No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
Hierarchical Bayesian modeling for the spatial analysis of robberies in Toronto, Canada
Abstract
This paper investigates the geographic variation of robbery risk in Toronto, Canada. A hierarchical Bayesian modeling approach is used for estimating the relative risk of robberies across Toronto’s 140 neighbourhood districts in 2017. The association between robbery risk and various socio-economic explanatory variables (i.e., business density, education and income levels) are analyzed using a Poisson-based spatial regression model. Markov Chain Monte Carlo model fitting is utilized for the estimation of relative risk and associated regression parameters. Results reveal that elevated levels of robbery risk are predominant in the eastern, north-western and southern neighbourhoods of Toronto whereas, lower risk areas are situated in the central neighbourhoods. Across all neighbourhoods, there was a geographical difference in robbery risk, ranging from 0.17 (95% CI 0.05–0.38) to 4.87 (95% CI 4.22–5.55). Education and income variables had a negative association with robberies at posterior probabilities of 96.9% and 85.5% respectively, whereas business density had a positive association with robberies at a posterior probability of 100%. Hence, neighbourhoods with higher amounts of businesses, lower education levels and lower household incomes tend to have a higher mean amount of robberies in Toronto and thus higher associated risks.
... Through the use of Bayesian spatial analysis, both Takahashi et al. (2017) and Law and Perlman (2018) presented mental health-based epidemiologic studies of Japan and Toronto, Canada respectively. Persad (2019a) and Marco et al. (2018) discuss the numerous methodological advantages of Bayesian regression methods over frequentist approaches for spatial applications. ...
... The 95% credible interval is the 95% probability that the parameter lies between the interval defined by an upper and lower bound. The Monte Carlo (MC) error value reflects the accuracy of estimated parameters and should generally be less than 5% of the parameter's SD (Persad 2019a). The MC errors of estimated parameters in this study were less than 5% of their respective SDs. ...
... Exceedance probabilities are used to highlight the spatial units where the posterior probability of mental illness risk is greater than 1. Exceedance probabilities nearer to 1.0 are useful in highlighting 'hot-spots' with higher risk (Persad 2019a). From Figure 2(b), it is noticeable mental illness risk due to the spatial random effect terms (i.e. both the spatially correlated and spatial heterogeneity terms) had more impact in the northern PHUs compared to the southern areal units. ...
Mental illness is a predominant medical condition in Canada. Marginalized groups in the Canadian population such as those with low income, the poorly educated and ethnic minorities are susceptible to mental health disorders. Using mental health-related emergency department visits as an indicator of mental illness cases, we employ a Bayesian spatio-temporal regression model to estimate mental illness risk across the 35 public health units of Ontario, Canada from 2006 to 2017. The association between mental illness and the following marginalization-related factors: material deprivation, residential instability and ethnic concentration is also evaluated. Over the assessed period, the relative risk of mental illness ranged from 0.45 (95% CI: 0.44–0.46) to 3.29 (95% CI: 3.20–3.37). Health units with elevated levels of material deprivation and residential instability were positively associated with increased mental illness risk whilst areas with higher ethnic concentration were linked with lower risk. Findings showed that the temporal trend of risk continuously increased over the 11 year period, with health units in northern Ontario experiencing higher risk compared to southern units. The management of psychiatric disorders presents a significant challenge to the Canadian health-care system. An understanding of the geographic distribution of mental health risk across space and time can be useful for improved policy-making and public health monitoring.
... The spatial frequentist techniques include the zero-inflated negative binomial model (Liu et al., 2018;Swartout et al., 2015), geographically weighted negative binomial regression (GWNBR) (Chen et al., 2020;Wang et al., 2017), spatial Durbin (R. P. Haining & Li, 2020), and spatial spline regression models (Sangalli et al., 2013). Additionally, with the advancement of computational power, Bayesian spatial techniques have gained considerable popularity, such as the Bayesian Poisson hierarchical regression (Law & Haining, 2004;Law & Quick, 2013;Persad, 2020;Quick et al., 2017), Bayesian semiparametric joint quantile regression (Bresson et al., 2021;Chen & Tokdar, 2021;Jang & Wang, 2015;Kottas & Krnjajić, 2009), Bayesian cross-classified multilevel spatial (and temporal) modeling (Quick, 2019) and Bayesian spatial network learning (Baumgartner et al., 2005;Mahmud et al., 2016). Each of these techniques is applied considering different aspects of crime and poses its own advantages and disadvantages. ...
Background setting
Traditional spatial or non-spatial regression techniques require individual variables to be defined as dependent and independent variables, often assuming a unidirectional and (global) linear relationship between the variables under study. This research studies the Bayesian shared component spatial (BSCS) modeling as an alternative approach to identifying local associations between two or more variables and their spatial patterns.
Methods
The variables to be studied, young offenders (YO) and violent crimes (VC), are treated as (multiple) outcomes in the BSCS model. Separate non-BSCS models that treat YO as the outcome variable and VC as the independent variable have also been developed. Results are compared in terms of model fit, risk estimates, and identification of hotspot areas.
