A Structural Direct Demand Model for Inter-regional Commodity Flow Forecasting

Transcription

1 A Structural Direct Demand Model for Inter-regional Commodity Flow Forecasting Fatemeh Ranaiefar Ph.D. Candidate Institute of Transportation Studies University of California Irvine, CA, USA, Joseph Y.J. Chow Canada Research Chair in Transportation Systems Engineering Assistant Professor Department of Civil Engineering Ryerson University Toronto, ON, Canada, MB K joseph.chow@ryerson.ca Michael G. McNally Professor Department of Civil and Environmental Engineering Institute of Transportation Studies University of California Irvine, CA, USA, mmcnally@uci.edu Stephen G. Ritchie Professor Department of Civil and Environmental Engineering Institute of Transportation Studies University of California Irvine, CA, USA, sritchie@uci.edu Submitted: July, 0 Word Count: Tables and Figures: Tables + Figures = 00 words Total Word Count: To be considered for Presentation in the rd TRB Annual Meeting only

2 Ranaiefar, Chow, McNally, Ritchie 0 0 ABSTRACT A new framework for inter-regional commodity flow forecasting is presented to improve estimates of freight demand for inter-regional and statewide transportation models. The Structural Equations for Multi-Commodity OD Distribution (SEMCOD) model is based on simultaneous direct demand equations with structural relationships between dependent and independent variables of the model. SEMCOD is a flexible model that integrates the generation and distribution steps in conventional four-step demand models. This integration provides consistent estimates for elasticity analysis of effective factors for freight flows at the OD level and for productions and attractions at the zone level. Also, the model is sensitive to policies that increase or decrease generalized transportation cost, not only for flow distribution but also by measuring the change in marginal production and attraction of each zone. Unlike gravity-type models, this framework provides the opportunity to identify homogenous clusters of ODs and to more accurately estimate parameters for each cluster. The proposed model is estimated using the Freight Analysis Framework (FAF) and other publicly available data sources for commodity groups. Elasticity of different factors on production, attraction and flow of different commodity groups with respect to industry specific employment, population, industrial GDP, variables related to consumption and production of energy and land use variables, are studied. Considering cross relationships between supply chains of different commodity groups in the model significantly improved the fitness of the model. The fitness measures confirm satisfactory performance of the model. Keywords: freight transportation, distribution models, commodity generation models, Structural Equation Modeling, direct demand models

3 Ranaiefar, Chow, McNally, Ritchie INTRODUCTION There is an increasing interest in forecasting commodity flows and understanding the factors influencing these flows due to increasing globalization and sustainability demands. While a majority of prior research on commodity flows has been driven by economists for macroeconomic policymaking [-], the increasing need in recent years for aligning infrastructure investments (e.g., ports, roads, rail, intermodal facilities) with these policies has driven the development of new methods and models in commodity flow forecasting, particularly at the interregional level [-]. Due to limitations in private sector freight data, recent models developed for interregional freight and commodity flow forecasting tend to follow a sequential approach much like the passenger-oriented Four Step Model []. A survey of statewide models developed in the United States as of 0, showed that among the states that had some type of freight forecast model, more than 0% of them are simple four-step oriented models. One particular feature that has generally been embraced by modelers and researchers is the separation of commodity flow forecasting into two steps: a commodity generation step (provided exogenously in some models) and a distribution step (e.g. the class C and D models in [] and [-]). However, the sequential paradigm in passenger four step models is a heuristic approach with limited theoretical basis, and considered inferior relative to integrated forecasting approaches[]. Further, errors earlier in the sequence tend to propagate through the model []. One might argue that in passenger models it is adequate to at least keep trip generation and distribution separate since destination choices made by commuters depend on the spatial configuration whereas the propensity for travel can be related only to demographic factors like income level, age, or number of vehicles owned. In the case of commodities, however, the production, consumption, and distribution of goods are generally integrated decisions made by firms as part of supply chain management. We adopt Jara-Díaz s [] view of the multidimensional nature of the product in freight commodity flows, that a transportation output is ideally a flow defined as a vector along origindestination, commodity, and period dimensions. It is essentially a service that is defined by all these dimensions, and trying to forecast such a product in a sequential manner would not capture the multifaceted nature of freight demand. In particular, the flow of commodity is not a derived demand in the same sense as passenger travel where no utility is gained in the travel/transport process, because freight transportation is a profitable service that contributes to the GDP of an economy. In line with this argument, we propose that commodity flow should ideally be modeled using an integrated approach that combines generation and distribution. One such model is the direct demand model [-]. Furthermore, some of these commodities should be highly interrelated with one another, as shown in Ranaiefar et al. []. We identify and estimate a structural equation model comprising direct demand functions for groups of commodities. Given the heterogeneous availability of data between domestic flows and imports/exports, we test our argument on only domestic flows using publicly available data so that the model can be easily replicated for any geographical region with the same types of data. The remainder of the paper is organized as follows. Section is a literature review. Section provides details on the data preparation. Section presents the structural direct demand model specification and estimations results. In section different analyses of model s outputs are discussed. Our conclusion and closing remarks are presented in Section.

