Discontinuities due to survey redesigns : a structural time series approach
7
6
5
4
smoothed trend violence data violence smoothed trend property data property
12.5
10.0
3 1995 2000 2005 2010 1995 2000 2005 2010
smoothed trend vandalism data vandalism smoothed trend no stop data no stop
10 1
1.25
1.00
0.75
1995 2000 2005 2010 1995 2000 2005 2010
smoothed trend other data other smoothed trend total data total
25
0.50
0.25 1995 2000 2005 2010
20
1995 2000 2005 2010
(a) M2 None Smoothed trend
6
5
smoothed signal violence data violence smoothed signal property data property
12.5
10.0
4 1995 2000 2005 2010 1995 2000 2005 2010
12.5 smoothed signal vandalism data vandalism smoothed signal no stop data no stop
1.75
1.50
10.0 1.25
1.00
1995 2000 2005 2010 1995 2000 2005 2010
1.00 smoothed signal other data other smoothed signal total data total
30.0
27.5
0.75
0.50
1995 2000 2005 2010
25.0
22.5
20.0 1995 2000 2005 2010
(b) M2 None Smoothed signal
Figure 7: M2 None
60
6 smoothed trend violence data violence smoothed trend property data property
15
4 10
12.5
10.0
7.5
5.0
1.0
1995 2000 2005 2010 1995 2000 2005 2010
2.0
smoothed trend vandalism data vandalism smoothed trend no stop data no stop
1.5
1.0
0.5
1995 2000 2005 2010 1995 2000 2005 2010
smoothed trend other data other smoothed trend total data total
30
0.5
20
1995 2000 2005 2010 1995 2000 2005 2010
(a) M2 None Smoothed trend without Intervention 3
6 smoothed signal violence data violence smoothed signal property data property
5
12.5
4 1995 2000 2005 2010
10.0
1995 2000 2005 2010
12.5 smoothed signal vandalism data vandalism smoothed signal no stop data no stop
1.75
1.50
10.0
1.0
1.25
1995 2000 2005 2010 1.00 1995 2000 2005 2010
smoothed signal other data other smoothed signal total data total
30
25
0.5
1995 2000 2005 2010 1995 2000 2005 2010
(b) M2 None Smoothed signal without Intervention 3
Figure 8: M2 None without Intervention 3
61
6
5
15
smoothed trend violence data violence smoothed trend property data property
12.5
10.0
1995 2000 2005 2010
2.0
1995 2000 2005 2010
smoothed trend vandalism data vandalism smoothed trend no stop data no stop
1.5
10
1.0
1.0
1995 2000 2005 2010 0.5 1995 2000 2005 2010
smoothed trend other data other smoothed trend total data total
30.0
27.5
0.5 1995 2000 2005 2010
25.0
22.5
20.0 1995 2000 2005 2010
(a) M3 ⋆ None Smoothed trend
6
5
4
12.5
10.0
smoothed signal violence data violence smoothed signal property data property
14
13
12
11
1995 2000 2005 2010
2.0
1995 2000 2005 2010
smoothed theta vandalism data vandalism smoothed theta no stop data no stop
1.5
1.0
1995 2000 2005 2010 0.5 1995 2000 2005 2010
1.0 smoothed theta other data other smoothed theta total data total
27.5
25.0
0.5
1995 2000 2005 2010 1995 2000 2005 2010
(b) M3 ⋆ None Smoothed signal
Figure 9: M3 ⋆ None
62
6
5
4
15.0
12.5
10.0
7.5
5.0
1.0
smoothed trend violence data violence smoothed trend property data property
15
10
1995 2000 2005 2010
2.0
1995 2000 2005 2010
smoothed trend vandalism data vandalism smoothed trend no stop data no stop
1.5
1.0
1995 2000 2005 2010 0.5 1995 2000 2005 2010
smoothed trend other data other smoothed trend total data total
30
25
0.5 1995 2000 2005 2010 1995 2000 2005 2010
80
smoothed trend POLICE total data POLICE total
60 1995 2000 2005 2010
(a) M4 ⋆ None Smoothed trend
6
5
4
15.0
12.5
10.0
7.5
1.00
0.75
0.50
smoothed signal violence data violence smoothed signal property data property
14
1995 2000 2005 2010
13
12
11 1995 2000 2005 2010
smoothed signal vandalism data vandalism smoothed signal no stop data no stop
1.75
1995 2000 2005 2010
1.50
1.25
1.00 1995 2000 2005 2010
smoothed signal other data other smoothed signal total data total
1995 2000 2005 2010
30.0
27.5
25.0
22.5 1995 2000 2005 2010
80
smoothed signal POLICE total data POLICE total
1995 2000 2005 2010
(b) M4 ⋆ None Smoothed signal
Figure 10: M4 ⋆ None
63
6 smoothed trend violence real data violence smoothed trend property data property
5
12.5
4 1995 2000 2005 2010
10.0
1995 2000 2005 2010
12.5
10.0
smoothed trend vandalism data vandalism
1.75 smoothed trend no stop data no stop
1.50
1.25
30.0
27.5
25.0
22.5
20.0
1995 2000 2005 2010
smoothed trend total data total
1995 2000 2005 2010
1.00 1995 2000 2005 2010
(a) M5 ⋆ Smoothed trend National
7.5 smoothed trend violence man data violence 15.0 smoothed trend property man data property
12.5
5.0
1995 2000 2005 2010 10.0 1995 2000 2005 2010
15 smoothed trend vandalism man data vandalism 2.0 smoothed trend no stop man data no stop
1.5
10
1995 2000 2005 2010
1.0
0.5 1995 2000 2005 2010
30 smoothed trend total man data total
25
1995 2000 2005 2010
(b) M5 ⋆ Smoothed trend Men
6 smoothed trend violence woman data violence smoothed trend property woman data property
4
10
2 1995 2000 2005 2010 1995 2000 2005 2010
12.5 smoothed trend vandalism woman data vandalism smoothed trend no stop woman data no stop
2
10.0
7.5
5.0 1995 2000 2005 2010
1
1995 2000 2005 2010
25 smoothed trend total woman data total
20
1995 2000 2005 2010
(c) M5 ⋆ Smoothed trend Women
Figure 11: Smoothed trends M5 ⋆
64
6 smoothed signal violence data violence smoothed signal property data property
14
5
4 1995 2000 2005 2010
12
1995 2000 2005 2010
12.5
10.0
smoothed signal vandalism data vandalism
1.75 smoothed signal no stop data no stop
1.50
1.25
1995 2000 2005 2010 1.00 1995 2000 2005 2010
27.5
smoothed signal total data total
25.0
1995 2000 2005 2010
(a) M5 ⋆ Smoothed signal National
7
smoothed signal violence data violence smoothed signal property data property
14
5 1995 2000 2005 2010
12
1995 2000 2005 2010
15.0 smoothed signal vandalism data vandalism smoothed signal no stop data no stop
2.0
12.5
1.5
1.0
1995 2000 2005 2010 0.5 1995 2000 2005 2010
30.0
smoothed signal total data total
27.5
1995 2000 2005 2010
(b) M5 ⋆ Smoothed signal Men
5
4
smoothed signal violence data violence smoothed signal property data property
12.5
15
1995 2000 2005 2010 1995 2000 2005 2010
smoothed signal vandalism data vandalism smoothed signal no stop data no stop
2
10
27.5
25.0
1995 2000 2005 2010
smoothed signal total data total
1
1995 2000 2005 2010
22.5
20.0 1995 2000 2005 2010
(c) M5 ⋆ Smoothed signal Women
Figure 12: Smoothed signals M5 ⋆
65
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