Results
Compared to the traditional non-BSCS models, the BSCS models fitted the data better and identified a strong spatial association between YO and VC. Using the BSCS technique allowed both the YO and VC to be modeled as outcome variables, assuming common data-generating processes that are influenced by a set of socioeconomic covariates. The BSCS technique offered smooth and easy mapping of the identified association, with the maps displaying the common (shared) and separate (individual) hotspots of YO and VC.
Conclusions
The proposed method can transform existing association analyses from methods requiring inputs as dependent and independent variables to outcome variables only and shift the reliance on regression coefficients to probability risk maps for characterizing (local) associations between the outcomes.
A multivariate Bayesian spatial modeling approach was used to jointly model the counts of two types of crime, i.e., burglary and non-motor vehicle theft, and explore the geographic pattern of crime risks and relevant risk factors. In contrast to the univariate model, which assumes independence across outcomes, the multivariate approach takes into account potential correlations between crimes. Six independent variables are included in the model as potential risk factors. In order to fully present this method, both the multivariate model and its univariate counterpart are examined. We fitted the two models to the data and assessed them using the deviance information criterion. A comparison of the results from the two models indicates that the multivariate model was superior to the univariate model. Our results show that population density and bar density are clearly associated with both burglary and non-motor vehicle theft risks and indicate a close relationship between these two types of crime. The posterior means and 2.5% percentile of type-specific crime risks estimated by the multivariate model were mapped to uncover the geographic patterns. The implications, limitations and future work of the study are discussed in the concluding section.
A Bayesian random effects modeling approach was used to examine the influence of neighborhood characteristics on burglary risks in Jianghan District, Wuhan, China. This random effects model is essentially spatial; a spatially structured random effects term and an unstructured random effects term are added to the traditional non-spatial Poisson regression model. Based on social disorganization and routine activity theories, five covariates extracted from the available data at the neighborhood level were used in the modeling. Three regression models were fitted and compared by the deviance information criterion to identify which model best fit our data. A comparison of the results from the three models indicates that the Bayesian random effects model is superior to the non-spatial models in fitting the data and estimating regression coefficients. Our results also show that neighborhoods with above average bar density and department store density have higher burglary risks. Neighborhood-specific burglary risks and posterior probabilities of neighborhoods having a burglary risk greater than 1.0 were mapped, indicating the neighborhoods that should warrant more attention and be prioritized for crime intervention and reduction. Implications and limitations of the study are discussed in our concluding section.
This research analyzes the association between alcohol outlets and reported violent crime at the small-area level in the Region of Waterloo, Ontario, Canada. Alcohol outlets are hypothesized to be associated with high violent crime, primarily because they bring together large numbers of potential offenders and targets, and from a policy perspective, alcohol outlets are a modifiable land use risk factor that can be addressed through land use planning and policy. Results show that both on- and off-premise alcohol outlets are positively associated with reported violent crime after accounting for socioeconomic characteristics. Using small-area risk estimates resulting from Bayesian spatial regression models, map decomposition visualizes the geographic pattern of violent crime risk and the contribution of specific risk factors at the small-area scale, and violent crime hotspots are identified based on posterior probability of relative risk. Applying results to land use planning and policy, we identify small-areas that may be preferred for proposed alcohol outlets based on specific criteria such as low violent crime risk and low risk due to alcohol outlets. We also discuss how the results of this research inform law enforcement initiatives.
The paper investigates the dependences between levels of severity of road traffic accidents, accounting at the same time for spatial and temporal correlations. The study analyses road traffic accidents data at ward level in England over the period 2005–2013. We include in our model multivariate spatially structured and unstructured effects to capture the dependences between severities, within a Bayesian hierarchical formulation. We also include a temporal component to capture the time effects and we carry out an extensive model comparison. The results show important associations in both spatially structured and unstructured effects between severities, and a downward temporal trend is observed for low and high levels of severity. Maps of posterior accident rates indicate elevated risk within big cities for accidents of low severity and in suburban areas in the north and on the southern coast of England for accidents of high severity. The posterior probability of extreme rates is used to suggest the presence of hot spots in a public health perspective.
Informed by Galtung (1969), Anderson (2012) and Wacquant (2001), this paper argues that a lifetime of spiralling and everyday state structural violence and overtly racist criminal profiling principally targeted at young Black men living in the Toronto Community Housing Corporation prepares them for prison. Moreover, it contends that interpersonal violence, transmitted from generation to generation and producing a vicious cycle, is a manifestation of institutionalized and systemic inequity. In the context of a hypermasculine culture, young Black men are both victims and participants in a dialectic of interpersonal-structural violence. Routinely precipitated by powerful state actors and agencies of criminal justice, public policy and assorted moral entrepreneurs, young Black men have their masculinity weaponized and prisonized by the states low-intensity declaration of war against them, and, among others, the poor, LGBTQ, immigrants, and First Nations and other people of colour.
