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Discrete choice model of agricultural shipper's mode choice.


This article presents disaggregate mode choice model for shippers of agricultural freight. We have used disaggregated revealed preference (RP) data of grain movement from elevators to develop the model. The utility function includes attributes of the modes, attributes of the shippers, and interaction between the two. We initially estimate the mode choice probability assuming the random component of the utility function to have logit distribution, price agreement between shippers and carriers, variation of railcars availability, and variation of equipment ownership annul the assumptions of the logit model. To overcome this problem we introduced heteroscedastic extreme value model, probit model and mixed-logit model. Based on estimated McFadden's likelihood ratio, it is observed that probit model is the best fit. We estimated demand elasticity to assess the sensitivity of mode choice probability to changes in cost of shipment, elevator capacity and quantity of shipment. To validate the model's prediction accuracy we estimated hit ratio of the forecast mode choice for individual shipment; the result was satisfactory.


Discrete choice model, demand elasticity, mode choice, logit model, forecasting mode choice


The US agricultural sector is the largest user of freight transportation services in the country. Trucks are the prime mode for transporting agricultural freight, closely followed by railroads (US Department of Agriculture 2009). Brennan (1998), in his study on capacity analysis of US rail systems, states that there is a change in the share of transportation mode for agricultural freight. A study undertaken by Vachal and Benson (2008) also identifies this trend of mode shift from railroad to truck for agricultural freight. This trend in mode shift has generated a need to analyze the determinants of mode choice for agricultural freight. It is also necessary to understand the sensitivity of mode choice decision to the change in causal variables. In this article, a number of models are presented that predict shipper's choice of mode between truck and railroad. The term "shippers" refers to shippers of agricultural commodities, which includes mostly elevator managers and individuals entrusted with the responsibility to ship grains from elevators to final destinations. The study is based on disaggregated revealed preference (RP) data of grain movement. The RP data is developed from "Grain Movement and Storage Reports" data available from the North Dakota Public Service Commission (NDPSC). NDPSC is acknowledged for giving access to these unique data that are usually expensive to collect and are time-consuming to develop. The NDPSC report is the repository of information on agricultural shipments for all registered elevators in North Dakota. In a previous study Vachal and Tolliver (2001) had used aggregate stated preference (SP) data to identify key factors influencing mode choice by shippers. The findings of this research by Vachal and Tolliver have aided in our model-building process.

We developed binary discrete choice model using disaggregate revealed preference data to compute the utility functions of the two available modes of transportation and to estimate the choice probability. The modeling process relies on the basic assumption that the elevator operators are knowledgeable of the price structure, shipment time, and reliability of the two competing modes. For agricultural goods the logistic costs of a shipment are primarily storage cost, transportation cost, terminal cost, cost of ownership, demurrage cost, and loss/spoilage during shipment. In the absence of information, some of these parameters are aggregated in the random component of the utility function. To simplify estimation we initially assume the random component of the utility function to have a logit distribution. In the shipment data, there are multiple observations from the same shipper and there are oftentimes shipper-specific discounts and other shipper-specific factors that influence mode choice. These nullify the assumptions of the logit model. To overcome the limitations of the logit model, we introduced heteroscedastic extreme value, probit and mixed-logit model. Rich et al. (2009), in a study on freight mode choice, stated that due to heterogeneity of commodity type the transferability and comparison of choice model for freight shipment becomes difficult. In this present study, we specifically model grain shipment, which unlike manufactured goods are homogenous to a large extent: It is expected that transferability of these results would be comparatively straightforward.

In the following section, we discuss research needs of the present study and this is followed by the section on literature review of previous freight mode choice studies. The next two sections describe the modeling flame work and analysis of results. The final two sections present the elasticity of demand and forecasting of mode choice.

