Calibration and Test of a Discrete Choice Model with Endogenous Choice Sets

Conventional discrete choice models assume implicitly that the choice set is independent of the decisionmaker's preferences conditional on the explanatory variables of the models. This assumption is implausible in many choice situations where the decisionmaker selects his or her choice set. This paper estimates and tests a discrete choice model with endogenous choice sets based on Horowitz' theoretical work. To calibrate the model, a new probability simulator is introduced and a sequential estimation procedure is developed. The model and calibration methods are tested in an empirical application as well as Monte Carlo simulations. The empirical results are used to test the theory of endogenous choice sets and to examine the differences between the new model and a conventional choice model in parameter estimates and predicted choice probabilities. The empirical results strongly suggest that ignoring the endogeneity of choice sets in choice modeling can have serious consequences in applications.     

Analyzing Cross-classified Data with Inherent Spatial Dependence

Despite considerable recent progress in the methods available for the log-linear analysis of categorical data arising from complex sampling schemes, only a few papers have been published that deal with the parallel phenomenon of dependence induced by spatial sampling. This paper aims to add to the general awareness of this topic and suggests some new ideas for tackling the problems raised. In the paper it is shown that the method that has been proposed for the valid selection of log-linear models given spatially dependent data and some derivative methods are somewhat conservative when compared to an approach based on a model of spatial dependence outlined in section 4. The method also serves as a data exploratory technique to enhance the use of the more robust conservative approach.     

Measuring Impacts of Condition Variables in Rule‐Based Models of Space‐Time Choice Behavior: Method and Empirical Illustration

The use of rule‐based systems for modeling space‐time choice has gained increasing research interests over the last years. The potential advantage of the rule‐based approach is that it can handle interactions between a large set of predictors. Decision tree induction methods are available and have been explored for deriving rules from data. However, the complexity of the structures that are generated by such knowledge discovery methods hampers an interpretation of the rule‐set in behavioral terms with as a consequence that the models typically remain a black box. To solve this problem, this paper develops a method for measuring the size and direction of the impact of condition variables on the choice variable as predicted by the model. The paper illustrates the method based on location and transport‐mode choice models that are part of Albatross model—an activity‐based model of space‐time choice.     

BAYSIAN INFERENCE FOR ORDERED RESPONSE DATA WITH A DYNAMIC SPATIAL‐ORDERED PROBIT MODEL

ABSTRACT Many databases involve ordered discrete responses in a temporal and spatial context, including, for example, land development intensity levels, vehicle ownership, and pavement conditions. An appreciation of such behaviors requires rigorous statistical methods, recognizing spatial effects and dynamic processes. This study develops a dynamic spatial‐ordered probit (DSOP) model in order to capture patterns of spatial and temporal autocorrelation in ordered categorical response data. This model is estimated in a Bayesian framework using Gibbs sampling and data augmentation, in order to generate all autocorrelated latent variables. It incorporates spatial effects in an ordered probit model by allowing for interregional spatial interactions and heteroskedasticity, along with random effects across regions or any clusters of observational units. The model assumes an autoregressive, AR(1), process across latent response values, thereby recognizing time‐series dynamics in panel data sets. The model code and estimation approach is tested on simulated data sets, in order to reproduce known parameter values and provide insights into estimation performance, yielding much more accurate estimates than standard, nonspatial techniques. The proposed and tested DSOP model is felt to be a significant contribution to the field of spatial econometrics, where binary applications (for discrete response data) have been seen as the cutting edge. The Bayesian framework and Gibbs sampling techniques used here permit such complexity, in world of two‐dimensional autocorrelation.     

SELECTION BIAS IN SPATIAL ECONOMETRIC MODELS

ABSTRACT. The problem of spatial autocorrelation has been ignored in selection-bias models estimated with spatial data. Spatial autocorrelation is a serious problem in these models because the heteroskedasticity with which it commonly is associated causes inconsistent parameter estimates in models with discrete dependent variables. This paper proposes estimators for commonly-employed spatial models with selection bias. A maximum-likelihood estimator is applied to data on land use and values in 1920s Chicago. Evidence of significant heteroskedasticity and selection bias is found.     