Conditional autoregressive models are commonly used to represent spatial autocorrelation in data relating to a set of non-overlapping areal units, which arise in a wide variety of applications including agriculture, education, epidemiology and image analysis. Such models are typically specified in a hierarchical Bayesian framework, with inference based on Markov chain Monte Carlo (MCMC) simulation. The most widely used software to fit such models is WinBUGS or OpenBUGS, but in this paper we introduce the R package CARBayes. The main advantage of CARBayes compared with the BUGS software is its ease of use, because: (1) the spatial adjacency information is easy to specify as a binary neighbourhood matrix; and (2) given the neighbourhood matrix the models can be implemented by a single function call in R. This paper outlines the general class of Bayesian hierarchical models that can be implemented in the CARBayes software, describes their implementation via MCMC simulation techniques, and illustrates their use with two worked examples in the fields of house price analysis and disease mapping.
In this article, we focus on geocoded data for pediatric brain cancer in Florida. Specifically, we examine zip code level pediatric brain cancer counts from the Florida Association of Pediatric Tumor Programs (FAPTP) childhood cancer registry from 2000–2010 and assess the degree of spatial clustering in these data. We assume Bayesian models for relative risk and examine a variety of posterior measures that indicate excess risk (exceedence probability of relative risk or positive residual). We assume a standard Poisson convolution model and examine a zero-inflated (ZI) model with a factored intercept. We conclude that there is evidence of excess risk in a number of relatively dispersed zip codes across the state but there appears to be some concentration of high excess risk in Polk, Lake, and Sumter counties (west of Orlando and north east of Tampa). These excesses are confirmed across the models.
Public interest in the influence of neighbourhoods on immigrant integration in Canadian society has been growing in recent years; yet, there are few studies that explain the effect of neighbour-hoods on immigrant experiences of exclusion in Canada. Drawing on in-depth interviews (12 males and 13 females) and a focus group discussion (five females and three males) conducted with Ghanaian immigrant youth between the ages of 18 to 30 from the Ghanaian community in the Jane and Finch neighbourhood of Toronto in May to June, 2011, this paper discusses the experiences of social and spatial exclusion among Ghanaian immigrant youth. Drawing on socio-spatial dialectics, the findings suggest that Ghanaian immigrant youth experiences of socio-spatial exclusion are intertwined in a dialectical process involving the Jane and Finch neighbourhood and the general public. In particular, the youth negotiate access to employment opportunities, shopping malls and counter exclusion through reformulation of resumes, and masking of their actual neighbourhoods. This paper fills an important gap in our knowledge of the lived experiences of African immigrant youth and contributes to our understanding of the dynamics of neighbourhood stigmatization and its impact on residents’ integration into the larger society.
Résumé:
Au moment où le public s’intéresse davantage à l’impact des quartiers de résidence sur l’intégration des immigrants à la société canadienne, peu d’études explorent l’influence qu’a le voisinage sur les expériences d’inclusion et d’exclusion des immigrants au Canada. Pour cette raison, cet article traite des expériences d’exclusion spatiale et sociale chez des jeunes immigrants Ghanéens âgés de 18 à 30 qui habitent le quartier de Jane et Finch à Toronto. Nous basant sur des entrevues semi-dirigées approfondies menées auprès de 12 hommes et 13 femmes ainsi que un groupe de discussion organisé avec trois hommes et cinq femmes, nous montrons que l’exclusion sociospatiale que ces jeunes subissent est située dans un processus dialectique qui englobe à la fois les jeunes et le public. La dialectique socio-spatiale nous permet également à conclure que les jeunes résistent à l’exclusion en question et négocient leur accès à l’emploi et aux centres commerciaux par le biais de la reformulation du CV et le masquage du nom de quartier. De cette façon, cet article cet article comble les lacunes en matière de vécu des jeunes immigrants africains et nous permet de mieux comprendre les dynamiques de la stigmatisation basée sur le lieu de résidence et l’impact que celle-ci a sur l’intégration des immigrants au sein de la société canadienne.
Toronto’s Census Metropolitan Area (CMA) has faced on-going challenges concerning its demographic shifts in the urban and rural fringe tending to become a megacity over the coming decades, due to rapid population increase and urban amalgamation. For this research we examine past urban land use transitions in Toronto’s CMA based on collected remote sensing data between 1973 and 2010. A Markov Cellular Automata approach is used deriving the CMA urban future based on the existing and planned strategies for Ontario. This is done by a combination of multi-criteria evaluation processes originating transition probabilities that allow a better understanding of the regions urban future by 2030. While the transition probabilities are incorporated from the traditional Markov Chain process, the variables for suitability are measured through a text mining approach, by incorporating several planning documents. The result offers a more integrative vision of policymaker’s preference of future planning instruments, allowing for the creation of a better integration of propensity of future growth indicators. The northern part of Toronto is expected to register continuous growth in the coming decades, while agricultural land will continue to decrease. Urban areas after 2020 tend to become more clustered suggesting an importance of planning of green spaces within the Toronto.