4 Ranaiefar, Chow, McNally, Ritchie LITERATURE REVIEW. Generation and Distribution Models As suggested by Figure, a majority of interregional freight commodity models follow a sequential commodity generation-distribution approach. Different methodologies for trip generation models have been used in freight and passenger models including growth factors, linear regression [-0], cross classification [], spatial regression [-] and structural equation modeling []. These models relate socioeconomic factors to the production and consumption of commodities. On the other hand, trip distribution models were developed to forecast aggregate behavior of passenger trips for different planning horizons. Some methods are designed for short term predictions, such as different variations of Fratar [] or growth factor methods using an OD matrix from the base year. These methods cannot be used to fill in unobserved cells of partially observed trip matrices. In addition, they do not take into account the changes in transport cost [] and therefore are not sensitive to infrastructure investments. A family of gravity models (initially inspired by analogy to Newtonian mechanics) became increasingly popular, although there was initially no formal theory to confirm that personal travel behavior is similar to movement of particles in space. The volume of flow between an origin and a destination is directly related to total productions at the origin and total attractions at the destination and is inversely related to a generalized impedance function []. Wilson [] provided a theoretical grounding for gravity models based on statistical rather than Newtonian mechanics by deriving the family of models using entropy maximization. Due to the economic nature of freight distribution, some models have been developed with an input-output structure [] to capture the relationships between commodities from different industries (class E models in []). A basic IO model does not provide sensitivity to impedances or other zonal attributes, but multiregional IO models have embedded gravity models to account for both impedances and interrelationships between industries ([],[]). Kockelman et al. s [0] model (Random Utility Based Multi-Region Input-Output, RUBMRIO) embedded a logit distribution model instead of a gravity model in the IO structure to provide sensitivity to zone-based attributes as well. The existence and uniqueness of the solution was proven []. While this approach can capture interrelationships between industries (e.g., supply chain effects) in a macroscopic scale, its structure is not designed for evaluating substitution effects or elasticities between two variables, and requires commodity generation to be modeled separately.. Direct Demand Model In regional science theory, spatial interaction models have been developed to model transaction flows or migration of population between regions. The goal is to predict the flow directly based on demographic or economic parameters. In other words, these are comparable to noconstraint gravity models. Working with spatial econometric models requires special data preparation due to ) spatial dependency between the observations and ) spatial heterogeneity in the relationships. Spatial dependency means that observations at one location depend on observations at other locations. Spatial heterogeneity refers to variation in relationships over space. In the most general case we might expect a different relationship to hold for every point in space [0]. A basic spatial interaction model is defined in equation (), where is any transaction between region i and region j such as dollar value or tonnages of goods, number of

5 Ranaiefar, Chow, McNally, Ritchie people migrated, or amount of information transferred; ( ) is a function based on parameters in the origin such as population or wage, ( ) is a function based on measures of attractiveness in destination such as number of jobs, and ( ) shows relative accessibility or cost of flow or transaction between origin and destination. =( ).( ).( ) (Eq.) In the transportation literature, this model is known as a direct demand distribution model. The equation is rewritten in a log-linear form for ease of computation. Direct demand models have been used in a few studies such as [-]. These models work well for interregional settings with sparse OD pairs. Oum [] examined the different types of direct demand model structures, suggesting a translog demand system is more flexible than linear, loglinear, or logit models based on aggregate market share data. The hindrance of the direct demand method for the trip distribution problem is lack of control over total inflow and outflow of each zone. This pitfall can be overcome by post-processing the trip OD matrix based on accessory data. We developed a multi-commodity direct demand model with a structural equation modeling (SEM) framework. SEM is a flexible linear-in-parameters multivariate statistical modeling technique that has gained acceptance in the travel behavior research community []. SEM is a more generalized form of linear regression that allows endogenous variables to serve as causal variables for other endogenous variables, and can identify unobservable factors called latent variables (hence the structure). There are different methods of estimating the parameters of these models, such as full information maximum likelihood estimation or three-stage least squares estimation. SEM allows for both confirmatory and exploratory modeling, such that hypothesized causal relationships and correlations can be tested []. SEM can be used to capture inter-dependencies between flows of different commodity groups and supply channels, effectively inferring the unobserved supply chain and land use relationships at an aggregate industrial level, much like economic input-output models []. SEM is used as a confirmatory approach in this study: the structure design is hypothesized and the sample data are evaluated to confirm whether they fit the hypothesized design. Even if a good fitting structure naturally exists, it needs to be identified prior to the estimation. DATA PREPARATION. Zonal Attributes To explain the proposed methodology we used the FAF data base []. FAF is a public data source and provides tonnage of commodity flows between FAF regions in the United States including Alaska and Hawaii. The zones are designed to separate metropolitan areas from the remainder of each state. Figure shows FAF regions in the U.S.

