A Spatial Statistics Methodology for Inspector Allocation Against Fare Evasion

Four types of fare evasion: A qualitative study from Melbourne, Australia

An empirical model for the psychology of deliberate and unintentional fare evasion

The Geographically Weighted Regression (GWR) is a method of spatial statistical analysis which allows the exploration of geographical differences in the linear effect of one or more predictor variables upon a response variable. The parameters of this linear regression model are locally determined for every point of the space by processing a sample of distance decay weighted neighboring observations. While this use of locally linear regression has proved appealing in the area of spatial econometrics, it also presents some limitations. First, the form of the GWR regression surface is globally defined over the whole sample space, although the parameters of the surface are locally estimated for every space point. Second, the GWR estimation is founded on the assumption that all predictor variables are equally relevant in the regression surface, without dealing with spatially localized collinearity problems. Third, time dependence among observations taken at consecutive time points is not considered as information-bearing for future predictions. In this paper, a tree-structured approach is adapted to recover the functional form of a GWR model only at the local level. A stepwise approach is employed to determine the local form of each GWR model by selecting only the most promising predictors. Parameters of these predictors are estimated at every point of the local area. Finally, a time-space transfer technique is tailored to capitalize on the time dimension of GWR trees learned in the past and to adapt them towards the present. Experiments confirm that the tree-based construction of GWR models improves both the local estimation of parameters of GWR and the global estimation of parameters performed by classical model trees. Furthermore, the effectiveness of the time-space transfer technique is investigated.

Research using a global regression model might not be appropriate to find out the factors that influence strategic food prices based on spatial characteristics. To analyze the spatial effect, Geographically Weighted Regression (GWR) was employed. GWR models are better than OLS, which is indicated by the higher R2 GWR and lower AIC values. The GWR analysis provides the following findings: (1) the wholesale price most influential on the retail price of medium rice and red chili both during the main harvest and non-harvest periods; (2) the harvest pattern results in the effect of production and producer prices on the retail prices of the major harvest and non-harvest periods. Management of inter-regional distribution must be carried out to maintain supply stability and disparity in food prices between regions; (3) producer prices are integrated with trader prices in the district of production centers and surrounding areas while the integration of food prices at the consumer level occurs in the main economic center area of the region. These aspects have different effects for each region and district because the estimated parameters can be positive or negative. Testing during the harvest season (April) and non-harvest can also produce estimates that vary according to the specific characteristics of each location. Keywords: spatial analysis, Geographically Weighted Regression (GWR), retail prices, wholesale price, spatial distribution patterns