Research Needs

The study discussed in this article addressed concerns regarding infrastructure requirements faced by the transportation planners and policymakers of North Dakota. Section 23 of the North Dakota Senate Bill 2032 mandated Upper Great Plains Transportation Institute (UGPTI) to conduct a study to identify transportation infrastructure requirements in the state (Tolliver and Dybing 2007). In that study a freight demand model was developed with special emphasis on agricultural products. In a railroad planning study by UGPTI it was observed that there is capacity constraint in class 1 railroads in the state, and the capacity constraints are increasing the cost of shipments (Ziegler 2007). Railroad operation is capital intensive; excess capacity increases the total cost of operation, whereas a lack of capacity will result in loss of competitive advantage of the state. The railroad planning study identified the need to understand the future demand of railroad, so that judicious decisions can be made to match demand and capacity (Cambridge Systematics 2003). This study also stated that agricultural commodity plays a vital role in the transportation planning process because it comprises the bulk of the freight, approximately 62 percent, of all goods moving in and out of North Dakota.

Transportation planners are concerned that highways would be adversely affected if the freight movement shifts from rail transport to truck. Improved mode choice forecasting techniques will enable transportation planners to assess demand of individual modes and make judicious investments to prevent the unwanted mode shift. Research undertaken by the Center for Urban Transportation Research Florida (2009) observes that economy and society both benefit if the optimal share of freight movement by railroad and truck is determined. The report states that there will be a mode shift from freight rail to truck, with truck tonnage likely doubling in the next twenty years. A report published by the US Department of Agriculture (2005), observes that the US agricultural sector is the largest user of freight transportation services and accounts for almost one-third of all freight transportation services. According to the USDA report, in order to maintain leadership in exporting agricultural products in the global market an efficient transportation system is essential. Agricultural products are priced low with transportation cost being a substantial part of the final cost. This cost structure makes agricultural products very sensitive to transportation input. A study by Eriksen, Norton, and Bertels (1998) found that trucks have a greater share of hauling crop freight to the final market compared to railroad. Researchers noted that this mode share ratio is unexpected; crop freight which is a low-value, bulky commodity, and transported over long distances is expected to be hauled by railroad. This ambiguity, in regards to mode selection for agricultural sector, would justify further research to analyze the mode choice criteria for agricultural freight.

Rural roads, which include county and township roads, make up approximately 75 percent of the total miles in the US road system (US DOT 1997). These roads carry the increased truck traffic of agricultural freight, requiring state and local government to make judicious use of highway funds to maintain the local roads at the desired service level. A NDPSC report indicated that agricultural shippers are facing widespread transportation problems (North Dakota Public Service Commission 2004). During harvest season this problem escalates because of insufficient rail service and storage space, resulting in ground storage of crops. The NDPSC report reveals a need for thorough analysis of transportation demand for all available modes. Brennan's (1998) research on US railroad system capacity stated that before the Staggers Rail Act of 1989 the railroad system had excess capacity. After this Act, railroad facilities were downsized, resulting in an increased rate of crop shipment. The rate increases have caused significant mode shift from railroad to truck. Brennan's study identified a need to detect areas of railroad expansion, based on forecasted demand. It is apparent from these research findings that an in-depth analysis of mode selection of agricultural freight is necessary.

Literature Review

There are a number of studies undertaken on freight mode choice modeling, using both aggregate and disaggregate data. Jiang, Johnson, and Calzada (1999) did a research on freight mode choice in France. They developed a nested logit model to relate freight demand characteristics to mode choice. They surveyed shippers to develop a national-level disaggregate RP data. Ben-Akiva, Bolduc, and Park (2008) developed a hybrid choice model to estimate choice probability, based on relative utility of respective modes. They built base model using RP data collected from shippers of five commodities; thereafter they employed SP data to relate unobserved service quality variables to observed variables. Cook et al. (1999) identified factors that affect shippers' choice of mode between railroad and truck such as reliability, availability, price, and transit time. The significance of these factors depended on the commodity type. According to Cook et al., price is the most important criteria for coal shipment; however, for food grains the most important criteria is the availability of transportation mode. For food grains, storage loss is a significant portion of postproduction loss; hence, the shippers would prefer to ship their grains at the earliest possible time.