6 Ranaiefar, Chow, McNally, Ritchie FIGURE. FAF regions in United States []. In FAF there are commodity groups based on -digit Standard Classification of Transported Goods (SCTG) classifications. For the purpose of this study, these commodities were grouped into exclusive groups as shown in Table. This grouping was designed based on the characteristics of industries, major mode for each group and trip length distribution []. Commodity group G- Agriculture products G- Wood, paper and printed products -,.. G Crude petroleum G_Fuel and oil products G- Gravel/ sand and other non metallic minerals G- Coal and metallic mineral G-Food, beverage, tobacco products -,..0 G- Manufactured products G-Chemical/pharmaceutical products 0-,.. G0- Nonmetal mineral products,,.. G- Metal manufactured products -,00.. G- Waste material G- Electronics G- Transportation equipments -,.. G- Logs and lumber Sum TABLE. Commodity groups Total production -dig SCTG (K ton) in U.S -,,0.,..,,,0,. 0-,,. ores -,,0..,0,,0,,,00,..,,..0,, 0..,0.. -,, 00 Share of total

7 Ranaiefar, Chow, McNally, Ritchie Explanatory variables were collected from public data sources. Employment and number of establishments, population, agriculture related variables such as farm acreages and tonnage of sold livestock, manufacturing sector GDP, energy-related data such as capacities of refineries, annual consumption and production of power plants of different types are examples of these variables. Details of data preparation steps are explained in []. Network distances between origin and destination pairs are calculated based on the FAF national network. Travel time and travel cost function for every commodity group for available modes including truck, rail and multi-modal are estimated using the Carload Waybill Sample [], sample of truckload fares and other empirical studies [0], regional fuel price [0], and payload factors for each commodity group.. Measures of Attractiveness The value of each cell in the OD table depends on characteristics of the origin, characteristics of the destination, and measures of attractiveness between them. Some of the measures have a negative relationship, meaning smaller values result in higher attraction. Measures are calculated across available modes, including truck, rail and truck-rail. The following are measures of attractiveness considered in this study: Distance (miles): shortest distance on road network or Euclidean distance, as well as functions of these measures such as ln(dist), exp(dist), dist α. Travel time (hours): uncongested travel time based on posted speed limits on network links for trucks and based on rail waybill data for rail cargo Average shipment cost ($/ton-mile): estimated based on sample data for different commodity groups for each mode, fuel price, and spatial dummies for each region Utility: estimated based on generalized cost of transportation for each mode Utility with spatial variables: estimated based on generalized cost of transportation for each mode and spatial dummies for each zone. Distance has a major role in each of the above measures. Due to proprietary nature of freight data there is no public data about logistic contracts, actual supply channel costs, shipment size, and frequency of shipments, which are important components of goods movement cost. In this study, transportation cost is viewed as an operational cost or average basic rate ($/ton-mile). Figure shows the correlation of flow of each commodity group with some of the above mentioned measures. G refers to commodity group, Dist refers to distance, LN refers to natural logarithm function and LGSM-UTIL refers to log-sum of utility. The logarithmic form shows the strongest correlation for most commodities. The term utility is used in the negative direction, so ODs with higher utility absorb more flow ceteris paribus.

8 Ranaiefar, Chow, McNally, Ritchie 0 Correlation G G G G G G G G G0 G G G G G G &DIST LN( DIST) LN(G) &LN( DIST) LN(G)& LGSM UTIL FIGURE. Correlation of flow and impedance measures. Demand for freight transportation may show inconsistent behavior with transportation operational cost, fuel price or distance for most of the commodities, although the elasticity is not negligible []. Figure shows the correlation between logarithm of flow and logarithm of distance for sets of ODs within each distance range. Generally the relationship gets weaker as distance is increased. The strength of the relationship for most of the commodities declines sharply after about 00 miles. For crude petroleum, G, the trend is very different due to the major share of pipeline flow in contrast to other commodities. Some commodity groups show statistically insignificant relationships when distance is greater than 000 miles, such as agriculture products (G) or Gas and fuel oil (G) or Gravel (G). FIGURE. Histogram of Correlation of log of flow (vertical axis) and log of distance for selected commodity groups for each distance range Figure shows that having only one single model with one set of parameters is not sufficient to explain flow patterns in different distance classes and might lead to inaccurate estimations. This

