample of surveyed households from the Jerusalem HTS 00 and assessed in terms of the party size distribution predicted by each model. Of the three models, the non-ordered pair-wise propensities model replicated the party size distribution best. This model is easy to estimate, calibrate and very efficient in application. Thus, the non-ordered pair-wise propensities model was adopted for the current version of the Jerusalem ABM. One of the possible future extensions of the models discussed in this paper could be a full integration of person participation with joint activity generation step. These two sub-models currently have many duplicative variables. In reality, joint activity generation and participation steps are closely intertwined. Joint activity cannot be generated by the household if there is no interested participant (or more exactly a pair of participants). The presented models have a potential to be generalized to incorporate the joint activity generation step. In this case, the individual participation step described in this paper should include cases where a joint activity was not implemented by the household rather than being conditional upon the implemented activity. In this case, failure to form a party would be a natural outcome indicating on the household choice not to have such an activity rather than a trigger to restart the simulation. This approach would be closer to the general concept of agent-based modeling where the group-wise behavior is emergent through a microsimulation mechanism and is not constrained at the household level.

12 References Bhat, C.R., K.G. Goulias, R.M. Pendyala, R. Paleti, R. Sidharthan, L. Schmitt, and H-H. Hu (0), "A Household-Level Activity Pattern Generation Model with an Application for Southern California," Transportation, Vol. 0, No., pp Cherchye L, Muynck TD, DeRock B (0). Non-cooperative household consumption with caring. Working paper, Tillburg Univeristy. Wang D, Li J (009) A model of household time allocation taking into consideration of hiring domestic helpers. Transportation Research Part B (): 0-. Only a sub-set of references are cited due to space constraints, full paper will have the exhaustive list of references