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Effectiveness of sentencing July 2011 1. criminal justice system 2. current thinking 3. statistical methods 4. results + implications 1. criminal justice system 2. current situation 3. statistical methods 4. results + implications 1. criminal justice system 2. current situation 3. statistical methods 4. results + implications 1. criminal justice system 2. current situation 3. statistical methods 4. results + implications 1. criminal justice system 1. criminal justice system idiot’s guide court non-custodial out of court cautions reprimands warnings police fines other court orders court custodial short long less 12M 12M or more no community orders supervision probation requirements prison suspended sentence orders supervision seriousness court non-custodial out of court cautions reprimands warnings police fines other court orders court custodial short long less 12M 12M or more no community orders supervision probation requirements prison suspended sentence orders supervision seriousness court non-custodial out of court cautions reprimands warnings police fines other court orders court custodial short long less 12M 12M or more no community orders supervision probation requirements prison suspended sentence orders supervision seriousness court non-custodial out of court cautions reprimands warnings police fines other court orders court custodial short long less 12M 12M or more no community orders supervision probation requirements prison suspended sentence orders supervision seriousness court non-custodial out of court cautions reprimands warnings police fines other court orders court custodial short long less 12M 12M or more no community orders supervision probation requirements prison suspended sentence orders supervision seriousness court non-custodial out of court cautions reprimands warnings police fines other court orders court custodial short long less 12M 12M or more no community orders supervision probation requirements prison suspended sentence orders supervision seriousness court non-custodial out of court cautions reprimands warnings police fines other court orders community orders suspended sentence orders court non-custodial out of court cautions reprimands warnings police fines other court orders requirements court non-custodial out of court cautions reprimands warnings police fines other court orders probation court non-custodial out of court cautions reprimands warnings police fines other court orders probation seriousness court custodial short long less 12M 12M or more no supervision prison supervision court non-custodial out of court cautions reprimands warnings police fines other court orders probation seriousness court custodial short long less 12M 12M or more no supervision prison supervision court non-custodial out of court cautions reprimands warnings police fines other court orders probation seriousness court custodial short long less 12M 12M or more prison court non-custodial out of court cautions reprimands warnings police fines other court orders probation seriousness court custodial short long less 12M 12M or more no supervision supervision court non-custodial out of court cautions reprimands warnings police fines other court orders probation seriousness court custodial short long less 12M 12M or more no supervision supervision court non-custodial out of court cautions reprimands warnings police fines other court orders probation seriousness court custodial short long less 12M 12M or more no supervision supervision 2. current situation 2. current situation 2008 2. current situation 2008 before this work comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% however comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 39.9% 35.4% prev 18 37 37 28 rate 52.0% 58.9% 50.0% 39.4% rv matched rate 40,513 53.6% 58.8% 9,276 47.1% 39.7% 28 30 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 39.9% 35.4% prev 18 37 37 28 rate 52.0% 58.9% 50.0% 39.4% rv matched rate 40,513 53.6% 58.8% 9,276 47.1% 39.7% 28 30 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 39.9% 35.4% prev 18 37 37 28 rate 52.0% 58.9% 50.0% 39.4% rv matched rate 40,513 53.6% 58.8% 9,276 47.1% 39.7% 28 30 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 39.9% 35.4% prev 18 37 37 28 rate 52.0% 58.9% 50.0% 39.4% rv matched rate 28 39.1% 34.4% comparisons not valid 40,513 9,276 53.6% 58.8% 47.1% 39.7% 30 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 39.9% 35.4% prev 18 37 37 28 rate 52.0% 58.9% 50.0% 39.4% rv matched rate similar offenders 40,513 9,276 53.6% 58.8% 47.1% 39.7% 28 30 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 39.9% 35.4% prev 18 37 37 28 rate 52.0% 58.9% 50.0% 39.4% rv matched rate similar offenders 40,513 9,276 53.6% 58.8% 47.1% 39.7% 28 30 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 