The investigation of individual heterogeneity in vital rates has recently received growing attention among population ecologists. Individual heterogeneity in wild animal populations has been accounted for and quantified by including individually varying effects in models for mark–recapture data, but the real need for underlying individual effects to account for observed levels of individual variation has recently been questioned by the work of Tuljapurkar et al. (Ecology Letters, 12, 93, 2009) on dynamic heterogeneity. Model-selection approaches based on information criteria or Bayes factors have been used to address this question. Here, we suggest that, in addition to model-selection, model-checking methods can provide additional important insights to tackle this issue, as they allow one to evaluate a model's misfit in terms of ecologically meaningful measures. Specifically, we propose the use of posterior predictive checks to explicitly assess discrepancies between a model and the data, and we explain how to incorporate model checking into the inferential process used to assess the practical implications of ignoring individual heterogeneity. Posterior predictive checking is a straightforward and flexible approach for performing model checks in a Bayesian framework that is based on comparisons of observed data to model-generated replications of the data, where parameter uncertainty is incorporated through use of the posterior distribution. If discrepancy measures are chosen carefully and are relevant to the scientific context, posterior predictive checks can provide important information allowing for more efficient model refinement. We illustrate this approach using analyses of vital rates with long-term mark–recapture data for Weddell seals and emphasize its utility for identifying shortfalls or successes of a model at representing a biological process or pattern of interest.
This paper uses spatial data of cases of intimate partner violence against women (IPVAW) to examine neighborhood-level influences on small-area variations in IPVAW risk in a police district of the city of Valencia (Spain). To analyze area variations in IPVAW risk and its association with neighborhood-level explanatory variables we use a Bayesian spatial random-effects modeling approach, as well as disease mapping methods to represent risk probabilities in each area. Analyses show that IPVAW cases are more likely in areas of high immigrant concentration, high public disorder and crime, and high physical disorder. Results also show a spatial component indicating remaining variability attributable to spatially structured random effects. Bayesian spatial modeling offers a new perspective to identify IPVAW high and low risk areas, and provides a new avenue for the design of better-informed prevention and intervention strategies.
Crime levels have risen significantly in Argentina during recent years. In this study, we analyze the relationship between crime victimization and income distribution.
In this paper we present a "routine activity approach" for analyzing crime rate trends and cycles. Rather than emphasizing the characteristics of offenders, with this approach we concentrate upon the circumstances in which they carry out predatory criminal acts. Most criminal acts require convergence in space and time of likely offenders, suitable targets and the absence of capable guardians against crime. Human ecological theory facilitates an investigation into the way in which social structure produces this convergence, hence allowing illegal activities to feed upon the legal activities of everyday life. In particular, we hypothesize that the dispersion of activities away from households and families increases the opportunity for crime and thus generates higher crime rates. A variety of data is presented in support of the hypothesis, which helps explain crime rate trends in the United States 1947-1974 as a byproduct of changes in such variables as labor force participation and single-adult households.
Systems biology employs mathematical modelling to further our understanding of biochemical pathways. Since the amount of experimental data on which the models are parameterized is often limited, these models exhibit large uncertainty in both parameters and predictions. Statistical methods can be used to select experiments that will reduce such uncertainty in an optimal manner. However, existing methods for optimal experiment design (OED) rely on assumptions that are inappropriate when data are scarce considering model complexity.
We have developed a novel method to perform OED for models that cope with large parameter uncertainty. We employ a Bayesian approach involving importance sampling of the posterior predictive distribution to predict the efficacy of a new measurement at reducing the uncertainty of a selected prediction. We demonstrate the method by applying it to a case where we show that specific combinations of experiments result in more precise predictions.
Source code is available at: http://bmi.bmt.tue.nl/sysbio/software/pua.html.
In this article, we use a unique data set on criminal behaviour to analyse the effects of education on offences and crimes committed. The findings suggest that substantial savings on the social costs of crime can be obtained by investing in education. We find that the probability of committing crimes like shop lifting, vandalism and threat, assault and injury decrease with years of education. The probability of committing tax fraud, however, increases with years of education. We further find that higher educated people have more permissive attitudes and social norms towards criminal behaviour.
Using the 2002 Ethnic Diversity Survey, this article examines the ethnic differences in university education attainment among the children of immigrants in Canada. We found that most groups achieve clear upward mobility across generations, while such upward pattern is not observed among Blacks and Filipinos. Asians (with the exception of Filipinos) attain higher academic achievements than most groups of European origins even when accounting for group variations in family background, and social and ethnic capital. Parental education was important in explaining the relatively low university completion rates among the second generation Portuguese and Italians. Rural residence of the father’s generation was an important factor for the second generation Dutch and German youth, reflecting the different settlement patterns of these various groups. Our findings suggest that race/ethnicity has become a salient factor in educational stratification.