GIScience 2016 Short Paper Proceedings Semi-parametric Geographically Weighted Regression (S- GWR): a Case Study on Invasive Plant Species Distribution in Subtropical Nepal Qunshan Zhao 1 , Elizabeth A. Wentz 1 , Stewart Fotheringham 1 , Scott T. Yabiku 2 , Sharon J. Hall 3 , Jennifer E. Glick 2 , Jie Dai 4 , Michele Clark 3 , Hannah Heavenrich 3 Center for Geographical Information Science, School of Geographical Sciences and Urban Planning, Arizona State University, Tempe, AZ 85287, USA Email: {qszhao; wentz; sfotheri}@asu.edu Department of Sociology and Criminology, Pennsylvania State University, University Park, PA 16802, USA Email: {sty105; jeg115}@psu.edu School of Life Sciences, Arizona State University, Tempe, AZ 85287, USA Email: {sharonjhall; mdclar10; hheavenr}@asu.edu Department of Geography, San Diego State University, San Diego, CA 92182, USA Email: jdai@rohan.sdsu.edu Abstract Geographically weighted regression (GWR) is a spatial statistical methodology to explore the impact of non-stationarity on the interaction between spatially measured dependent and inde- pendent variables. In this paper we use a semi-parametric geographically weighted regression (S- GWR) and demonstrate the effectiveness of the method on a case study on socio-ecological fac- tors on forest vulnerability. The case study is based on community forests in and around the buffer zone of Chitwan National Park, Nepal, a biodiversity hotspot that is being rapidly degrad- ed by exotic invasive plant species. This research integrated heterogeneous data sources such as observational ecological surveys, household interviews, and remotely sensed imagery. These data were utilized to extract and represent invasive plant species coverage, human activity inten- sity, topographical parameters and vegetation greenness indices. Research findings both demon- strate the S-GWR method and offer possible interventions that could slow the catastrophic spread of invasive plant species in Chitwan, Nepal. 1. Introduction Geographically weighted regression (GWR) is a spatial analysis method that uses the spatial dis- tribution of dependent and independent variables to specify non-stationarity to quantify the driv- ers of spatially dependent processes. GWR has been widely applied in application domains such as species distribution modeling in ecology and crime analysis in sociology (Foody 2004; Zhang and Song 2013). This paper presents a semi-parametric geographically weighted regression (S- GWR) method to model the factors that influence the spatial distribution of invasive plants in Nepal. We chose to use a semi-parametric model to include both parametric and non-parametric variables in the model specification. The S-GWR is implemented in a case study on the relation- ship between socio-ecological factors and invasive plant species in Chitwan, Nepal. Invasive plant species are considered as a serious global environmental threat to ecosystem structure and function by creating disturbances in ecosystems, reducing native species diversity and abundance, limiting human usage of ecosystems and triggering environmental changes. It is an emergent research topic to prevent invasive plant species spread and alleviate their influences in forest ecosystems. The case study aims to quantify the relationships between invasive plant species coverage and socio-ecological factors in community forests (CFs) in Chitwan, Nepal. We

This article presents a large case study of fare evasion on bus lines in the city of Lisbon, Portugal, a common problem in dense urban areas. Focus is put on geographic factors, and an analysis is carried out using a generalized spatial two-step least-squares regression (GS2SLS). The large database, spanning one year of fare evasion reports, made it possible to segregate the analysis according to type of day (workday or weekend) and time period (rush hours, nighttime, etc.). Results show that indeed the type of day and time period lead to considerable differences between the seven models analyzed. It was found that the number of inspection actions is the strongest predictor of evasion, with geographic factors also playing a role in predicting fare evasion. Consideration of this spatial component made it possible to find moderate evidence for dissuasive effects of inspection actions in some models and of pockets of evasive tendencies in other models, which appear in the statistical error term. Interestingly, and contrary to other studies, age was found to have almost no influence on the propensity to evade fares. From a managerial point of view, this study highlights the importance of running inspection actions systematically and closely monitoring their outcomes. From a more theoretical standpoint, it suggests further research on geographic factors is needed to fully understand spatial patterns of evasion.

This study discusses the analysis of the causes of flooding in Samarinda City using geographically weighted regression (GWR) method of spatial statistics. Samarinda City has an area that is prone to flooding. Floods in Samarinda City occur due to excess surface runoff and not being accommodated in the Mahakam watersheds so that water overflows. The factors that cause flooding in Samarinda City are natural factors such as high rainfall, the topography of the area, and the tides of the Mahakam watersheds. The second factor is humans, mainly due to the element of population growth followed by an increase in the need for infrastructure, housing, clean water facilities, education, and other community services. The results of spatial statistical analysis obtained that the best model was the GWR model with R2 of 0.92 and MSE value of 0.202. Based on these results, the concept of flood control in Samarinda City was divided into three parts, namely flood control in the upstream, middle and downstream areas. The upstream flood control concept could be implemented by repairing damaged watersheds conditions and increasing watersheds resistance. The concept of flood control in the middle area could be implemented by reducing flooding and reducing surface runoff. Meanwhile, the concept of flood control in the downstream area could be implemented by facilitating the flow of existing drainage done by increasing the capacity of the drainage channel water and protecting the flow in the channel from the influence of the tide of the Mahakam River.