9 Ranaiefar, Chow, McNally, Ritchie 0 0 contradicts the assumptions of a conventional gravity distribution model where OD pairs over all distances typically are treated equally with a single set of parameters calibrated for the friction factors. While this assumption might be sufficient for passenger travel demand models where the distances between zones do not differ that greatly compared to freight, it makes a big difference in the commodity based models as our experimental results indicate. STRUCTURAL EQUATIONS FOR MULTI-COMMODITY OD DISTRIBUTION MODEL (SEMCOD) SEMCOD is an interregional multi-commodity flow distribution model based on spatial econometric interaction model (or direct demand distribution) in structural equations modeling (SEM) framework. Because SEM is a confirmatory modeling approach, the fitness depends heavily on the knowledge obtained during the data mining process in the data preparation phase. The SEM framework is a flexible tool that provides the opportunity to include relationships between OD pairs, interdependency of flow between different commodity groups, and relationships between independent variables while simultaneously estimating all parameters of the model. The parameters of the model are estimated based on the base year observed OD flows from FAF for 00 [].. Model Specification The general formulation, presented in Equation (), is a second order log-linear model, or a translog model. Brief explanation of each term in the equation is shown in the gray shade area under each term. 0 where is flow of commodity group m from zone i to zone j; is the set of demo-economic attributes of the origin zone; is the set of demo-economic attributes of the destination zone; ( ) ( ) is the origin/destination interaction term for different demo-economic variables; is the distance between origin and destination; and is a logsum of the generalized cost of transportation between the origin and destination for all available modes of transportation for every commodity group. Based on FAF data, if one mode of transportation has not been used between an OD pair for a special commodity group, that mode has not been considered in the logsum function for the base year scenario. For intrazonal flows, is a measure of the size of the zone and is a measure of the generalized cost of transportation in zone i. In this study, is defined as the diameter of a circle with the same area of the respective zone for disaggregated FAZs. For FAF regions, the intrazonal distances are directly imported from the FAF database. Based on the FAF data, % of intrazonal commodity flows are transported by truck so is defined as the log of average cost of transporting kton of

10 Ranaiefar, Chow, McNally, Ritchie commodity m for the average trip length in zone i. ( ) measures the cross effect of other industries on commodity flow of group m.,,,, are the parameters of the model and estimated via Maximum Likelihood using SPSS-AMOS. As explained in Section, not all ODs follow the same pattern and share the same characteristics. Thus it is not possible to estimate an accurate and statistically meaningful model for all OD pairs. The ODs are clustered into exclusive distance-based clusters (one of the advantages offered by our model is this flexibility to cluster): ) Intra-state flows; ) inter-state flows between adjacent zones or zones with a maximum distance of 00 miles based on the road network; ) inter-state flows between non adjacent zones with distance between 00 and 00 miles; and ) inter-state flows with distances greater than 00 miles. Although clustering ODs improve the fitness of the model, it should be noted that it may cause issues for ODs close to boundary conditions. To increase the stability of clusters, ODs are not allowed to change their cluster membership unless the change in distance is at least %. Given the large regions in FAF, intra-state flows are much higher than inter-state flows. Separating intra-state flows improves the fitness of the model and provides the opportunity to apply the model to finer geographic zones. The first class has ODs and they cover % of total annual domestic tonnage flows. Most states have FAF regions; a few states such as California, Texas, Louisiana, or Florida have more than FAF regions. In these states the intrastate flows are very significant and do not have the same behavior as flows to destinations in other states, even if the distances might be similar. Analysis of trip length distribution of flows for different transportation modes shows that transportation by railway is more attractive for ODs with distances larger than 00 miles. % of the tonnages transported by rail are moved over 00 miles. Resor and Blaze [], and Lim and Thill [] also reported that in North America the break-even distance of intermodal freight system is about 00 miles by using market observation. Thus, 00 miles is the break point of class and. There are, ODs in class. They cover % of total annual domestic tonnage flows. Class and have % of domestic flows and cover, ODs. This classification is applied to all commodity groups except group, crude petroleum. The OD flow matrix for this commodity is very sparse. Only,00 ODs (% of all ODs) have annual flow of greater than kton. This group is treated separately. In this paper, only results for the first two clusters are reported. The final estimates are depicted in Table, presented in an appendix at the end of the paper due to size limitation (Detailed results are available upon request to authors).. Model Fitness Evaluation The goodness-of-fit of the model is measured with two categories of measurements. The first category of measurements evaluates the overall fitness of the model in the SEM framework. The second evaluates the performance of the model as a generation-distribution model and compares the estimated and observed trip OD metrics... Category : SEM fitness Hooper et al. [] summarized different fitness measures in the SEM literature. Bollen and Long [] suggested guidelines for presenting fitness indices of structural models. The Chi-Square test is not relevant here because the data is not multivariate normal; thus, other fitness measures of the predictive ability of the model should be considered []. The Independent Model assumes there is no structure in place and serves as a baseline for comparison. The proposed