Reggiani, Nijkamp, and Tsang (1998), in a study on interregional freight transportation mode choice, developed a logit model and a neural network (NN) model to analyze the flow of freight, particularly food products in Europe in a multiregional perspective. In this project, the researchers investigated modal choice based on two principal parameters: freight cost and transportation time. Cullinane and Toy (2000) used content analysis methodology to identify attributes that can be employed in a SP mode choice model. In some studies, researchers had set an upper limit to the number of attributes used in an SP model. Pearmain et al. (1971) suggested that the upper limit of causal variables be set at seven. This study observed that the five important factors affecting route and mode choice are cost, speed, time, characteristics of the goods, and service. In the absence of RP data, Shinghal and Fowkes (2002) used SP data to identify determinants of mode choice. The attributes identified include cost, door-to-door transit time, reliability, and frequency of service. The alternative modes used in that study were the existing road service, new road service, intermodal container service, and rail service. Their study revealed that intermodal services are preferable for high-value and finished goods, whereas rail service is preferable for bulk goods.

Reviewing previous studies provides an overview of existing mode choice models in freight transportation. A basic modeling framework is identified and the uniqueness of each study is observed along with the shortcomings. Agricultural commodities constitute part of the freight in some of these studies; however, there is not any single study identified that dealt entirely with agricultural commodities.

Marathon and Denicoff (2011) in their research report observed that domestic demand of agricultural products has been rising for the last two decades and the export market is mostly static. The rise in domestic demand has favored truck over rail transport because of the shorter haul from the field to processing plants. Goldsby (2000) states that US grain shippers have a competitive advantage because of available storage capacity. Due to unavailability of storage facilities, competing grain-producing countries trade their grain in poor market conditions.

Modeling Framework

Background Information

The main objective of an elevator manager is to maximize the net price received for a given commodity. The net price is estimated by subtracting the total logistics cost of shipping the commodity from the price received at the terminal market. Grains are transported in bulk due to their low value and homogenous nature of the product. The logistic cost optimization is computed by selecting the destination market, mode of shipment, quantity of shipment, time of shipment, and use of a transshipment/consolidation center. Primarily three types of grain movement from the elevators exist: (a) subterminal elevator to the final destination, (b) satellite elevator to the final destination, and (c) satellite elevator to the subterminal elevator. The decision whether to include a subterminal elevator between a satellite elevator and final destination creates the possibility of reducing the total logistics cost.

The grains are moved from the satellite elevators to the subterminal elevators mostly by truck transport because of the short hauling distance. Moreover, most of the satellite elevators do not have a railroad facility at the elevator location. Most of the subterminal elevators, on the other hand, have a railroad facility, allowing them the liberty to choose between railroad and truck modes. The railroad facility at the elevator differs in terms of track capacity, which determines the number of rail cars the elevator can accommodate at a time. The track capacity determines the level of access the shippers have and is referred to as the "shipper's size," which in turn affects the haulage rate offered by the railroad companies. The five levels of the "shipper's size" are (a) no rail: no rail access, (b) single car: 1 to 24 cars, (c) multicar: 25-49 cars, (d) unit-train: 50-99 cars, and (e) shuttle: l00 cars or more. Truck ownership also affects the mode choice at the elevators. Another factor influencing mode choice is the availability of backhaul for the truck shipment. There is considerable backhaul of fertilizer from Minneapolis and Duluth during spring; this affects the truck rate structure, hence the mode choice.

In a study to analyze trend in grain transportation for Great Plains Elevators, 471 elevators were surveyed by Vachal and Tolliver (200l). They identified four key factors affecting mode choices: availability of equipment, shipment rate, receiver's freight requirement, and reliability of service. This survey showed that elevators with shuttle train capacity have a higher probability to ship grain by railroad than those elevators with lower capacity.

