1. Effectiveness of sentencing July 2011

2. 1. criminal justice system 2. current thinking 3. statistical methods 4. results + implications

3. 1. criminal justice system 2. current situation 3. statistical methods 4. results + implications

4. 1. criminal justice system 2. current situation 3. statistical methods 4. results + implications

5. 1. criminal justice system 2. current situation 3. statistical methods 4. results + implications

6. 1. criminal justice system

7. idiot’s guide

8. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police prison probation cautions reprimands warnings community orders suspended sentence orders requirements supervision no supervision

9. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police prison probation cautions reprimands warnings community orders suspended sentence orders requirements supervision no supervision

10. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police prison probation cautions reprimands warnings community orders suspended sentence orders requirements supervision no supervision

11. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police prison probation cautions reprimands warnings community orders suspended sentence orders requirements supervision no supervision

12. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police prison probation cautions reprimands warnings community orders suspended sentence orders requirements supervision no supervision

13. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police prison probation cautions reprimands warnings community orders suspended sentence orders requirements supervision no supervision

14. fines other out of court court non-custodial court orders police cautions reprimands warnings community orders suspended sentence orders

15. fines other out of court court non-custodial court orders police cautions reprimands warnings requirements

16. fines other out of court court non-custodial court orders police probation cautions reprimands warnings

17. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police prison probation cautions reprimands warnings supervision no supervision

18. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police prison probation cautions reprimands warnings supervision no supervision

19. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police prison probation cautions reprimands warnings

20. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police probation cautions reprimands warnings supervision no supervision

21. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police probation cautions reprimands warnings supervision no supervision

22. seriousness fines other short less 12M long 12M or more out of court court non-custodial court custodial court orders police probation cautions reprimands warnings supervision no supervision

23. 2. current situation

24. 2008

25. 2. current situation 2008 before this work

26. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

27. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

28. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

29. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

30. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

31. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

32. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

33. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

34. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

35. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

36. however

37. 1837 28 30 prev 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate rv matched comparison 1 comparison 2 comparison 3

38. 1837 28 30 prev 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate rv matched comparison 1 comparison 2 comparison 3

39. 1837 28 30 prev 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate rv matched comparison 1 comparison 2 comparison 3

40. 1837 28 30 prev 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate rv matched comparison 1 comparison 2 comparison 3 comparisons not valid

41. 1837 28 30 prev 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate rv matched comparison 1 comparison 2 comparison 3 similar offenders

42. 1837 28 30 prev 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate rv matched comparison 1 comparison 2 comparison 3 similar offenders

43. 1837 28 30 prev 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate rv matched comparison 1 comparison 2 comparison 3 similar offenders

44. 3. statistical methods

45. ideally randomised control trial

46. 3. statistical methods ideally randomised control trial well constructed matched groups

47. two methods

48. exact matching

49. two methods exact matching propensity score model

50. propensity score matching

51. logistic regression

52. propensity score matching logistic regression predicted values → propensity scores

53. propensity score matching logistic regression predicted values → propensity scores matching

54. easy

55. example in R

56. comparison 1 court orders vs prison <12M

57. step 1. logistic regression

58. 0 response variable 1

59. 0 court order response variable 1 short less 12M

60. 0 court order response variable 1 short less 12M explanatory variables =

61. 0 court order response variable age + gender + offence type + ethnicity + age of first offence + copas rate 1 short less 12M explanatory variables =

62. 0 court order response variable age + gender + offence type + ethnicity + age of first offence + copas rate 1 short less 12M explanatory variables = log.reg <- glm(sentence ~ age + factor(gender) + factor(offence) + factor(ethnic) + age_first_off + copas, family = binomial, data = dataset_name)

63. 0 court order response variable age + gender + offence type + ethnicity + age of first offence + copas rate 1 short less 12M explanatory variables = log.reg <- glm(sentence ~ age + factor(gender) + factor(offence) + factor(ethnic) + age_first_off + copas, family = binomial, data = dataset_name)

64. 0 court order response variable age + gender + offence type + ethnicity + age of first offence + copas rate 1 short less 12M explanatory variables = log.reg <- glm(sentence ~ age + factor(gender) + factor(offence) + factor(ethnic) + age_first_off + copas, family = binomial, data = dataset_name)

65. 0 court order response variable age + gender + offence type + ethnicity + age of first offence + copas rate 1 short less 12M explanatory variables = log.reg <- glm(sentence ~ age + factor(gender) + factor(offence) + factor(ethnic) + age_first_off + copas, family = binomial, data = dataset_name)

66. 0 court order response variable age + gender + offence type + ethnicity + age of first offence + copas rate 1 short less 12M explanatory variables = log.reg <- glm(sentence ~ age + factor(gender) + factor(offence) + factor(ethnic) + age_first_off + copas, family = binomial, data = dataset_name)

67. step 2. match propensities

68. Match(reoffending, sentence, log.reg$fitted, M=1, ties = FALSE, caliper = 0.05, replace = TRUE)

69. step 2. match propensities Match(reoffending, sentence, log.reg$fitted, M=1, ties = FALSE, caliper = 0.05, replace = TRUE)

70. step 2. match propensities Match(reoffending, sentence, log.reg$fitted, M=1, ties = FALSE, caliper = 0.05, replace = TRUE)

71. step 2. match propensities Match(reoffending, sentence, log.reg$fitted, M=1, ties = FALSE, caliper = 0.05, replace = TRUE)

72. step 2. match propensities Match(reoffending, sentence, log.reg$fitted, M=1, ties = FALSE, caliper = 0.05, replace = FALSE)

73. that is it

74. what does this mean visually?

75. court orders short less 12M age = 44 assault police prev = 1 p custody = 3.5% age = 26 drugs C prev = 2 p custody = 3.5%

76. court orders short less 12M age = 29 shoplifting prev = 85 p custody = 70% age = 26 breach ASBO prev = 83 p custody = 70%

77. 4. results + implications

78. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

79. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

80. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

81. implications

82. logistic model → well specified

83. implications logistic model → well specified dealing with missing information

84. missing information

85. random variable correlated with re-offending

86. missing information random variable correlated with re-offending new.var <- 0.7*reoffending + rnorm(mean =0, sd=1)

87. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

88. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

89. 143,000 court orders short less 12M short less 12M long 1-2y long 1-2y long 2-4y 41,000 11,000 10,000 36.2%59.4% 39.9% 35.4% 40,5349,2857,030 52.0%58.9%50.0%39.4%39.1%34.4% 40,5139,2767,026 53.6%58.8%47.1%39.7%38.2%34.8% E&W rate matched rate rv matched comparison 1 comparison 2 comparison 3

90. conclusions

91. PSM → easy to implement

92. conclusions PSM → easy to implement PSM → hard to validate

93. conclusions PSM → easy to implement PSM → hard to validate robust information on effect of prison

94. 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

95. questions