11 Ranaiefar, Chow, McNally, Ritchie Hypothesized Model considers statistically significant and theoretically meaningful correlations between independent variables and structural relationships between dependent variables. Clearly, the proposed model outperforms independent linear models in all measures, as shown in Table a. The most fundamental measures to indicate how well the proposed model fit sample data are called absolute fitness measures. Root mean square error of approximation (RMSEA) is the most well-known measure for this purpose. RMSEA is measure of poorness of fit -- the lower it is, the better the fitness of model. Models with RMSEA less than 0.0 show a good fit []. The overall RMSEA for cluster one and two in this model is 0.0. TABLE. Model Fit Indices: SEMCOD fit indices (a), statistic for each commodity group (b) (a) SEMCOD Model Fit Index Independent Hypothesized Model model Goodness-of-fit index (GFI) Normed fit index (NFI) Akaike information criterion (AIC) 00.. Incremental fit index (IFI) Comparative fit index (CFI) Expected Cross-Validation Index (ECVI) Root Mean Square Error of Approximation (RMSEA) * rejected at =0.0 ** rejected at = (b) Commodity group G 0 G G 0* G * G 0* G G 0 G * G0 G G G G * G *.. Category : Estimated matrix fitness Kundsen and Fotheringham [] reviewed eight representative goodness-of-fit statistics to compare estimated and observed matrices. The statistics are evaluated with respect to error sensitivity and hypothesis testing. Based on their analysis the relationship between the value of an ideal goodness-of-fit statistic and level of error should be linear. Unlike the chi-square statistic, the ideal goodness-of-fit statistic should also be insensitive to variations in data magnitudes. They ran several simulated experiments and concluded that the most accurate statistics appear to be SRMSE, Ψ, and Φ. The Φ statistic defined as Φ=, where and are respectively elements of a posterior and prior discrete probability distribution. This statistic has limits of zero and positive infinity and is transitive. Since Φ statistic is in absolute value, it is not sensitive to the distribution of over and under predictions. It has no known theoretical distribution and its variance is estimated below by 'bootstrap' methods. The Ψ statistic is introduced by Ayeni [] to overcome inadequate properties of Φ statistic. Ψ statistic is used in this study, shown in Equation (). Ψ= + (Eq.)

12 Ranaiefar, Chow, McNally, Ritchie Here, refers to estimated trip distribution from i to j and refers to observed trip distribution. =( + )/. The distribution of the Ψ statistic is with ( )( ) degrees of freedom. This statistic is transitive and is zero if the observed distribution matrix is exactly the same as the estimated distribution matrix. The upper limit of Ψ is, where m and n are the dimension of OD matrix. The Ψ statistics for all commodity groups are given in Table b. The null hypothesis is that the estimated distribution is equal to the observed distribution. The model is calibrated based on FAF regions. The critical values for with =, degrees of freedom at =0.0 and =0.0 are, respectively,, and,. If Ψ is less than the critical value we fail to reject the null hypothesis and we can assume the estimated and observed distributions are not different. The fitness results are shown in Table b. Six of the fourteen groups were rejected at =0.0, but none of them were rejected at =0.0. ANALYSIS We discuss a few examples to explain the advantages of SEMCOD. Final models for each commodity group have different specifications. They may have different variables because some variables might be excluded from one of the clusters due to unexpected sign of the estimates or the estimate is statistically not different from zero. Although this method integrates trip generation and distribution for all commodity groups, the OD classification will help to identify and prioritize the data gaps based on fitness measures for each cluster or each regression in each cluster. Researchers can identify the clusters with lower fitness measures and gather extra data or surveys only for those clusters to decrease data gathering and processing cost. The clustering framework also increases the interpretability of the model. It is more reliable to compare elasticities and impact of each factor when the model is built based on homogenous or similar observations. Allowing multiple clusters is another advantage and flexibility of SEMCOD compared to conventional gravity distribution. It is not possible to define multiple clusters of gravity models such that the total sum adds up to the marginal without redefining the problem significantly. In this section, elasticity analysis at flow level and at zone level is presented as one of main products of the proposed model.. Elasticity Analysis at the OD Level In SEMCOD, the dependent and independent variables are in logarithmic form. Therefore it is able to easily measure elasticities and explain aggregate industry-level interactions between supply channels of different commodity groups, and between total productions or consumptions with impedances. For example, Table shows that construction employment for a destination (Demp) affects flow of commodity group (mainly gravel and sand) in cluster in two ways (using SEM notation to show causal effect with direct arrows []): ) Demp G G, ) OEmp_DEmp G G is a low value bulk commodity group that is not economically reasonable to transport long distances, but it is one of the top commodity groups in terms of total tonnage movements. DEmp affects the flow of G0 (hydraulic cement and ready mix concrete) from origin i to destination j which will indirectly increase flow of G between the same Origin-Destination pair.