This paper considers the relationship between inequality and crime using data from urban counties. The behavior of property and violent crime are quite different. Inequality has no effect on property crime but a strong and robust impact on violent crime, with an elasticity above 0.5. By contrast, poverty and police activity have significant effects on property crime, but little on violent crime. Property crime is well explained by the economic theory of crime, while violent crime is better explained by strain and social disorganization theories. © 2000 by the President and Fellows of Harvard College and the Massachusetts Institute of Technolog
Using the 2002 Ethnic Diversity Survey, this article examines the group differences by national origin in university educational attainment among the children of immigrants in Canada. We found that children of immigrant parents in most source region groups achieve higher university completion rates than children of Canadian-born parents, partly due to higher education levels of their parents. Children of Chinese and Indian immigrants particularly attain higher academic achievements than children of Canadian-born parents. Parental education was also important in explaining the relatively low university completion rates among the second-generation Portuguese.
The R2WinBUGS package provides convenient functions to call WinBUGS from R. It automatically writes the data and scripts in a format readable by WinBUGS for processing in batch mode, which is possible since version 1.4. After the WinBUGS process has finished, it is possible either to read the resulting data into R by the package itself--which gives a compact graphical summary of inference and convergence diagnostics--or to use the facilities of the coda package for further analyses of the output. Examples are given to demonstrate the usage of this package.
Bayesian statistical methods have become widely used for data analysis and modelling in recent years, and the BUGS software has become the most popular software for Bayesian analysis worldwide. Authored by the team that originally developed this software, The BUGS Book provides a practical introduction to this program and its use. The text presents complete coverage of all the functionalities of BUGS, including prediction, missing data, model criticism, and prior sensitivity. It also features a large number of worked examples and a wide range of applications from various disciplines. The book introduces regression models, techniques for criticism and comparison, and a wide range of modelling issues before going into the vital area of hierarchical models, one of the most common applications of Bayesian methods. It deals with essentials of modelling without getting bogged down in complexity. The book emphasises model criticism, model comparison, sensitivity analysis to alternative priors, and thoughtful choice of prior distributions—all those aspects of the "art" of modelling that are easily overlooked in more theoretical expositions. More pragmatic than ideological, the authors systematically work through the large range of "tricks" that reveal the real power of the BUGS software, for example, dealing with missing data, censoring, grouped data, prediction, ranking, parameter constraints, and so on. Many of the examples are biostatistical, but they do not require domain knowledge and are generalisable to a wide range of other application areas. Full code and data for examples, exercises, and some solutions can be found on the book’s website.
Malvern, a neighbourhood in Toronto, Ontario, was turned into a designated area for affordable housing during its transformation into a modern community in the late 20thcentury. Any positive connotation that was once attached to ‘affordable housing’ as an idyllic space for hard-working residents quickly disappeared, however, and Malvern has repeatedly been labeled one of Toronto’s most dangerous neighbourhoods, in dire need of improvement. In this essay, I borrow from Omi and Winant (2015) to argue that the neighbourhood of Malvern is a racial project – that is, Malvern’s representations assign meaning to race, created not only through racist and classist planning, but also through the ways that Malvern is shared in the larger public, through media representations of Malvern, and the complex experiences and realities of its residents. Populated almost entirely by visible minorities, the mapping of criminal deviance alongside racialized individuals has ensured that Malvern and its residents continue to be marred by stigma and stereotypes, leaving residents feeling conflicted with internalized and arguably perverse understandings of themselves, and without the necessary support that disadvantaged neighbourhoods should receive. Today, Malvern is the product of purposeful, structural violence, with the people of Malvern perceived as lacking the civility to maintain the ideal space that was created for them. Using the work of Henri Lefebvre, this paper provides a detailed analysis of the way that Malvern was conceived and perceived to exist and the way that it continues to be lived as a racial project. Malvern, like other inner-city neighbourhoods in North America, has remained at a disadvantage since its inception. In this essay, I explore how the perception of Malvern came to be and how first-hand experiences within Malvern’s borders differ from those which are negatively portrayed in the media.
1: Introduction.- 2: The Scope of Spatial Econometrics.- 3: The Formal Expression of Spatial Effects.- 4: A Typology of Spatial Econometric Models.- 5: Spatial Stochastic Processes: Terminology and General Properties.- 6: The Maximum Likelihood Approach to Spatial Process Models.- 7: Alternative Approaches to Inference in Spatial Process Models.- 8: Spatial Dependence in Regression Error Terms.- 9: Spatial Heterogeneity.- 10: Models in Space and Time.- 11: Problem Areas in Estimation and Testing for Spatial Process Models.- 12: Operational Issues and Empirical Applications.- 13: Model Validation and Specification Tests in Spatial Econometric Models.- 14: Model Selection in Spatial Econometric Models.- 15: Conclusions.- References.