Evaluating inputs to models of hominin raw material selection: map resolution and path choices

Selection of an appropriate scale is an important decision in study design in many branches of science, since perceived patterns often change with the scales of spatial extent or resolution of an analysis. In previously published work, we created a resource selection model to determine the importance of several independent variables for the selection of lithic materials by hominins at a Middle Palaeolithic site in southern France. Two of these independent variables (calories exerted and difficulty of the terrain covered in travel from source to site) were calculated using elevation data extracted from maps. In the present paper, we examine the differences in model performance when the variables ‘Calories’ and ‘Difficulty’ are calculated using 1) three base maps for elevation that differed in map resolution (from finest to coarsest: a 1:25,000 topographic base map, SPOT DEM, and SRTM DEM), and 2) two different methods for determining the route from source to site (straight-line route and least-cost route; both methods exclude areas with slopes >60% from travel). Our best model was the one that used data calculated using the topographic base map; however, the SRTM DEM-based data produced models of essentially equal quality. Regardless of map scale, models that used data calculated using a straight-line route always outperformed models that used data calculated using a least-cost route. This supports our previous finding that a straight-line route is a more appropriate measure for the path from lithic source to site than a least-cost route. We conclude that the map resolution of each of the base maps used here is appropriate for analyses involving spatial data pertaining to Neandertal activity because this type of data is essentially always coarse-grained.     

RURAL RETAIL BUSINESS THRESHOLDS AND INTERDEPENDENCIES*

ABSTRACT. The occurrence of rural retail activity may be related to the concept of threshold, which suggests the direct relationship between surrounding populations and the hierarchical functions provided. Empirid studies have typically examined individual categories of retail firm concentration or multiplication in isolation of the extent of other retail activities. This study develops models of retail business concentration for sparsely populated rural markets, and emphasizes proper statistical treatment of the discrete firm-count data. The analytical approach specifies systems of multivariate count data models that can capture the interdependencies among merent types of retail firms. The degree of interdependence is tested and shown to be a significant statistical feature of the model of rural retail firm counts.     

LONG-TERM FORECASTING OF NONCOINTEGRATED AND COINTEGRATED REGIONAL AND NATIONAL MODELS*

ABSTRACT. Johansen's (1988) multivariate test for cointegration is first applied to four models involving quarterly state data and five variables, along with a national model based on Friedman and Kuttner's (1992) model of money demand, which uses three variables. Each regional model consists of frequently used national and state series, for which theory suggests the possible cointegration of several series pairs. Beginning with all five series, however, one state model is found to be cointegrated over each of 20 successive estimation intervals. The money demand model and one state model are not cointegrated over the same intervals. In the cointegrated case, five-year experimental forecasts show that error correction mechanism (ECM) and Bayesian ECM models outperform all other approaches. More importantly, forecasting performance improves further by respecifying the ECM model based on three cointegrated series pairs rather than the five-component cointegrating vector. For the two noncointegrated systems, the first-difference model suggested by the cointegration/ error correction literature is far superior to VAR in levels over both shortand long-term horizons.     

Prediction of Bike-sharing Trip Counts: Comparing Parametric Spatial Regression Models to a Geographically Weighted XGBoost Algorithm

Regression models are commonly applied in the analysis of transportation data. This research aims at broadening the range of methods used for this task by modeling the spatial distribution of bike-sharing trips in Cologne, Germany, applying both parametric regression models and a modified machine learning approach while incorporating measures to account for spatial autocorrelation. Independent variables included in the models consist of land use types, elements of the transport system and sociodemographic characteristics. Out of several regression models with different underlying distributions, a Tweedie generalized additive model is chosen by its values for AIC, RMSE, and sMAPE to be compared to an XGBoost model. To consider spatial relationships, spatial splines are included in the Tweedie model, while the estimations of the XGBoost model are modified using a geographically weighted regression. Both methods entail certain advantages: while XGBoost leads to far better values regarding RMSE and sMAPE and therefore to a better model fit, the Tweedie model allows an easier interpretation of the influence of the independent variables including spatial effects.     

New Estimates of Gravitational Attraction by Linear Programming

This paper uses data for intercity air-passenger travel to derive a set of general propulsion and attraction factors for twenty-five large U.S. cities. The paper develops a new way of examining the linkages between flows and nodal attraction. The technique is to assume that the flow data fit a simple gravity model, and then linear programming is used to maximize the consistency of the endogenous propulsion and attraction with the flow data. Various linear models are used to determine the pattern of urban attraction factors that are consistent with the gravitational flows. Linear programming as well as goal programming models are used to develop a set of analyses linking flows to urban hierarchies. Suggestions for further extensions of the method to address substantive issues of urban systems analysis are also provided.     