39.9% 35.4% prev 18 37 37 28 rate 52.0% 58.9% 50.0% 39.4% rv matched rate similar offenders 40,513 9,276 53.6% 58.8% 47.1% 39.7% 28 30 39.1% 34.4% 7,026 38.2% 34.8% 3. statistical methods 3. statistical methods ideally randomised control trial 3. statistical methods ideally randomised control trial well constructed matched groups two methods two methods exact matching two methods exact matching propensity score model propensity score matching propensity score matching logistic regression propensity score matching logistic regression predicted values → propensity scores propensity score matching logistic regression predicted values → propensity scores matching easy example in R comparison 1 court orders vs prison <12M step 1. logistic regression response variable 0 1 response variable 0 court order 1 short less 12M response variable 0 court order 1 short less 12M explanatory variables = response variable 0 court order 1 short less 12M explanatory variables = age + gender + offence type + ethnicity + age of first offence + copas rate response variable 0 court order 1 short less 12M explanatory variables = age + gender + offence type + ethnicity + age of first offence + copas rate log.reg <- glm(sentence ~ age + factor(gender) + factor(offence) + factor(ethnic) + age_first_off + copas, family = binomial, data = dataset_name) response variable 0 court order 1 short less 12M explanatory variables = age + gender + offence type + ethnicity + age of first offence + copas rate log.reg <- glm(sentence ~ age + factor(gender) + factor(offence) + factor(ethnic) + age_first_off + copas, family = binomial, data = dataset_name) response variable 0 court order 1 short less 12M explanatory variables = age + gender + offence type + ethnicity + age of first offence + copas rate log.reg <- glm(sentence ~ age + factor(gender) + factor(offence) + factor(ethnic) + age_first_off + copas, family = binomial, data = dataset_name) response variable 0 court order 1 short less 12M explanatory variables = age + gender + offence type + ethnicity + age of first offence + copas rate log.reg <- glm(sentence ~ age + factor(gender) + factor(offence) + factor(ethnic) + age_first_off + copas, family = binomial, data = dataset_name) response variable 0 court order 1 short less 12M explanatory variables = age + gender + offence type + ethnicity + age of first offence + copas rate log.reg <- glm(sentence ~ age + factor(gender) + factor(offence) + factor(ethnic) + age_first_off + copas, family = binomial, data = dataset_name) step 2. match propensities step 2. match propensities Match(reoffending, sentence, log.reg$fitted, M=1, ties = FALSE, caliper = 0.05, replace = TRUE) step 2. match propensities Match(reoffending, sentence, log.reg$fitted, M=1, ties = FALSE, caliper = 0.05, replace = TRUE) step 2. match propensities Match(reoffending, sentence, log.reg$fitted, M=1, ties = FALSE, caliper = 0.05, replace = TRUE) step 2. match propensities Match(reoffending, sentence, log.reg$fitted, M=1, ties = FALSE, caliper = 0.05, replace = TRUE) step 2. match propensities Match(reoffending, sentence, log.reg$fitted, M=1, ties = FALSE, caliper = 0.05, replace = FALSE) that is it what does this mean visually? court orders short less 12M age = 44 age = 26 assault police drugs C prev = 1 prev = 2 p custody = 3.5% p custody = 3.5% court orders short less 12M age = 29 age = 26 shoplifting breach ASBO prev = 85 prev = 83 p custody = 70% p custody = 70% 4. results + implications comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% implications implications logistic model → well specified implications logistic model → well specified dealing with missing information missing information missing information random variable correlated with re-offending missing information random variable correlated with re-offending new.var <- 0.7*reoffending + rnorm(mean=0, sd=1) comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% comparison 1 comparison 2 comparison 3 court orders short short long long long less 12M less 12M 1-2y 1-2y 2-4y E&W 143,000 41,000 41,000 11,000 11,000 10,000 rate 36.2% 59.4% 59.4% 39.9% 35.4% 40,534 matched rate 52.0% rv matched rate 58.9% 40,513 53.6% 58.8% 39.9% 9,285 50.0% 39.4% 9,276 47.1% 39.7% 7,030 39.1% 34.4% 7,026 38.2% 34.8% conclusions conclusions PSM → easy to implement conclusions PSM → easy to implement PSM → hard to validate conclusions PSM → easy to implement PSM → hard to validate robust information on effect of prison attributions American Dad, 20th Century Fox Television Archer, FX network The Boondocks, Cartoon Network Studios Firsky Dingo, Cartoon Network Studios Futurama, Fox Broadcasting Company Harvey Birdman, Attorney at Law, Cartoon Network Studios Johnny Bravo, Cartoon Network Studios Sealab 2021, Cartoon Network Studios questions
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