Discrete Choice Model Basic Concepts

In this section, we discuss the basic concepts of binomial discrete choice models which are used to estimate the probability of mode choice. These models are based on the concepts developed by Ben-Akiva and Lerman (1995), and Train (2003). The conceptual framework of the discrete choice model is shown in figure 1. The choice of a mode depends not only on attributes of the mode, but also on the attribute of the shippers, shippers' perception of the mode, and shippers' business requirement. The choice set [C.sub.n] is denoted as {1, 2}; where alternative [] is railroad and alternative 2 is truck. The utility function is defined in the form [] = U([], [S.sub.n]); where [] is the utility of alternative i for shipper n; [] is the vector of attributes of alternative i for shipper n, which includes cost of shipment and time of shipment; [S.sub.n] is the vector of attributes of shipper n, which consists of elevator capacity, line capacity at the elevator, commodity shipped, and quantity shipped. We can introduce the unobserved random component [[epsilon].sub.i] in the utility function. The random component of the utility function captures unobserved variation among elevators and unobserved attributes of the alternatives. In the initial model, the random component is assumed to have a logit distribution for analytical convenience; it is presumed that [epsilon].sub.jn] and [] are independent and identically distributed (IID). The choice probability function [P.sub.n](i) is formulated as [P.sub.n](i) = [e.sup.[beta]xi]/ ([e.sup.[beta]xi] + [e.sup.[beta]xj]); where [x.sub.i], is vector of causal variables of mode i, and [beta] is vector of estimated parameters of the variables.

Elevator Data

The elevator system in North Dakota has a vital role in the movement of grain from farms to final destinations. The 310 elevators in North Dakota have a total storage capacity of 239,949 thousand bushels and shipped 759,132 thousand bushels of grain to various destinations in the year 2004 (Vachal and Benson 2008). Elevators are classified into five groups, based on the numbers of rail cars an elevator can load without railroad switching. The rail haulage rate depends on the railcar loading capacity at the elevators. The grains are shipped from these elevators to Duluth-Superior, Minneapolis-St. Paul, Pacific North West, Minnesota, Gulf Ports, North Dakota, and other miscellaneous markets. The commodities handled by these elevators are primarily hard red spring wheat (A), durum (C), barley (E), sunflowers (G), corn (H), oats (J), soybeans (K), and dry edible beans (L). The letters noted in parentheses are the abbreviations for these commodities used by the NDPSC. The distribution and shipment data of the elevators are available from the NDPSC reports; this includes individual shipment record, by mode, from elevators to various destinations. The shipment report provides information on track capacity, elevator storage capacity, and quantity of each shipment. The dataset contains about 5,000 observations. A number of plots are developed to visually inspect the distribution pattern. In figure 2, choice of mode (Rail = x, Truck = z) is plotted alongside line capacity and quantity. This figure shows that with increase in line capacity and quantity of shipment the probability of choosing the railroad increases.


Fare Structure

To estimate distance and time of shipment, we developed a Geographic Information System (GIS) database of the elevators, the railroad network, highway network, and final destinations (figure 3). CUBE[C] modeling software is used to estimate distance and time of shipment. Uniform Railroad Costing System (URCS) software, developed by the Surface Transportation Board (STB), is used to estimate the railroad haulage cost from each of the elevators to the final destinations. In the URCS, the parameters required for cost estimation are (a) carrier code, (b) distance of the shipment, (c) type of shipment, (d) type of freight car, (e) number of freight cars, (f) type of movement, as related to service level, (g) car owner, (h) commodity type (the STCC Code), and (i) weight of the shipment (in tons per car). The truck cost model, developed by Berwick and Farooq (2003), is used to estimate the truck haulage rate.



