Alex Norr and Dr. Michael Clay, Department of Geography
INTRODUCTION
Integrated land use and transportation forecasting models are used to assist decision makers in the policy analysis and infrastructure capital improvements selection process (1, 2, and 3). These models are typically given precise, point-estimate inputs that are mathematically linked, through a series of submodels, to forecasted model outputs (4 and 5). These point-estimate inputs represent an unrealistic level of precision and a growing body of research is focusing on statistical techniques to model uncertainty in model inputs and parameters and tracking the effects of this uncertainty through the various submodels to the model outputs (see 4, 6, and 7 and literature cited therein for examples). Modeling uncertainty provides at least two benefits. First, it gives the model user a better understanding of how the modeling framework functions in uncertain conditions—thereby testing the robustness of the model as a whole—and second, it allows the outputs of the model to be presented within a set of confidence intervals—thereby determining whether or not the model is able to statistically differentiate between two policy or infrastructure investment alternatives.
SE3M has four components or modules. Three of these components make up the core of the model and a forth, the Graphic Visualization Tool (GVT), serves to enable three dimensional viewing of the modeled, scenario outputs. The three core components include: 1) a Large Zone Economic Model (LZEM)—a Lowry-type model that produces employment and population data at the sub-regional level—the large zones are similar in purpose, size, and function to the regional analysis districts (RADs) used in MEPLAN and PECAS (Abraham and Hunt, 1999; and Hunt and Abraham, 2005 respectively); 2) an agent-based, Bid-rent Land Use Model (BLUM) founded upon Bid-rent Theory (Alonso, 1964) disaggregates the results of LZEM and produces land uses/locations of households and employment at the 50 meter gridcell or legal land parcel level; and finally, 3) a traditional 4-step Travel Demand Model (TDM) that aggregates these land uses to the traffic analysis zone (TAZ) level and produces travel time (with network delay) and travel distance zone-to-zone “skims” for LZEM.
UNCERTAINTY ANALYSIS AND METHODS
Potential error ranges or uncertainty was introduced into LZEM by manipulating the two independent input parameters ([1]the dependency ratio (DP); and [2] the total non-basic employment in the base year divided by the total population) for each model run. The specified input changes were then compared to the associated output error—total population misplaced—in an effort to find the range within which the framework of LZEM can function. Initially, each parameter was shifted in the positive and the negative directions using the standard deviation derived from each of the models’ base-year (total island) data. Using the standard deviation, the marginal effective values were identified for both parameters in each model making it possible to generate additional values using Monte Carlo simulation.
Univariate Model Runs and Regression Analysis
The constant or fixed nature of the three model parameters ––friction factor, parameter 1 and 2–– leads to a multiplier effect. This influence generates a polynomial relationship in the model outputs. The plotted outputs display error in both directions as the inputs deviate from the estimated global values. The relative influence of each parameter is specific to each model due to the varying strengths of the local economies. Due to the direct connection parameters have with the local modeled economy, deriving a generic polynomial equation was not practical. The non-linear relationship between the model inputs and outputs presented a unique problem. It is desired to have model output data fit to a specified curve in order to give the model user the ability to estimate model outputs based on the available input data. Because the model outputs are nonlinear each data set was divided into two groups using the estimated global parameters for each model as the dividing point.
Multivariate Analysis
Multivariate analysis varies multiple inputs simultaneously through the same Monte Carlo sampling method used in the univariate analysis. An additional 100 values were generated for each parameter in each model, the models were then run with 100 randomly paired parameter values. Model outputs were regressed on model inputs to reveal similar logistic and linear relationships discovered in the univariate analysis.
CONCLUSIONS
This study has presented a comprehensive initial inquiry into how the Large Zone Economic Module submodule of the SE3M modeling framework deals with error and uncertainty in model inputs and parameters. While much diagnostic and analytical work is still needed, LZEM has demonstrated a reasonable amount of robustness when dealing with a wide range of parameter variation. Additionally, this analysis provides evidence that LZEM has the capability of offering valuable insights for policy makers working within a wide range of economic structures.
In sum, the three case study areas of Guam, Puerto Rico, and Oahu, Hawaii—where models had previously been created for the model transferability study—were successfully used in this study to examine the impact of uncertain model inputs/parameters on model outputs. In all but a few instances the model produced acceptable levels of error or deviations from the base case. Issues with extreme parameter values and comparatively impoverished economic structures were discovered as vulnerabilities of the LZEM framework as expected. Now as planners seek to refine this and other allocation models they can integrate error into their analysis in a straightforward way and identify the elements of their analysis that may have a greater proportion of error associated with the outcome and adjust conclusions accordingly