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age_crime_curve_europe.qmd
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age_crime_curve_europe.qmd
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---
title: "The age-crime curve and the crime drop in (some of) Northern Europe"
title-slide-attributes:
data-background-image: "resources/background.png"
bibliography: comparative_acc.bib
author: "Dr. Ben Matthews | University of Stirling"
date: "2023-06-28"
logo: "resources/primary-logo.png"
format: revealjs
editor: visual
---
## Before we begin
- This is *extremely* work-in-progress!
- Any and all comments much appreciated
## Background
- We can analyse change in the demographics of crime to refine theories of the crime drop, some explanations for the crime drop fit better with period effects (implying a reasonably uniform change across age?) [@kim2016]
- Change in the age-crime curve (e.g. the debate over the 'invariance' of the shape of the age-crime curve) is also interesting for developmental criminologists [@hirschi1983; @farrington1986]
## Background
- Some evidence that the 'youth crime drop' differs in magnitude between countries [@matthews2018; @sivertsson2021; @farrell2015]
- But in general there are questions about how exactly 'international' the international crime drop is [@kotzé2019]
- But no (as far as I'm aware) systematic international comparison about how the demographics of crime have changed over the course of the crime drop
## Research Design
- Aim: compare changing age-crime curves across Northern Europe
- Why Northern Europe? Basically data availability
- In the future - possibly extend this analysis to include other countries where data are available
- Expanding the international scope could help contextualize other findings from studies using register data?
## Research Design
- Problem: little data available at year-of-age level, no guarantee that the same age-groups are used in different countries
- Solution: use `Penalized Composite Link Model` to construct smooth age-year-conviction surfaces from publicly available data
## Data
- Total conviction numbers by age for Scotland, Norway, Finland and Denmark
- Also available by sex (but not analysed separately here due to time constraints)
- Time periods covered:
- Scotland: 1990-2018
- Norway: 2002-2021
- Finland: 1990-2021
- Denmark: 1980-2021
- No data (that I could find) for Sweden or the Netherlands!
## Data
- Age bands used:
- Scotland: single year of age (!) from age 12
- Norway: 15-17; 18-20; 21-24; 25-29; 30-39; 40-49; 50-59; \>=60
- Finland: 15-17; 18-20; 21-24; 25-29; 30-39; 40-49; 50-59; 60-69; 70-79; \>=80
- Denmark: 15-24 single year of age; 25-29; 30-39; 40-49; 50-59; 60-69; 70-79; \>=80
## Data sources
- Scotland: [Data behind an interactive web app](https://github.com/jamiedo/sg-age-crime)
- Finland: [Statistics Finland](https://statfin.stat.fi/PXWeb/pxweb/en/StatFin_Passiivi/StatFin_Passiivi__syyttr/)
- Denmark: [Statistics Denmark](https://www.statbank.dk/statbank5a/selectvarval/define.asp?PLanguage=1&subword=tabsel&MainTable=STRAF40&PXSId=167619&tablestyle=&ST=SD&buttons=0)
- Norway: [Statistics Norway](https://www.ssb.no/en/statbank/table/10623)
- The same sources provided population data as well as conviction data
## Measures
- Prevalence (people convicted) or incidence (total convictions)?
- Scotland is incidence ("Convictions")
- Norway is [incidence](https://www.ssb.no/en/statbank/table/10623) ("sanctions")
- Finland I think is [prevalence](https://pxdata.stat.fi/PxWeb/pxweb/en/StatFin/StatFin__syyttr/statfin_syyttr_pxt_12d2.px/table/tableViewLayout1/) ("Convicted, number")
- Denmark is [incidence](https://www.statbank.dk/20338) ("Convictions") - although there is a separate statistical return for prevalence!
## Measures
- All crime types?
- Yes. At least this is... less controversially comparable (at least after standardizing within country?)
- All sanctions?
- In Norway I removed on the spot fines because that's [what SSB (sometimes?) do](https://www.ssb.no/en/sosiale-forhold-og-kriminalitet/kriminalitet-og-rettsvesen/statistikk/straffereaksjoner) (and the age-crime curve looked very odd if I didn't) otherwise yes
## Methods
- Used `R` implementation of Penalized Composite Link Model (PCLM) using the package [`ungroup`](https://cran.r-project.org/web/packages/ungroup/index.html) [@pascariu2018]
- Because PCLM models convictions data and population data together to estimate a smooth surface of conviction rates, so you probably shouldn't look for disruptions in the time series (policy shocks or what have you)
- But you *can* look at overall trends
## Methods
- Measure conviction rates as:
- Crude rates
- Country standardized rates (divide the conviction rate for each age-year by the maximum single-age conviction rate for that country)
- Country-year standardized rates (divide the conviction rate for each age-year by the maximum single-age conviction rate for that country in that year)
## Research questions
- How (qualitatively) similar is the change in the age-crime curve between countries?