In figure 4 the estimated cost per ton-mile for railroad and truck versus distance are plotted. The railroad mode appears to be a dominant mode for longer distance haul, but there are factors like reliability, availability, and loading facility that might affect an individual shipper's response. Trucks have insignificant fixed and terminal costs compared to railroad; however, the variable costs of trucking are considerably higher than railroad. Shippers' past experiences with any particular mode might also influence the choice process based on their levels of satisfaction. Among the seven class 1 carriers in the United States, two carriers, namely Burlington Northern Santa Fe (BNSF) and Canadian Pacific (CPR), operate in North Dakota. Short-line carriers operating in North Dakota are the Dakota Missouri Valley and Western (DMVW), Northern Plains Railroad (NPR), and Red River Valley and Western (RRVW).

Estimation Analysis

Logit Choice Model

The 2004 elevator shipment data is used to build the binomial discrete choice model. In the original data set, some elevators do not have railroad connectivity; these elevators are removed from the dataset for the model building purpose. The logit model is built based on the assumptions of (a) systematic taste variation, (b) proportional substitution among alternatives, and (c) unobserved factors being independent over time (Ben-Akiva and Lerman 1995; Train 2003) The utility functions developed for model estimation is



Other Generalized Extreme Value Model

The logit model cannot account for multiple observations from the same respondent, and when there are unobserved factors correlated over time. The assumptions of a logit model are also invalidated when there is random test variance and there is restrictive substitution pattern. To overcome the shortcomings of the logit model, we developed a heteroscedastic extreme value (HEV) model, a probit model, and a mixed-logit model.

HEV, Probit Model and Mixed-Logit Model

Heteroscedastic and independent stochastic component, in the utility function, can be accounted for by using a HEV model or a probit model. It is highly likely that the unobserved factors influencing mode choice vary from one elevator to the other. Reasons for this variation can be the price agreement between a particular elevator and railroad or trucking company, variation of availability of railcars by different elevators, or ownership of railcars or trucks by the elevators. This variance in each alternative can be handled using the HEV model. One assumption of the HEV model is no correlation between unobserved factors (Bhat 1995). The limitation of the HEV model can be overcome using a probit model. The probit model allows random test variation and any pattern of substitution, and can handle panel data. The only assumption of the probit model is that the random component is normally distributed. In the probit model, the random component can be defined by a vector [[epsilon].sub.n] = [[[epsilon].sub.1n], [[epsilon].sub.2n]]; where [[epsilon].sub.1n], and [[epsilon].sub.2n] are the normally distributed random component of mode choice 1 and mode choice 2. The density of [[epsilon].sub.n] can be defined by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (Train 2003); where [OMEGA] is the covariance matrix and J is the number of error terms.

The unobserved heterogeneity across elevators and their sensitivity to observed exogenous variables can be modeled using a mixed-logit model. The utility function of a mixed-logit model can be defined as [] = [x.sup.'][beta] + [[xi]] + [[epsilon]]; where [x'][beta] is the deterministic component of the utility and [[xi]] + [[epsilon]] is stochastic component of the utility. [[xi]] is the random component, which may be correlated among alternatives for each elevator, and is assumed to have a general distribution, [[epsilon]] is the random term, which is assumed to have IID Gumbel distribution (SAS Institute 2008).

Goodness-of-Fit Statistics and Result Interpretation

The goodness-of-fit in the discrete choice model is tested by the likelihood ratio index; this is similar to the [R.sup.2] value used in the linear model (McFadden 1974). Researchers have developed a number of other ways to test the goodness-of-fit of the discrete choice model. Estrella (1998) suggested two measures for the goodness-of-fit of the discrete choice model. These two measures can be defined as




where N is the number of observations, and K is the number of estimated parameters. The results of the test statistic for our model are shown in table 1. Based on the McFadden likelihood ratio, it is observed that the probit model is the best fit.