Duration Modeling of Spatial Point Patterns

This paper attempts to further the research by Odland and Ellis (1992) in applying event history methodology to the analysis of spatial point patterns (that is, event patterns). Its empirical focus is the event pattern derived from the adoption of an agricultural innovation, the Harvestore, in southern Ontario, Canada, from 1963 to 1986. Event history analysis involves the use of discrete-state, continuous-time stochastic models to investigate a temporal longitudinal record on discrete variables. Event history models are usually concerned with durations of time between events and the effects of intertemporal time dependencies on future event occurrences. As such, they are often referred to as duration models. Many of the methods used in event history analysis allow the use of other nonnegative interval measurements in place of standard temporal intervals to investigate a series of events. In particular, spatial intervals (or durations) of distances between events may also be accommodated by event history models. Our analysis extends the previous research of Odland and Ellis (1992) by using a wider range of parametric models to explore duration dependence, investigating the role of spatial censoring, and using a more extensive set of explanatory variables. In addition, simulation experiments and graphical tests are used to evaluate the empirical event pattern against one generated from Complete Spatial Randomness. Results indicate that the event pattern formed by the Harvestore adopter farms is clustered (that is, is described by positive duration dependency), the sales agent is a significant factor in the distribution of adopters, and that contrasting results are obtained from the analysis using censored data versus uncensored data.     

Bayesian Model Averaging for Spatial Econometric Models

We extend the literature on Bayesian model comparison for ordinary least-squares regression models to include spatial autoregressive and spatial error models. Our focus is on comparing models that consist of different matrices of explanatory variables. A Markov Chain Monte Carlo model composition methodology labeled MC ³ by Madigan and York is developed for two types of spatial econometric models that are frequently used in the literature. The methodology deals with cases where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. Estimates and inferences are produced by averaging over models using the posterior model probabilities as weights, a procedure known as Bayesian model averaging. We illustrate the methods using a spatial econometric model of origin–destination population migration flows between the 48 U.S. states and the District of Columbia during the 1990–2000 period.     

The Impact of Telecommuting on the Activity Spaces of Participants

A spatial analysis of the activity spaces of telecommuters, based on the geocoded travel diary data from the State of California Telecommuting Pilot Project, is performed to analyze the impacts of telecommuting. The study analyzes the spatial location, orientation, and extent of the activity locations within the “activity spaces” of telecommuters and a nontelecommuting control group. To be able to quantitatively compare and contrast the travel patterns and the distribution of trip ends within the activity space, several spatial indicators have been defined. Several hypotheses concerning the selection of activity locations by individuals are presented and the impact of telecommuting on the selection of locations for activity is analyzed. Key findings include: on telecommuting days, 86 percent of telecommuters' activities are performed closer to home than to work, compared to 56 percent on normal commuting days; and destinations on telecommuting days are more evenly distributed in all directions around the home, whereas a majority of destinations on commuting days are oriented toward the work location. To be able to understand the influence of the contributing factors toward the selection of nonwork activity locations, potential causal relationships between the influencing factors and the activity location choice are investigated. Several plausible log-linear model structures for cross-classified data provide a good fit to these relationships. Key results include: interaction effects of activity location with commute distance and with trip purpose are present in all the best-fitting models, confirming the importance of these two variables in the selection of activity location; the interaction of activity location and income is also significant; and day status (telecommuting or not) of the employee influences the trip purpose, which in turn affects location.     

Identifying Narrative Descriptions in Agent-Based Models Representing Past Human-Environment Interactions

There is a growing use of bottom-up simulation models to reconstruct past human-environment interactions. Such detailed representations pose difficult questions not only in their design (the generality-realism trade-off) but also about the inferences that are made from them. The historical sciences are faced with seeking to make robust inferences from limited, potentially biased and/or incomplete samples from uncontrolled systems, and as a result have sometimes employed narrative explanation. By contrast, simulation models can be used experimentally and can generate large amounts of data. Here, using an agent-based model of hunter-gatherer foraging in a previously unexplored ecosystem, we consider how narratives might be identified from the trajectories produced by simulations. We show how machine learning methods can isolate qualitatively similar types of model behaviour based on summaries of model outcomes and time series. We stand to learn from this approach because it enables us to answer two questions: (i) under what conditions (representations and/or parameterisations) do we observe in the model what is recorded in the archaeological and/or palaeoenvironmental record? and (ii) does the model yield unobserved dynamics? If so, are they plausible? Using models to develop narratives is a logical extension of the bottom-up approach inherent in agent-based modelling and has the potential, alongside conventional methods of model evaluation, to aid in learning from the rich dynamics of such simulations.     

A Partitioning Model of Urban Retail Structure

A model based on renewal theory generates the number of retail establishments in a place as the outcome of a competitive partitioning process. The available market, measured for example by population or by existing retail sales, is shared among businesses until no market potential market remains. Competing businesses obtain different shares of the market, and the number of establishments is predicted as a discrete random variable. Several alternative formulations are presented of varying generality. One version is successfully tested, using GLIM, on ten business types (SIC two-digit classes) in 232 cities of New York State for 1977 and 1987. The model correctly predicts the form and the variance structure of the relationship between number of establishments and place size. It is shown how the model may be combined with models of city-size distributions to predict aggregate frequency distributions of retail establishments across urban systems.     