The quantity and subject matter of news coverage has been implicated in the success or failure of efforts to address social exclusion, poverty and other complex problems in disadvantaged city neighbourhoods. Using a methodology that combines traditional content analysis with computer-based mapping of geographic references in local news items, this study examines the Toronto Star newspaper's news coverage of 13 troubled neighbourhoods in Toronto, Canada. The results indicate that the paper is making only a limited contribution to the story-telling practices that are key to the development of neighbourhood engagement. It also suggests that media coverage may be a significant contributing factor to negative stereotyping that shapes internal and external opinions of the neighbourhoods. Both results have the potential to undermine strategies aimed at addressing problems such as social exclusion and poverty. Copyright © 2009 by the Institute of Urban Studies All rights of reproduction in any form reserved.
Disease Mapping and Map ReconstructionDisease Map Restoration
This paper adopts a Bayesian spatial modeling approach to investigate the distribution of young offender residences in York Region, Southern Ontario, Canada, at the census dissemination area level. Few geographic researches have analyzed offender (as opposed to offense) data at a large map scale (i.e., using a relatively small areal unit of analysis) to minimize aggregation effects. Providing context is the social disorganization theory, which hypothesizes that areas with economic deprivation, high population turnover, and high ethnic heterogeneity exhibit social disorganization and are expected to facilitate higher instances of young offenders. Non-spatial and spatial Poisson models indicate that spatial methods are superior to non-spatial models with respect to model fit and that index of ethnic heterogeneity, residential mobility (1 year moving rate), and percentage of residents receiving government transfer payments are, respectively, the most significant explanatory variables related to young offender location. These findings provide overwhelming support for social disorganization theory as it applies to offender location in York Region, Ontario. Targeting areas where prevalence of young offenders could or could not be explained by social disorganization through decomposing the estimated risk map are helpful for dealing with juvenile offenders in the region. Results prompt discussion into geographically targeted police services and young offender placement pertaining to risk of recidivism. We discuss possible reasons for differences and similarities between the previous findings (that analyzed offense data and/or were conducted at a smaller map scale) and our findings, limitations of our study, and practical outcomes of this research from a law enforcement perspective.
The hypothesis tested is that variations in rates of urban criminal violence largely result from differences in racial inequality in socioeconomic conditions. Data on the 125 largest American metropolitan areas (SMSAs) are used to ascertain whether this hypothesis can account for three correlates of violent crime differently interpreted in the literature. Criminal violence is positively related to location in the South, which has been interpreted as the result of the Southern tradition of violence. It is positively related to the proportion of blacks in an SMSA, which has been interpreted as reflecting a subculture of violence in ghettos. And it is positively related to poverty, which has been interpreted as the emphasis on toughness and excitement in the culture of poverty. The analysis reveals that socioeconomic inequality between races, as well as economic inequality generally, increases rates of criminal violence, but once economic inequalities are controlled poverty no longer influences these rates, neither does Southern location, and the proportion of blacks in the population hardly does. These results imply that if there is a culture of violence, its roots are pronounced economic inequalities, especially if associated with ascribed position.
A Monte Carlo experiment illustrates one of the pitfalls of spatial modeling. Specification tests indicate spatial autocorrelation when functional form misspecification is actually the only problem with the model. Incorrect functional forms and omitted variables that are correlated over space produce spurious spatial autocorrelation.
Informative priors can be a useful tool for epidemiologists to handle problems of sparse data in regression modeling. It is sometimes the case that an investigator is studying a population exposed to two agents, X and Y, where Y is the agent of primary interest. Previous research may suggest that the exposures have different effects on the health outcome of interest, one being more harmful than the other. Such information may be derived from epidemiologic analyses; however, in the case where such evidence is unavailable, knowledge can be drawn from toxicologic studies or other experimental research. Unfortunately, using toxicologic findings to develop informative priors in epidemiologic analyses requires strong assumptions, with no established method for its utilization. We present a method to help bridge the gap between animal and cellular studies and epidemiologic research by specification of an order-constrained prior. We illustrate this approach using an example from radiation epidemiology.
