A Comparison of the Performance of the Poisson and Multinomial Logit Models in the Spatial Transferability (Case Study: Household Work Trips)

Trip generation is the first stage of the conventional four-step travel forecasting framework. One of the most important characteristics of travel demand models is transferability. The cost of collecting data for travel demand modeling is high and increasing each year. Spatial transferability of travel forecasting models can potentially help in significant cost and time savings for areas that cannot invest in extensive data-collection and model development procedures. This paper is to compare the performance of the Poisson and multinomial logit models in the spatial transferability for household work trips. The models are estimated for the Qazvin and Eslamshahr cities based on data from the 2009 Qazvin travel habits surveys and 2013 Eslamshahr travel habits surveys. The sample include econometric-social attributes of 4479 households in Qazvin and 3183 households in Eslamshahr.
The measures for assessing transferability are Transferability Test Statistic (TTS), Transfer Index (TI), Transfer Rho-Square, like Root-Mean-Square-Error (RMSE), Relative aggregate Transfer error (RATE) and comparision plot of observed and predicted aggregate trip shares.
Results show that Qazvin and Eslamshahr final models include three explanatory variables: number of workers, number of cars and interaction these two variables furthermore Transferability Test Statistic reject the null hypothesis of the two cities parameters equality for two models. Also, result show that from Transfer Rho-Square and Root-Mean-Square-Error multinomial Logit model has better performance in transferability and from Transfer Index and Relative aggregate Transfer error Poisson model has better performance in transferability between Qazvin and Eslamshahr. compare plot of observed and predicted aggregate trip shares indicate that Multinomial Logit model models have better performance in terms of comparison of predicted share of every trip rate level with observed share.
Introduction
Trip generation is the first stage of the conventional four-step travel forecasting framework that estimates the number of trips to and from a traffic analysis zone. Using linear regression model is common in this step and generates an acceptable level of performance from the perspective of transport planning, however this model does not incorporate traveler behavior, integer and non-negative nature of trips. To overcome these limitations, several models have been suggested: count data models such as negative binomial and Poisson for deleting continuous and negative values; and discrete choice models such as logit and Probit for incorporating traveler behavior and preventing continuous and negative values.Furthermore one of the most important characteristics of travel demand models is transferability. Spatial transferability of travel forecasting models refers to the appropriateness of using models developed with data and information from one geographical region for travel forecasting purposes in another region. This topic is of considerable interest from both theoretical and practical standpoints. Theoretically, assessment of a model’s performance in different contexts provides insights into its ability to provide credible forecasts under different scenarios. From a practical standpoint, ability to transfer models from one region to another can help in significant cost and time savings for regions that cannot afford to invest in extensive data-collection procedures. Without transferability in time and space, the use of the model will be compromised due to either over or under-estimating demand, which will lead to inaccurate assessment of the associated transportation needs and poor allocation for infrastructure investment.
Methodology
Although a model is not “statistically” transferable, it could closely approximate behavior in the application context for all practical purposes. Measures of predictability have been used to make such practical assessments. These metrics measure the predictive accuracy of transferred models in the application context and can be classified into two categories: (1) aggregate prediction based transferability metrics (such as relative error measure and root-mean-square error), and (2) log-likelihood based transferability metrics (such as transfer rho-square and transfer index). Aggregate-level prediction-based transferability metrics such as the Root Mean Square Error (RMSE) provide a measure of error in the aggregate predictions (e.g. predicted mode shares) of the transferred model. The analyst needs to make assumptions on the level of acceptable error in predictive accuracy to determine whether a model is transferable. A cautionary note is in order here regarding the use of aggregate-level prediction metrics for transferability assessments. These metrics measure how well a transferred model reproduces aggregate-level behavior (e.g. mode shares) in the application context, but not necessarily the ability to adequately forecast changes in travel demand under different demographic, land-use and transportation system change scenarios.
Among the log-likelihood based transferability metrics, transfer rho-square describes how well a transferred model fits the data observed in the application context, relative to a reference model (e.g., a constants only model). The transfer index (TI) is a derived measure from transfer rho-square in that it is the ratio of a transferred model’s rho-square to the locally estimated model’s rho square. Thus, TI measures the goodness of fit of a transferred model relative to a locally estimated model (the closer the TI value is to 1, the more transferable is the model considered to be)
Discussion and Results
Model estimation relied on the statistical software package Stata. The selection of the final models considered coefficient reasonableness, check of logical relationships, chi-squared statistics, pseudo R², and t-statistics. The result show that Qazvin and Eslamshahr final models include three explanatory variables: number of workers, number of cars and interaction these two variables. Models coefficients have the correct sign and are significant at the 95% level and model statistics are with acceptable ranges.
Conclusions
Transferred Poisson model to Qazvin and Eslamshahr have Transfer Rho-Square, respectively, 0.08 and 0.06, Transfer Index, respectively, 0.83 and 0.77, Root-Mean-Square-Error, respectively, 0.69 and 0.37 and Relative Aggregate Transfer Error, respectively, 1.53 and 0.88 and Transferred multinomial logit model to Qazvin and Eslamshahr have Transfer Rho-Square, respectively, 0.21 and 0.08, Transfer Index, respectively, 0.72 and 0.48, Root-Mean-Square-Error, respectively, 0.24 and 0.35 and big values for Relative Aggregate Transfer Error, respectively.
This study shows that Transferability test statistic reject the null hypothesis of the two cities parameters equality for two models. Result show that from transfer Rho-Square and Root-Mean-Square-Error multinomial Logit model has better performance in transferability and from transfer index and relative aggregate transfer error Poisson model has better performance in transferability between Qazvin and Eslamshahr. compare plot of observed and predicted aggregate trip shares shows that multinomial logit model models have better performance in terms of comparison of predicted share of every trip rate level with observed share.