- How much (qualitatively) does the age-crime curve change within countries over time?
## Analytical plan
- Look at the results visually as a series of line charts and on the Lexis surface [@minton2020]
- Calculate relevant summary statistics (mode, median, mean age of conviction)
- In the future - possibly bespoke models and visualizations for comparing Lexis surfaces [@acosta2019]?
- Although visual analysis tends to give the same results as formal modelling [@jones2023]
## Results
## Comparing countries 1
## Comparing countries 2
## Comparing countries 3
## Comparing countries 4
## Summary statistics
## Discussion
- The crime drop is (mostly?) a youth crime drop across the four countries
- And the timings of biggest falls in youth convictions (cohorts born around 1990ish) are pretty consistent across the four countries (roughly after 2005ish?)
## Discussion
- But we don't see the same fall in convictions for older people across countries - only really see the slight increases in convictions 30s-40s in Scotland
- Increases in convictions for people around age 50 seen in Norway and Denmark are similar to results from US arrest data as reported by @farrell2015
- So perhaps this does fit better with a youth-focused explanation for the crime drop e.g. [@ball2023]
## Discussion
- I'd say that three of the four countries showed pretty 'classic' annual age-crime curves throughout the period analysed, but one didn't
- This is implies that there are pretty stark between country differences in how the age-crime curve has changed over time?
## Where next?
- I think there are two directions this research could go in:
- This initial analysis raises lots of questions about... crime types, other demographics (gender, ethnicity, income... etc) that could be answered by more bespoke data
- Having done this analysis for (some of) Northern Europe, I think maybe an even more maximalist approach would be preferable - extending this comparison to anywhere that publishes data on age and conviction? (Though through some non-systematic Googling, there was data available for Switzerland, New Zealand and South Korea...)
## Thank you! {.smaller background-image="resources/background.png"}
::: {#refs}
:::
## Bonus content {background-image="resources/background.png"}
## Methods
![[@rizzi2015], Figure 1: Statistical model for grouped data](resources/rizzi-2015-figure_one.png){width="80%" fig-alt="Figure 1. Statistical model for grouped data. The distribution of interest _γ_ is defined on a fine scale. Grouping composes several values of _γ_ to the values of _μ_, which are the expected counts for the grouped distribution. The observed data _y_ are realizations of Poisson random variables with expected values _μ_. The latent distribution _γ_ is to be estimated from the grouped counts _y_, which can be achieved by assuming that _γ_ is smooth."}
## Modelling Assumptions
- Model makes some assumptions:
- "neighboring elements in *γ* do not differ drastically"
- "The smoothness assumption is implemented in a roughness penalty on the coefficients *β*"
- There is a penalty term *λ* and what the model does is pick the 'best' value of *λ* as determined by AIC
- This means that - in the frequentist setting - the final results are 'optimal' but you might be concerned about propagating uncertainty in *λ* through your analysis
## Whence uncertainty estimates?
- Because there's a model in there there's also uncertainty about the by-age-year predicted counts
- You can get standard errors for your estimates/confidence intervals for the estimated conviction count/rate for each age in each year, but these seemed not to make much difference to the results from a quick look so I haven't bothered here
- This is because the age categories were coarse at older ages where there were also fewer convictions
## What if I want to quantify how different age-crime surfaces are?
- I did look into ways of quantifying how different each country's age-crime surface was (things like 2D generalizations of [Kolmogorov-Smirnov tests](https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test) and that sort of thing), to quantify how 'similar' the age-crime surfaces are
- Can frame this as either 'how similar' (continuous) or 'are they statistically significantly different from each other' (discrete)
- Problem is that the time series are different lengths (for methods like [Kullback-Leibler divergence](https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence) at least this is a problem)?
- Methods do exist but seem opaque to me - so I haven't bothered (yet)
## The lexis surface
## Cohort results
## Comparing countries 5
## Comparing countries 6
## Comparing countries 7