BACKGROUND Introduction Data Sets Bayesian Inference and Modeling Likelihood Models Prior Distributions Posterior Distributions Predictive Distributions Bayesian Hierarchical Modeling Hierarchical Models Posterior Inference Exercises Computational Issues Posterior Sampling Markov Chain Monte Carlo Methods Metropolis and Metropolis-Hastings Algorithms Gibbs Sampling Perfect Sampling Posterior and Likelihood Approximations Exercises Residuals and Goodness-of-Fit Model Goodness-of-Fit Measures General Residuals Bayesian Residuals Predictive Residuals and the Bootstrap Interpretation of Residuals in a Bayesian Setting Exceedence Probabilities Exercises THEMES Disease Map Reconstruction and Relative Risk Estimation An Introduction to Case Event and Count Likelihoods Specification of the Predictor in Case Event and Count Models Simple Case and Count Data Models with Uncorrelated Random Effects Correlated Heterogeneity Models Convolution Models Model Comparison and Goodness-of-Fit Diagnostics Alternative Risk Models Edge Effects Exercises Disease Cluster Detection Cluster Definitions Cluster Detection using Residuals Cluster Detection using Posterior Measures Cluster Models Edge Detection and Wombling Ecological Analysis General Case of Regression Biases and Misclassification Error Putative Hazard Models Multiple Scale Analysis Modifiable Areal Unit Problem (MAUP) Misaligned Data Problem (MIDP) Multivariate Disease Analysis Notation for Multivariate Analysis Two Diseases Multiple Diseases Spatial Survival and Longitudinal Analyses General Issues Spatial Survival Analysis Spatial Longitudinal Analysis Extensions to Repeated Events Spatiotemporal Disease Mapping Case Event Data Count Data Alternative Models Infectious Diseases Appendix A: Basic R and WinBUGS Appendix B: Selected WinBUGS Code Appendix C: R Code for Thematic Mapping References Index
Concern has been expressed in Toronto since the 1970s about the ‘ghettoisation’ of black tenants in Metropolitan Toronto Housing Authority (MTHA) public housing. Very little specific evidence exists, however, about the incidence of blacks in MTHA housing. The objectives of the present study are to provide a more detailed perspective on the incidence of blacks in MTHA housing compared to the rest of Toronto and the segregation of blacks within the MTHA system. The results indicate that the proportion of black tenants in MTHA housing increased from 4.2 per cent in 1971 to 27.4 per cent in 1986, a much greater increase than for blacks in the rest of Toronto. Explanations include the recent black Caribbean immigration to Toronto, income constraints, family composition and supply, cost and discriminatory constraints in Toronto's rental housing market. The evidence also suggests that there is some concentration of blacks within MTHA housing, especially in suburban high rise developments. The most likely explanation is a form of ‘constrained choice’.
While conducting research on the occupational and educational aspirations and expectations of secondary-school students in Kenya during 1972, I obtained quantitative and qualitative data from a sample of 699 African students indicating that the problem of crime among unemployed school leavers is likely to substantially worsen in the coming years. The purpose of this article is to present that data within the context of a discussion of secondary education, unemployment, and crime in Kenya.
This study tests the effect of the composition and distribution of economic resources and race/ethnicity in cities, as well as how they are geographically distributed within these cities, on crime rates during a 30-year period. Using data on 352 cities from 1970 to 2000 in metropolitan areas that experienced a large growth in population after World War II, this study theorizes that the effect of racial/ethnic or economic segregation on crime is stronger in cities in which race/ethnicity or income are more salient (because of greater heterogeneity or inequality). We test and find that higher levels of segregation in cities with high levels of racial/ethnic heterogeneity lead to particularly high overall levels of the types of crime studied here (aggravated assaults, robberies, burglaries, and motor vehicle thefts). Similarly, higher levels of economic segregation lead to much higher levels of crime in cities with higher levels of inequality.
Why do robbers choose a particular area to commit an offense? Do they rob close to home? Do they search for areas with suitable and attractive targets? What keeps them away from certain areas? To answer these questions, a model is developed of how robbers choose target areas. The model draws on various theoretical and empirical tra-ditions, which include environmental criminology, journey to crime research, gang research, and social disorganization theory. Testing the model on cleared robbery cases in Chicago in the years 1996–1998, we demonstrate that robbery location choice is related to characteristics of target areas, to areas where offenders live, to joint characteristics of the resident and target areas, and to characteristics of the offenders them-selves. The presence of illegal markets and other crime generators and crime attractors make areas attractive for robbers, whereas collective efficacy seems to keep them out. Distance as well as racial and ethnic segregation restrict the mobility of offenders.
Spatial nonstationarity is a condition in which a simple “global” model cannot explain the relationships between some sets of variables. The nature of the model must alter over space to reflect the structure within the data. In this paper, a technique is developed, termed geographically weighted regression, which attempts to capture this variation by calibrating a multiple regression model which allows different relationships to exist at different points in space. This technique is loosely based on kernel regression. The method itself is introduced and related issues such as the choice of a spatial weighting function are discussed. Following this, a series of related statistical tests are considered which can be described generally as tests for spatial nonstationarity. Using Monte Carlo methods, techniques are proposed for investigating the null hypothesis that the data may be described by a global model rather than a non-stationary one and also for testing whether individual regression coefficients are stable over geographic space. These techniques are demonstrated on a data set from the 1991 U.K. census relating car ownership rates to social class and male unemployment. The paper concludes by discussing ways in which the technique can be extended.
This paper reports the fitting of a number of Bayesian logistic models with spatially structured or/and unstructured random effects to binary data with the purpose of explaining the distribution of high-intensity crime areas (HIAs) in the city of Sheffield, England. Bayesian approaches to spatial modeling are attracting considerable interest at the present time. This is because of the availability of rigorously tested software for fitting a certain class of spatial models. This paper considers issues associated with the specification, estimation, and validation, including sensitivity analysis, of spatial models using the WinBUGS software. It pays particular attention to the visualization of results. We discuss a map decomposition strategy and an approach that examines properties of the full posterior distribution. The Bayesian spatial model reported provides some interesting insights into the different factors underlying the existence of the three police-defined HIAs in Sheffield.