Recent developments in spatial analysis and spatial data have allowed researchers to investigate various geographical factors in the quantitative analysis of conflict and war (Ward in Polit Geogr 21(2):155–158, 2002). Despite the importance of territory in interstate conflict, there has been a limited interest in the application of spatial analysis to the study of territorial conflict. Using geographically weighted regression (GWR) we evaluated the existing explanations of territorial conflict provided by a global scale analysis that assumes a spatial consistency in the explanatory variables. Specifically, we revisited Paul Huth’s foundational work by using GWR to examine the spatial pattern in the sign and significance of the variables. The result of GWR shows that the escalation of territorial conflict cannot be fully explained by one universal model. There is a high level of spatial variation in the regression parameters and the explanatory power of the model varies over space. A k-means cluster analysis was implemented for a further investigation of the regional pattern of the underlying causes of territorial disputes. The result of our GWR suggests the necessity and possibility to pursue a local or regional scale approach to the study of territorial conflict, an approach that challenges an epistemology of seeking a single explanation for the causes of conflict that neglects regional context. The spatial heterogeneity in the causes of territorial conflict escalation we find is framed within a narrative of the intertwined processes of colonialism, Cold War legacies, and competition for resources.

Geographically Weighted Regression (GWR) is increasingly used in spatial analyses of social and environmental data. It allows spatial heterogeneities in processes and relationships to be investigated through a series of local regression models rather than a single global one. Standard GWR assumes that relationships between the response and predictor variables operate at the same spatial scale, which is frequently not the case. To address this, several GWR variants have been proposed. This paper describes a route map to decide whether to use a GWR model or not, and if so which of three core variants to apply: a standard GWR, a mixed GWR or a multiscale GWR (MS‐GWR). The route map comprises 3 primary steps that should always be undertaken: (1) a basic linear regression, (2) a MS‐GWR, and (3) investigations of the results of these in order to decide whether to use a GWR approach, and if so for determining the appropriate GWR variant. The paper also highlights the importance of investigating a number of secondary issues at global and local scales including collinearity, the influence of outliers, and dependent error terms. Code and data for the case study used to illustrate the route map are provided.

The Normalized Difference Vegetation Index (NDVI) and rainfall data were used to model the spatial relationship between vegetation and rainfall. Their correlation in previous studies was typically based on a global regression model, which assumed that the correlation was constant across space. The NDVI–rainfall association, on the other hand, is spatially non-stationary, non-linear, scale-dependent, and influenced by local factors (e.g., soil background). In this study, two statistical methods are used in the modeling, i.e., traditional ordinary least squares (OLS) regression and geographically weighted regression (GWR), to evaluate the NDVI–rainfall relationship. The GWR was implemented annually in the growing seasons of 2000 and 2016, using climate data (Normalized Vegetation Difference Index and rainfall). The NDVI–rainfall relationship in the studied Bisha watershed (an eco-sensitive zone with a complex landscape) was found to have a stable operating scale of around 12 km. The findings support the hypothesis that the OLS model’s average impression could not accurately represent local conditions. By addressing spatial non-stationarity, the GWR approach greatly improves the model’s accuracy and predictive ability. In analyzing the relationship between NDVI patterns and rainfall, our research has shown that GWR outperforms a global OLS model. This superiority stems primarily from the consideration of the relationship’s spatial variance across the study area. Global regression techniques such as OLS can overlook local details, implying that a large portion of the variance in NDVI is unexplained. It appears that rainfall is the most significant factor in deciding the distribution of vegetation in these regions. Furthermore, rainfall had weak relationships with areas predominantly located around wetlands, suggesting the need for additional factors to describe NDVI variations. The GWR method performed better in terms of accuracy, predictive power, and reduced residual autocorrelation. Thus, GWR is recommended as an explanatory and exploratory technique when relations between variables are subject to spatial variability. Since the GWR is a local form of spatial analysis that aligned to local conditions, it has the potential for more accurate prediction; however, a larger amount of data is needed to allow a reliable local fitting.