13 Ranaiefar, Chow, McNally, Ritchie A percent increase in DEmp results in 0. 0.=0. percent additional tons of G transported between origin i and destination j per year (plus the direct effect of through the interaction term). This result is intuitive since the two commodity groups may share the same supply channels and have a strong relationship between industries producing and consuming these products. There is also the effect of complementary products: both gravel and cement are usually needed for any construction project. On the other hand, the interaction variable OEmp_DEmp (interaction variable for mining employment, except oil and gas, at origin and construction employment at destination) shows that production and consumption of G between production zone i and consumption zone j are highly interrelated. An increase in Demp by 0 results in additional tons of G0 transported between origin i and destination j, which leads to (.0+0. Oemp) additional tons of G transported between origin i and destination j per year, ceteris paribus. This model framework gives a better understanding of supply chain elasticities between explanatory variables of different commodity groups, which was largely ignored in previous freight forecast studies.. Elasticity Analysis at the Zone Level SEMCOD estimates flows, which provide total domestic production and attraction at each zone if summed up along one j or i, respectively. Thus, it is possible to derive elasticities for the productions and attraction with respect to the explanatory variables. For example, total domestic production of zone i,, is the sum of equation on all destination zones j considering the clustering identity of each OD pair. The elasticity of with respect to generalized cost,, and any production factors at origin,, is shown in equations and respectively. E, =, ( Eq.) E(, )=, +, ( ) ( Eq.) Note that the parameters are cluster-specific. The index C is added to sum up each OD pair with respect to its own cluster. Elasticity of production of freight with respect to any demand factors at destination, or changes in distance can be calculated directly by the derivative of with respect to that variable. We can also compare the result with estimated elasticities by Ranaiefar et al. [] for total production (domestic and exports). For example elasticity of total production of commodity group, logs and lumber, with respect to OEmp (forestry and logging employment) is.. This elasticity for domestic flows for all four clusters are 0., 0., 0.0 and 0.0, respectively. The total export of commodity group from the Los Angeles FAF region is. kton in 00. Therefore, the elasticity estimated from total generation model and SEMCOD are expected to be close. With Los Angeles as the origin, there are destinations from cluster one, from cluster two, from cluster three and 0 from cluster four. The production elasticity is =., which shows the consistency of these two models. In other word, a one-person increase in employment in the forestry and logging industry in the Los Angeles region will result in about, Tons of logs produced from the proposed model. The -0. difference in the elasticity can be attributed to the simultaneous consideration of flow-based factors.

14 Ranaiefar, Chow, McNally, Ritchie Cross Elasticity Analysis The proposed model estimates the flow of most commodity groups simultaneously. Natural commodities that are relatively scarce, including crude petroleum (G) and metallic minerals and coal (G), show very different patterns and insignificant correlations with other commodity groups. Therefore, these groups were estimated separately. The cross elasticity of commodity group n measures the responsiveness of the flow of group n to a change in the flow of another commodity group. A negative cross elasticity denotes two groups which include goods that are complements, while a positive cross elasticity denotes two groups which include goods that are substitute products. For example, the cross elasticity between G0 and G as discussed in the previous section is G. G. It is also possible to estimate cross elasticities between different zones. A one-person increase in Emp (forestry and logging employment) in Los Angeles FAF region will increase the total production of G (logs and lumber) in Los Angeles by tons per year, which will also increase the flow of G (manufactured products) from San Diego to Los Angeles by tons per year. Thus the cross elasticity of production of G in San Diego with respect to production of G in Los Angeles is: (, )=.. CONCLUSION A new framework for inter-regional commodity flow forecasting is presented to provide better estimates of freight demand for regional and statewide transportation models. The Structural Equations for Multi-Commodity OD Distribution model (SEMCOD) is based on simultaneous direct demand equations with structural relationships between dependent and independent variables of the model. The strengths and advantages of the proposed model with respect to a sequential gravity type model are explained with several examples based on a case study using FAF data. SEMCOD model provide the flexibility to group OD pairs into homogenous clusters and estimate a separate model for each cluster. This clustering can improve the fitness of the model and interpretability of the results. Estimation of elasticities for different factors in freight production, attraction, and distribution within a consistent framework is an important feature of SEMCOD. In addition, it is possible to perform cross-elasticity analysis between different commodity groups, clusters, origins or between different destinations to evaluate the effect of changes in demographic, economic or land use variables on inter-regional commodity flow. This study is part of an ongoing project to develop the California Statewide Freight Forecasting Model (CSFFM). The project is currently in the validation phase using 00 provisional FAF data as a benchmark. The model presented here will work together with the total generation model presented previously by Ranaiefar et al. [] via a post processing procedure to estimate domestic flows as well as total imports and exports for each commodity group. In future research, the performance of SEMCOD with a comparable sequential four-step gravity-type model will be assessed. Further studies should be conducted on the effect of different hypothesized structures with different levels of complexity or different clustering formats on the accuracy of freight forecasts. ACKNOWLEDGEMENTS The research reported in this paper was supported by the California Department of Transportation. The authors gratefully acknowledge the assistance provided by Doug MacIvor, Kalin Pacheco, and Diane Jacobs from the California Department of Transportation. The