Prior studies have separately suggested the importance of physical distance or social distance effects for the creation of neighborhood ties. This project adopts a case study approach and simultaneously tests for propinquity and homophily effects on neighborhood ties by employing a full-network sample from a recently developed New Urbanist neighborhood within a mid-sized southern city. The authors find that physical distance reduces the likelihood of weak or strong ties forming, suggesting the importance of accounting for propinquity when estimating social tie formation. The authors simultaneously find that social distance along wealth reduces the likelihood of weak ties forming. Social distance on life course markers—age, marital status, and the presence of children—reduces the formation of weak ties. Consistent with the systemic model, each additional month of shared residence in the neighborhood increases both weak and strong ties. An important innovation is this study's ability to directly compare the effects of physical distance and social distance, placing them into equivalent units: a 10 percent increase in home value difference is equivalent to a 5.6 percent increase in physical distance.
Based on a previous township-scale model, a spatio-temporal framework is proposed to study the fluctuations of avalanche occurrence possibly resulting from climate change. The regional annual component is isolated from the total variability using a two-factor nonlinear analysis of variance. Moreover, relying on a Conditional AutoRegressive sub-model for the spatial effects, the structured time trend is distinguished from the random noise with different time series sub-models including autocorrelative, periodic and change-point models. The hierarchical structure obtained takes into account the uncertainty related to the estimation of the annual component for the quantification of the time trend. Bayesian inference is performed using Monte Carlo simulations. This allows a comparison of the different time series models and the prediction of future activity in an explicit unsteady context. Application to the northern French Alps illustrates the information provided by the model's different components, mainly the spatial and temporal terms as well as the spatio-temporal fluctuation of the relative risk. For instance, it shows no strong modifications in mean avalanche activity or in the number of winters of low or high activity over the last 60 years. This suggests that climate change has recently had little impact on the avalanching rhythm in this region. However, significant temporal patterns are highlighted: a complex combination of abrupt changes and pseudo-periodic cycles of approximately 15 years. For anticipating the future response of snow avalanches to climate change, correlating them with fluctuations of the constraining climatic factors is now necessary.
There has been much recent interest in Bayesian image analysis, including such topics as removal of blur and noise, detection of object boundaries, classification of textures, and reconstruction of two- or three-dimensional scenes from noisy lower-dimensional views. Perhaps the most straightforward task is that of image restoration, though it is often suggested that this is an area of relatively minor practical importance. The present paper argues the contrary, since many problems in the analysis of spatial data can be interpreted as problems of image restoration. Furthermore, the amounts of data involved allow routine use of computer intensive methods, such as the Gibbs sampler, that are not yet practicable for conventional images. Two examples are given, one in archeology, the other in epidemiology. These are preceded by a partial review of pixel-based Bayesian image analysis.
Bayesian inference is becoming a common statistical approach to phylogenetic estimation because, among other reasons, it allows
for rapid analysis of large data sets with complex evolutionary models. Conveniently, Bayesian phylogenetic methods use currently
available stochastic models of sequence evolution. However, as with other model-based approaches, the results of Bayesian
inference are conditional on the assumed model of evolution: inadequate models (models that poorly fit the data) may result
in erroneous inferences. In this article, I present a Bayesian phylogenetic method that evaluates the adequacy of evolutionary
models using posterior predictive distributions. By evaluating a model's posterior predictive performance, an adequate model
can be selected for a Bayesian phylogenetic study. Although I present a single test statistic that assesses the overall (global)
performance of a phylogenetic model, a variety of test statistics can be tailored to evaluate specific features (local performance)
of evolutionary models to identify sources failure. The method presented here, unlike the likelihood-ratio test and parametric
bootstrap, accounts for uncertainty in the phylogeny and model parameters.
Spatial effects are endemic in models based on spatially referenced data. The increased awareness of the relevance of spatial interactions, spatial externalities and networking effects among actors, evoked the area of spatial econometrics. Spatial econometrics focuses on the specification and estimation of regression models explicitly incorporating such spatial effects. The multidimensionality of spatial effects calls for misspecification tests and estimators that are notably different from techniques designed for the analysis of time series. With that in mind, we introduce the notion of spatial effects, referring to both heterogeneity and interdependence of phenomena occurring in two-dimensional space. Spatial autocorrelation or dependence can be detected by means of cross-correlation statistics in univariate as well as multivariate data settings. We review tools for exploratory spatial data analysis and misspecification tests for spatial effects in linear regress! ion models. A discussion of specification strategies and an overview of available software for spatial regression analysis, including their main functionalities, intend to give practitioners of spatial data analysis a head start.