an ecological analysis of crime and antisocial behaviour in english output areas, 2011/12 regression...
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An ecological analysis of crime and antisocial behaviour in English Output Areas, 2011/12
Regression modelling of spatially hierarchical count data
Overview
1. Background
2. Data
3. Count data models
4. Extension to multilevel models
5. Extension to spatial models
6. Results and conclusions
Purpose of research
Ecological factors affecting crime incidence:
Demographic
Physical Environment
Social Economic
Purpose of research
• Unit of analysis: Output areas• Modern techniques:
- Count data models
- Hierarchical data models
- Spatial models
• Contextualise raw statistics often quoted• Coverage: full population• Interrogate ‘newly’ available data• Illustrate the use of open data
Context
• Increasing divergence between police recorded crime and the Crime Survey of England and Wales
→Crime statistics de-designation – January 2014
→House of Commons PASC report – April 2014
→HMIC report – November 2014
• August 2011 riots
Crime Data
Source: data.police.uk
Period: 2011/12
Given
And
the coefficient of variation is given by
An appropriate sample size is therefore determined based on Cochran’s formula
Covariate data
• 2011 Census variablese.g. young adult population, sex ratios, race, divorce
rates, household structure, qualifications, method of travel to work, employment, population density
• ONS Neighbourhood Statistics variablese.g. benefit claimants, small area income estimates
• DCLG variablesindices of deprivation and land use
• Summary classificationsOutput Area Classifications and Rural Urban
Classifications
Count data models – Poisson regressionPoisson probability density function (PDF):
Model form:
Rate parameterisation:
Variance = mean = μ
Goodness of fit tests:
Violation of equidispersion
• Causes of apparent overdispersion:- Omitted explanatory variables- Outliers- Omitted interaction terms- Omitted variable transformations- Mis-specified link function
• Tests of equidispersion:- Pearson/Deviance dispersion statistics ≠ 1- Boundary likelihood ratio test:
- Score test: H0:α=0; H1:α≠0
Count data models – Negative binomial model (NB2)
• Origin from binomial PDF• Wide range of formulations
e.g. NB-C, NB1, NB2, NB-P, geometric negative binomial etc
• Traditional formulation is the NB2 model• Derivation of NB2 model as a GLM:
- Poisson PDF with heterogeneity “gamma”- Derive the NB-C model- Convert to log-linked form
Variance: μ + μ2/v μ + αμ2
Hierarchical count data models
property crime rates per 1000 fixed assets by police force area
total crime rate per usual resident by police force for Output Area populations in the sample
Multilevel NB2 model
The level 1 variance is
Controlling for unobserved spatial dependencies
Moran’s I is the linear association between a value and the weighted average of its neighbours
Final model
Pearson dispersion statistic < 1.148
Results
Variance:
Between police force variability is significant:
Results
Parameter Estimate
Standard Error
Exponentiated Parameter Estimate
Fixed Part (truncated) fixed intercept -3.393 0.328 0.034perc_age16_29_meancentred 0.04 0.005 1.041sex_ratio_perc_meancentred -0.004 0.001 0.996divorced_percent_meancentred 0.017 0.006 1.017perc_leaders_meancentred 0.027 0.005 1.027spatial lag 0.006 0.001
Random Part random intercept 0.014 0.007
ancillary parameter 0.685 0.024
Conclusions and policy implications
• There are significant differences in crime rates across police force areas
• Urbanisation has the strongest influence on the relative risk of crime in output areas
• The relative affluence rather than absolute affluence of an area has an impact on crime
• Racial composition and immigrant populations have no significant impact on crimes in England
Questions?
Contact details
Chuka Ilochi
Abbey 2, Floor 5
BIS
1 Victoria Street
London SW1H 0ET
Email: [email protected]
Tel: 0207 215 3691