15 Ranaiefar, Chow, McNally, Ritchie contents of this paper reflect the views of the authors who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the State of California. This paper does not constitute a standard, specification, or regulation. REFERENCES [] Samuelson, P.A. Spatial Price Equilibrium and Linear Programming, American Economic Review, (),, -0. [] Takayama, T., Judge, G.G. Equilibrium Among Spatially Separated Markets: A Reformulation, Econometrica: Journal of the Econometric Society, (),, 0-. [] Harker, P.T., Friesz, T.L. Prediction of Intercity Freight Flows, I: Theory, Transportation Research Part B 0(), a, -. [] Harker, P.T., Friesz, T.L. Prediction of Intercity Freight Flows, II: Mathematical Formulations, Transportation Research Part B, 0(), b, -. [] Regan, A.C., Garrido, R.A. Modelling Freight Demand and Shipper Behaviour: State of the Art, Future Directions. In: Hensher, D. (ed.) Travel Behaviour Research. Pergamon-Elsevier Science, Amsterdam, 00. [] Chow, J.Y.J., Yang, C.H., Regan, A.C. State-of-The-Art of Freight Forecast Modeling: Lessons Learned and the Road Ahead. Transportation, (), 00, [] Tavasszy, L.A., Ruijgrok, K., Davydenko, I. Incorporating Logistics in Freight Transport Demand Models: State-of-The-Art and Research Opportunities. Transport Reviews, (), 0, 0-. [] National Cooperative Highway Research Program Report 0, Forecasting Statewide Freight Toolkits. Transportation Research Board, Washington D.C., 00. [] Sivakumar, A., Bhat, C. Fractional Split-Distribution Model for Statewide Commodity-Flow Analysis. Transportation Research Record: Journal of the Transportation Research Board. No. 0, 00, 0. [0] Kockelman, K.M., Jin, L., Zhao, Y., Ruiz-Jur, N., Tracking Land Use, Transport, and Industrial Production Using Random-Utility-Based Multiregional Input-Output Models: Applications for Texas Trade, Journal of Transport Geography, (), 00, -. [] Ham, H., Kim, T.J., Boyce, D. Implementation and Estimation of a Combined Model of Interregional, Multimodal Commodity Shipments and Transportation Network Flows, Transportation Research Part B, (), 00, -. [] Park, J.Y., Cho, J.K., Gordon, P., Moore II, J.E., Richardson, H.W., Yoon, S.S. Adding a Freight Network to a National Interstate Input-Output Model: A TransNIEMO Application For California. Journal of Transport Geography, (), 0, 0-. [] Ranaiefar, F., Chow, J.Y.J., Rodriguez-Roman, D., Camargo, P.V., Ritchie, S.G., Geographic Scalability and Supply Chain Elasticity of A Structural Commodity Generation Model Using Public Data. Transportation Research Record: Journal of the Transportation Research Board, in press. 0. [] Boyce, D. Is The Sequential Travel Forecasting Paradigm Counterproductive? ASCE Journal of Urban Planning and Development, (), 00, -. [] Zhao, Y., Kockelman, K.M. The Propagation of Uncertainty through Travel Demand Models: An Exploratory Analysis. The Annals of Regional Science, (), 00, -. [] Jara-Díaz, S.R. Freight Transportation Multi-output Analysis. Transportation Research Part A, (),, -. [] Oum, T.H. Alternative Demand Models and their Elasticity Estimates. Journal of Transport Economics and Policy, (),, -. [] Ortúzar, J.D., Willumsen, L.G. Modeling Transport, th Ed., John Wiley & Sons, Inc., 0 [] Cambridge Systematics, Quick Response Freight Manual, Report DOT-T--0, U.S. Department of Transportation and U.S. Environmental Protection Agency, Washington, D.C.,.

16 Ranaiefar, Chow, McNally, Ritchie [0] Southworth, F. Freight Transportation Planning: Models and Methods. In Transportation Systems Planning: Methods And Applications, ed. Goulias, K.G., CRC Press, 00. [] Bastida, C., Holguín-Veras, J. Freight Generation Models: Comparative Analysis of Regression Models and Multiple Classification Analysis. In Transportation Research Record: Journal of the Transportation Research Board. No.0, Transportation Research Board of the National Academies, Washington, D.C., 00, -. [] Novak, D.C., Hodgdon, C., Guo, F., Aultman-Hall, L. Nationwide Freight Generation Models: A Spatial Regression Approach, Networks and Spatial Economics, (), 0, -. [] Chun, Y., Kim, H., Kim, C. Modeling Interregional Commodity Flows with Incorporating Network Autocorrelation in Spatial Interaction Models: an Application of The U.S. Interstate Commodity Flows. Computers, Environment and Urban Systems, (), 0, -. [] Fratar, T. Vehicular Trip Distribution by Successive Approximation, Traffic Quarterly, (),, -. [] Evans, S.P. A Relationship between the Gravity Model For Trip Distribution and The Transportation Problem in Linear Programming, Transportation Research, Vol.,, -. [] Wilson, A.G. A Statistical Theory of Spatial Distribution Models. Transportation Research, (),, -. [] Leontief, W. Quantitative Input and Output Relations in the Economic Systems of The United States, The Review of Economics and Statistics, (),, 0-. [] Wilson, A. G. Inter-Regional Commodity Flows: Entropy Maximizing Methods. Geographical Analysis. (), 0, -. [] Zhao, Y., Kockelman, K.M. The Random-Utility-Based Multiregional Input-Output Model: Solution Existence and Uniqueness. Transportation Research Part B, (), 00, -0. [0] LeSage J., Pace, R.K. Introduction To Spatial Econometrics, CRC Press, New York, 00. [] Kraft, G. Demand for Intercity Passenger Travel in the Washington-Boston Corridor. North-East Corridor Project Report, Systems Analysis and Research Corporation, Boston, Mass. [] Domencich, T.A., Kraft, G. and Valette, J.P. Estimation of Urban Passenger Travel Behavior: An Economic Demand Model, Highway Research Record,,. [] Talvitie, A. A Direct Demand Model for Downtown Work Trips. Transportation, (),, -. [] Oum, T.H., Gillen, D.W. The Structure of Intercity Travel Demands in Canada: Theory Tests and Empirical Results. Transportation Research Part B, (), -. [] Golob, T.F. Structural Equation Modeling for Travel Behavior Research, Transportation Research Part B, (), 00, -. [] Kline, R.B. Principles and Practice of Structural Equation Modeling, The Guilford Press, New York, 00. [] Freight Analysis Framework FAF [] Carload Waybill Sample [] Proprietary trucking rate web site: [0] U.S. Department of Energy. Weekly Retail Gasoline and Diesel Prices. Accessed July, 0. [] Oum, T.H., Waters II, W. G., Yong, J.S. Concepts of Price Elasticities of Transport Demand and Recent Empirical Estimates: An Interpretative Survey, Journal of Transport Economics and Policy, (),, -. [] Resor, R.R., Blaze, J.R. Short-Haul Rail Intermodal; Can It Compete with Trucks? Transportation Research Record: Journal of the Transportation Research Board, No., 00,. [] Lim, H., Thill, J.C. Intermodal Freight Transportation and Regional Accessibility in the United States. Environment and Planning A, 0(), 00, [] Hooper, D., Coughlan, J., Mullen, M. Structural Equation Modeling: Guidelines for Determining Model Fit, Electronic Journal of Business Research Methods, (), 00, -0.