The parameter estimates of the probit model are shown in table 2. The negative value of the parameters for cost and time is understandable; the utility of any mode decreases with an increase in the ton-mile cost and time of shipment. The t-test shows that these two parameters are significant. Line capacity, which is alternative specific for the rail mode, has a positive parameter estimate. This can be explained by the fact that the utility of the rail mode increases with the increase in line capacity. With increase in line capacity, elevators can handle more rail cars at one time, which results in lower ton-mile cost. The variable elevator capacity, which is also alternative specific, has a negative parameter estimate; but the t-test result shows that it is not significant. This implies that the capacity of the elevator is not a significant factor in choosing a particular mode. The estimated parameter for quantity is positive. This implies that as the quantity shipped increases, the rail mode becomes preferable. The rate structure for unit-train shipment is lower than multicar shipment and single car shipment. If the quantity shipped is adequate, the shippers can avail lower rates of unit or multicar shipments, provided line capacity is available at the elevator. Estimated parameters of all commodities are positive, which implies that when all other explanatory variables are zero, the shippers would have a preference for the rail mode. Among all commodities, commodity E (barley) and commodity J (oats) have insignificant t-values. Hence, barley and oat have no particular mode preference.

Demand Elasticity

One important application of the mode choice model is to estimate elasticity of mode choice probability. Own price elasticity and cross price elasticity are estimated to assess the change of probability of mode choice due to changes in the explanatory variables. Here, elasticity of mode choice is estimated for some fixed percentage increases in cost. The cost can be related to fuel price and hence elasticity can be estimated using fuel price as an explanatory variable. In this project we estimated "aggregate elasticity," i.e. the sensitivity of all the shippers in choosing a mode in response to the change in parameters. This aggregate elasticity can be defined as


The estimation results of price elasticity of demand are shown in table 3. There was a previous study, by Train and Wilson (2004), on mode choice for grain shipments. The results of price elasticity in that paper are close to the results of this study. We classified the total population into subgroups based on commodity type, line capacity, and quantity of shipment; mode choice elasticity is estimated for each of these subgroups. We made a number of observations from the estimation results. The absolute value of own price elasticity for truck is more than rail for all groups. This suggests that shippers are more sensitive to price change in truck mode than that in the rail mode. In comparing the cross elasticity of rail and truck, it is observed that the elasticity of rail-truck is higher than truck-rail. This observation validates previous finding that shippers availing truck mode are more sensitive to price change compared to those availing railroad. It is observed that as the line capacity increases the cross elasticity rail-truck decreased, which is justified by the fact that elevators with lower line capacity are more sensitive to the truck rate than elevators with larger rail line capacity. This leads us to infer that trucks are better substitute for single-car shipments than for multicar or unit-train shipments.

Forecasting Mode Choice

Forecasting serves to fulfill the objective of this study, which is to predict the mode share of truck and railroad in transporting agricultural freight, due to change in the exogenous variables. Forecasting also served as a tool to validate the estimated model by comparing the forecasted mode share with that of the observed values. In this study, 2004 elevator shipment data are used to build the model. Using these estimated model parameters, and explanatory variables from 2008, the mode choice model is validated. Forecasting can be done to predict both disaggregate and aggregate demand. In this research we have done both, forecasting of disaggregate and aggregate demand for model validating. For disaggregate validation we use hit ratio, which measures the percentage of matches in the forecast with the observed data for each shipment. Unlike aggregate forecasting, hit ratio measures forecast mode choice for each individual shipment and can be defined as

Hit Ratio = [[SIGMA].sup.n.sub.i=1] [H.sub.i] / n

where [H.sub.i] = 1 if the prediction is correct and o if incorrect, n in total number of observations in the data set. We estimated the mode choice probability based on the 2008 explanatory variables, and compared it with the observed mode choice for each individual shipment. We estimated a hit ratio of 73 percent, which is significantly higher than 50-percent established acceptable predictive accuracy for the discrete choice model.