ISSUES IN SPATIAL DATA ANALYSIS

ABSTRACT.  Misspecified functional forms tend to produce biased estimates and spatially correlated errors. Imposing less structure than standard spatial lag models while being more amenable to large datasets, nonparametric and semiparametric methods offer significant advantages for spatial modeling. Fixed effect estimators have significant advantages when spatial effects are constant within well-defined zones, but their flexibility can produce variable, inefficient estimates while failing to account adequately for smooth spatial trends. Though estimators that are designed to measure treatment effects can potentially control for unobserved variables while eliminating the need to specify a functional form, they may be biased if the variables are not constant within discrete zones.     

Continuous Characterization of the Planform Geometry and Curvature of Meandering Rivers

The complex feedback between process and form that governs planform migration of meandering rivers is still incompletely understood. Current theoretical models aimed at predicting planform migration relate the rate of meander migration at a particular location to the channel curvature at and upstream of that location. However, these models are still incapable of reproducing complex forms of bend development, such as compound loops. Evaluation of such models requires a representation of planform curvature better than that provided by traditional methods where the curvature is calculated from directional change between the successive digitized points—an approach that provides a discrete representation of curvature dependent on the density of the digitized points used to characterize the channel planform. This article presents and evaluates a methodology that provides a continuous functional representation of the planform geometry and curvature of meandering rivers. The method involves the fitting of splines, specifically parametric cubic splines (PCSs), to discrete digitization data of the channel centerline (CL) and the arc-length parameterization of the resulting composite curve. The arc-length parameterized PCS-interpolated curve is then used to compute analytically the channel CL location and curvature for any value of the streamwise axis. Evaluation of the method involves examination of the effects of digitization interval size and digitization error on the characterization of the planform geometry and curvature using PCS fitting. The derivation of curvature values from continuous planform function for any location and any spatial interval overcomes the reliance either on average bend curvature values or on discrete curvature values based on digitized points.     

Multicollinearity and Parameter Estimation in Simultaneous-Equation Models of Fluvial Systems

Simultaneous-equation statistical models are an attractive method for directly analyzing interactions among components of geomorphic systems. This study demonstrates that the utility of simultaneous-equation analysis is limited for fluvial systems by inherent multicollinearity among hydrologic and morphologic variables. Although multicollinearity for observed data may not be severe, estimation procedures for simultaneous-equation models often enhance this multicollinearity to problematic levels. Diagnostic tests are applied to three models of fluvial systems to illustrate the severity of the problem. It is recommended that investigators who develop simultaneous-equation models perform appropriate diagnostic evaluations to determine the impact of multicollinearity on specific parameter estimates.     

Estimating a Destination-Choice Model from a Choice-based Sample with Limited Information

In most applications of multinomial logit and other probabilistic discrete-choice models, the estimation data set is either a simple random sample of the population of interest or an exogenously stratified sample. Often, however, it is cheaper and easier to sample individuals while they are carrying out the chosen activity of concern. This produces a choice-based sample, which presents important problems of estimation and inference. This paper is concerned with estimation of destination-choice models from choice-based samples when neither the aggregate market shares of alternatives nor the probability distribution of explanatory variables in the population is known. The method of Cosslett (1981) for estimating multinomial logit models from such data is summarized, and the limitations on information about choice behavior that can be recovered from the sample are explained. An empirical model of pharmacy choice in the Namur, Belgium, area is presented. It is shown that useful and important information about destination-choice behavior can be obtained from a choice-based sample, even without knowledge of aggregate market shares and the probability distribution of explanatory variables.     

A Structural Equation Approach to Models with Spatial Dependence

We introduce the class of structural equation models (SEMs) and corresponding estimation procedures into a spatial dependence framework. SEM allows both latent and observed variables within one and the same (causal) model. Compared with models with observed variables only, this feature makes it possible to obtain a closer correspondence between theory and empirics, to explicitly account for measurement errors, and to reduce multicollinearity. We extend the standard SEM maximum likelihood estimator to allow for spatial dependence and propose easily accessible SEM software like LISREL 8 and Mx. We present an illustration based on Anselin's Columbus, OH, crime data set. Furthermore, we combine the spatial lag model with the latent multiple-indicators–multiple-causes model and discuss estimation of this latent spatial lag model. We present an illustration based on the Anselin crime data set again.