Fare evasion in proof-of-payment transit systems: Deriving the optimum inspection level

Two popular data science analyses are spatial analysis and machine learning. The most popular spatial analysis is geographically weighted regression (GWR), and the most popular of machine learning is random forest (classification dan regression). The paper used GWR and Random Forest Regression (RFR) to find the variables that significantly impact life expectancy and compare two methods using RMSE. Knowledge of life expectancy and determining factors on life expectancy is essential because the increase in life expectancy is linked to a country's economic and social prosperity. The researcher employed life expectancy data as the dependent variable (Y) and some independent variables. At each observation location in Sumatra Region, the GWR model and significant independent variables are different. The RMSE value in the GWR model is 64.99. There are three variables with significant influence in most areas are X3 (percentage of proper sanitation households), X5 (number of doctors), and X7 (average years of schooling). The RMSE value in the RFR model is 84.04 with three variables importance: X3 (percentage of proper sanitation households), X5 (number of doctors), and X7 (average years of schooling) have the most influence. Keywords: GWR, Life Expectancy, RFR, RMSE.

<div>The widespread adoption of “proof-of-payment” ticketing systems by public transit corporations (PTCs) has renewed interest in the topic of fare evasion. Although this system has</div><div>many benefits, it has also been associated with higher rates of actual or perceived fare evasion. As such, many PTCs including the TTC in Toronto have also simultaneously invested in heightened measures to curb fare evasion. These measures, however, have usually taken the form of increased fines and policing, which have the potential to further disadvantage marginalized populations. A scoping literature review and case study analysis have been</div><div>employed to determine whether there is existing evidence that can make a case for the need for a more equitable solution to this problem, and to determine what alternative measures have been effective. Although there is much evidence to support the need for a more equitable approach, research into alternative measures is emerging and therefore somewhat inconclusive.</div>

Spatial statistical models are commonly used in geographical scenarios to ensure spatial variation is captured effectively. However, spatial models and cluster algorithms can be complicated and expensive. One of these algorithms is geographically weighted regression (GWR) which was proposed in the geography literature to allow relationships in a regression model to vary over space. In contrast to traditional linear regression models, which have constant regression coefficients over space, regression coefficients are estimated locally at spatially referenced data points with GWR. The motivation for the adaption of GWR is the idea that a set of constant regression coefficients cannot adequately capture spatially varying relationships between covariates and an outcome variable. GWR has been applied widely in diverse fields, such as ecology, forestry, epidemiology, neurology and astronomy. While frequentist GWR gives us point estimates and confidence intervals, Bayesian GWR enriches our understanding by including prior knowledge and providing probability distributions for parameters and predictions of interest. This paper pursues three main objectives. First, it introduces covariate effect clustering by integrating a Bayesian geographically weighted regression (BGWR) with a post-processing step that includes Gaussian mixture model and the Dirichlet process mixture model. Second, this paper examines situations in which a particular covariate holds significant importance in one region but not in another in the Bayesian framework. Lastly, it addresses computational challenges in existing BGWR, leading to enhancements in Markov chain Monte Carlo estimation suitable for large spatial datasets. The efficacy of the proposed method is demonstrated using simulated data and is further validated in a case study examining children's development domains in Queensland, Australia, using data provided by Children's Health Queensland and Australia's Early Development Census.

The potential of satellite data used for particular matter monitoring is a crucial subject in air quality research. PM10 is influenced by many meteorological factors and has a difference correlation with aerosol optical depth in different place. Geographically weighted regression (GWR) model have been proved to be an effective methods for spatial variation analysis. This paper presented results from a study of PM10 concentration from API in eastern China from 2005 to 2010. Wavelet analysis was used for analyzing the periodicity characteristics of PM10 and AOD. The correlations between PM10 and meteorological factors were also analyzed without AOD and with AOD added, respectively. Obvious spatial and seasonal non-stationary distributions of PM10 concentration were found with spatial auto-correlation analysis. PM10 concentration and AOD have similar periods and discontinuity characteristics in 41 months scale and 70 months scale. Correlation between PM10 concentration and meteorological factors were improved when AOD added as a factor, and the tempo-spatial distributions of the correlations were non-stationary in eastern China because of differences of the regional weather conditions and the pollution sources.