For aggregate demand forecasting, the elevators are classified into subgroups based on two parameters: line capacity and the quantity of shipment. The estimated model is used to forecast [P.sub.i]([x.sub.n], [??]), which is the probability of individual n choosing mode i; [] is the vector of explanatory variable for individual n; and [??] is the estimated model parameters. The estimated choice probability is used to calculate number of shippers choosing individual modes, using equation


where [??](i) is the estimated number of shippers choosing mode i for the subgroup T with [N.sub.T] members in the subgroup. The share of each of the modes can be estimated as follows:


Table 4 presents the estimated and observed share of choosing mode 1 for each of the subgroups. The subgroups are based on line capacity and quantity of shipment. The specific classes of line capacity are used because line capacity of fewer than 25 cars can accommodate a single car train; line capacity between 25 and 50 can accommodate a multiple-car train; and line capacity more than 50 can accommodate a unit train. It is observed that the root mean square error (RMSE) is higher for lower line capacity and for lower quantity of shipment. This is explained by the fact that for lower line capacity, and for lower quantity of shipment, the values of systematic utility for rail mode and truck mode are close. Hence, the random component becomes significant for mode choice, increasing the estimation error.


In this study, crop shipment data available from the North Dakota Public Service Commission are used to build disaggregate mode choice model. Using this unique data set, which is a record of agricultural freight movement from all registered elevators to the final destinations, mode choice probability is estimated. We initially assumed the random component to have a logit distribution. The assumptions of logit model are relaxed progressively in the heteroscedastic, probit, and mixed-logit models. We estimated elasticity mode choice probability to assess the sensitivity of mode selection to changes in explanatory variables. The 2004 base year model is validated with 2008 grain movement data.

In the section on research needs, we discussed how previous studies have identified the research requirement to accurately forecast demand of transportation modes for agricultural freight shipment. This mode choice forecasting enables judicious allocation of funds to expand capacity of specific modes. The modeling framework used in this study should be easily transferrable to other in other states. Those states that do not have detailed disaggregate data on grain movement can use either publicly available data, or proprietary data for model building purpose. Some of the publicly available data sources are commodity flow survey (CFS) data, freight analysis framework (FAF) data, rail waybill data, and maritime statistics data. These aggregated datasets can be disaggregated to county level, using employment information available from county business patterns (CBD) data, and commodity by industry input-output (I-O) tables (Mitra and Tolliver 2009). If funds are available, states can use proprietary data like TRANSEARCH database developed by Global Insight.

One limitation of this study is the failure to capture all the components of logistics cost. The logistics cost component, included in the utility function, is the transportation cost. It is true that transportation cost is a major component of the logistics cost, but at times other components of logistics cost like storage cost, handling cost, ordering cost, and opportunity cost can have major effect on mode choice decision. In future studies, the model can be improved by incorporating some of these logistics costs in the set of explanatory variables. With more information on the logistics cost, the random component of the utility function can be reduced. This would greatly improve the prediction accuracy of the model. Another important recommendation for future research is to extend the purview of the research beyond the state boundaries; this would eliminate any state-specific bias in the model. All these improvements will help to overcome the limitations of the modeling framework presented in this research.


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Subhro Mitra

Division of Urban and Professional Studies

University of North Texas at Dallas

7400 University Hills Blvd

Dallas, Texas 75241

Table 1/Goodness of Fit Statistics

                         Logit      HEV     Probit

Log Likelihood (Logt)   -2187     -2176     -2132

Log Likelihood          -3394     -3394     -3394
Null (LogL(O))

Likelihood Ratio (R)    2415.2    2437.3    2525.3

Upper Bound of R (U)    6788.7    6788.7    6788.7

Aldrich-Nelson          0.3303    0.3323    0.3402

Cragg-Uhler 1           0.3893    0.3921    0.4029

Cragg-Uhler 2           0.5191    0.5228    0.5372

R2E1                    0.4564    0.4602    0.4753

R2E2                    0.4519    0.4557    0.4708

McFadden's LRI          3558      0.359     0.372

Veall-Zimmermann        0.5686    0.572     0.5857


Log Likelihood (Logt)   -2134

Log Likelihood          -3394
Null (LogL(O))