17 Ranaiefar, Chow, McNally, Ritchie 0 [] Bollen, K. A., Long, J.S., Testing Structural Equation Models, Sage Publications, Newbury Park, California,, -. [] McIntosh, C.N. Rethinking Fit Assessment in Structural Equation Modeling: A Commentary and Elaboration On Barrett (00). Personality and Individual Differences, (), 00,. [] Knudsen, D.C., Fotheringham, A.S. Matrix Comparison, Goodness-of-Fit, and Spatial Interaction Modeling, International Regional Science Review, 0(),, -. [] Ayeni, B. The Testing of Hypotheses on Interaction Data Matrices, Geographical Analysis, (),, -. [] North American Industry Classification System Commodity Group G G G TABLE. SEMCOD results for cluster and Cluster Cluster Independent Variable Standard Critical Standard Coefficient Coefficient Error Ratio Error Critical Ratio D_livestock D_Pop DEmp DEmp log_distance M O_HRVLand OEmp D_Pop DEmp DEmp DEmp DEmp log_distance M OEmp OEmp OEmp OEmp OEmp OEmp D_Pop DEmp DEmp DEmp log_distance M OEmp_DEmp OEmp OEmp OEmp OEmp OoilProd ORefinCap

18 Ranaiefar, Chow, McNally, Ritchie Commodity Group G G G G G0 Independent Variable Coefficient Cluster Cluster Standard Error Critical Ratio Coefficient Standard Error Critical Ratio D_Pop DEmp G G log_distance M OEmp_DEmp OEmp_DEmp D_Pop DEmp DEmp log_distance M OEmp OEmp OEmp D_HarvLand D_Pop DEmp DEmp DEmp log_distance O_D OEmp OEmp OEmp D DEmp DEmp G G log_distance M OEmp_DEmp OEmp_DEmp OEmp OEmp OEmp OEmp ORefinCap DEmp DEmp DEmp log_distance M OEmp_DEmp OEmp

19 Ranaiefar, Chow, McNally, Ritchie Commodity Group G G G G G Independent Variable Coefficient Cluster Cluster Standard Error Critical Ratio Coefficient Standard Error Critical Ratio DEmp DEmp DEmp DEmp DEmp log_distance O_D O_D OEmp OEmp OEmp DEmp DEmp DEmp log_distance M OEmp_DEmp O OEmp OEmp OEmp OEmp D_Pop DEm_tot DEmp log_distance O_D OEmp OEmp OEmp DEm_tot DEmp DEmp G G log_distance OEmp_DEmp OEmp_DEmp OEmp OEmp OEmp OEmp DEmp DEmp G log_distance M

20 Ranaiefar, Chow, McNally, Ritchie Commodity Group Independent Variable Coefficient Cluster Cluster Standard Error Critical Ratio Coefficient Standard Error Critical Ratio OEmp OEmp Legend: D: Variable is related to destination zone, O: Variable is related to origin zone EmpXX(X): or digit employment based on NAICS industry classification xxx [] Pop: Population, RefinCap: total capacity of refineries in the zone HRVLand: acreage of harvested land, Livestock: ktons of sold livestock Mx: The logsum utility for commodity group x