Likelihood Ratio (R)    2519.8    2 *(LogL-LogLO)

Upper Bound of R (U)    6788.7    -2* LogLo

Aldrich-Nelson          0.3397    R / (R + N)

Cragg-Uhler 1           0.4022    1 - exp(-R / N)

Cragg-Uhler 2           0.5363    (1-exp(-R/N))/(1 - exp(-U/N))

R2E1                    0.4743    1 - (1 - R/U)^(U/N)

R2E2                    0.4702    1-((LogL-K)/LogLO)^(-2/N*LogLO)

McFadden's LRI          0.3712    R / U

Veall-Zimmermann        0.5848    (R * (U + N)) / (U * (R + N))

Table 2/Parameter Estimation Results of the Probit Model

Parameter        Estimates    Standard Error   t Value

Cost              -0.0597        0.005639       -10.59
Time              -0.0317        0.006231       -5.08
Line_cap           0.0128        0.001261       10.12
Elev_capacity    -8.33E-08      6.1274E-8       -1.36
Quantity          1.59E-05      7.6844E-7       20.66
Comm_a             1.0261         0.1359         7.55
Comm_c             0.7857         0.1405         5.59
Comm_e            -0.0212         0.1401        -0.15
Comm_g             1.2452         0.1735         7.18
Comm_h             1.7295         0.2154         8.03
Comm_j             0.3155         0.2030         1.55
Comm_k             0.5753         0.1817         3.17
comm_1             0.0848         0.1887         0.45

Table 3/Price Elasticity of Demand

Commodity Group        Rail-Rail    Rail-Truck

Comm A                  -0.7498       2.3366
Comm C                  -0.7511       2.3385
Comm E                  -0.7500       2.3343
Comm G                  -0.7548       2.3550
Comm H                  -0.7499       2.3346
Comm J                  -0.7539       2.3508
Comm K                  -0.7497       2.3341
Comm L                  -0.7548       2.3510

Line Capacity Group

Line_Cap< 25            -0.7548       2.5550
Line_Cap < 50           -0.7558       2.3544
Line_Cap = > 50         -0.7500       2.3343

Quantity Group

Quantity < 5000         -0.7499       2.3346
Quantity < 10000        -0.7503       2.3366
Quantity < 100000       -0.7500       2.3343
Quantity > 100000       -0.7497       2.3341

Commodity Group        Truck-Truck    Truck-Rail

Comm A                   -1.9222        1.5974
Comm C                   -1.9232        1.5983
Comm E                   -1.9262        1.6008
Comm G                   -1.8935        1.5792
Comm H                   -1.9255        1.6001
Comm J                   -1.8979        1.5822
Comm K                   -1.9256        1.6002
Comm L                   -1.8930        1.5793

Line Capacity Group

Line_Cap< 25             -1.8935        1.5792
Line_Cap < 50            -1.8797        1.5719
Line_Cap = > 50          -1.9262        1.4008

Quantity Group

Quantity < 5000          -1.9255        1.6001
Quantity < 10000         -1.9196        1.5963
Quantity < 100000        -1.9262        1.6008
Quantity > 100000        -1.9256        1.6002

Table 4/RMSE of the Forecasted Mode Choice Based on Different Groups

                                     Mode Share of Railroad
Line Capacity    of Shipment    Observed   Estimated    RMSE

< 25 Rail Cars   < 5000 tons    31%        20%          0.35
                 < 1000 tons    17%        21%          0.24
                 > 1000 tons    -          -            -

< 50 Rail Cars   < 5000 tons    40%        27%          0.33
                 < 1000 tons    50%        30%          0.4
                 > 1000 tons    50%        36%          0.28

> 50 Rail Cars   < 5000 tons    81%        60%          0.26
                 < 1000 tons    98%        80%          0.18
                 > 1000 tons    99%        88%          0.11
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Author:Mitra, Subhro
Publication:Transportation Journal
Geographic Code:1USA
Date:Jan 1, 2013
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