Discontinuities due to survey redesigns : a structural time series approach

APPENDIX

Table 12 – Victimization series, 1992-2010. Provided by Statistics Netherlands
Year Violence Property Vandalism No stop* Other Total Survey Sample
size
1992 5.4 13.5 8.7 1.5 0.5 24.4 LPSS 3949
1993 5.1 13.5 10.3 1.2 0.8 25.0 LPSS 4934
1994 5.2 13.8 9.9 1.6 0.6 26.0 LPSS 5503
1995 5.4 13.9 9.7 1.4 0.7 25.0 LPSS 5936
1996 4.2 12.5 8.8 1.3 0.6 23.1 LPSS 5773
1997 5.0 13.2 10.4 1.3 0.5 25.5 PSLC 8838
1998 5.6 13.0 11.1 1.2 0.7 26.2 PSLC 9007
1999 5.5 12.5 11.6 1.5 0.6 26.2 PSLC 10952
2000 5.0 12.3 11.0 1.5 0.6 25.7 PSLC 8756
2001 5.8 12.0 10.5 1.3 0.7 24.9 PSLC 10326
2002 6.0 12.8 12.1 1.5 0.7 27.2 PSLC 8399
2003 5.7 11.9 11.1 1.4 0.8 25.6 PSLC 10862
2004 5.2 11.9 11.4 1.3 0.8 25.4 PSLC 9989
2005 5.8 14.4 13.0 1.7 0.9 28.8 SM 5242
2006 5.1 13.7 12.0 1.6 1.0 27.2 SM 20685
2007 5.3 12.3 11.7 1.5 0.8 25.8 SM 19128
2008 5.4 13.2 13.6 - 1.0 26.1 ISM 62803
2009 5.7 13.3 14.2 - 1.0 26.9 ISM 198122
2010 5.5 12.5 12.7 - 0.9 25.4 ISM 39220
Bold Year - year of redesign of the underlying survey process.
* - ”Failure to stop after an accident”

50

A

Diagnostic test results

51

Model
M1

M1

M1

M1⋆

M1⋆

M1⋆

Table 13 – Diagnostic test results for M1 and M2
Transformation/ Breakdowns
Test name Violence Property Vandalism No stop* Other ^Total

None
Skewness -0.23 0.48 -0.69 0.76 -0.07 -0.12
Excess Kurtosis -1.06 0.10 0.81 -0.66 -0.30 -0.67
Heterosk. test 1.16 2.73 5.12 0.31 0.71 4.46
DW stat. 2.11 2.33 1.91 2.49 2.24 2.28
Log
Skewness -0.31 0.58 -0.41 0.76 0.25 -0.16
Excess Kurtosis -0.95 0.16 -0.07 -0.65 -0.25 -0.68
Heterosk. test 0.91 2.93 3.13 0.30 0.82 3.88
DW stat. 2.06 2.33 1.93 2.43 1.71 2.27
Logit
Skewness -0.31 0.57 -0.45 0.76 0.25 -0.15
Excess Kurtosis -0.95 0.15 0.04 -0.66 -0.25 -0.68
Heterosk. test 0.92 2.91 3.34 0.30 0.83 4.07
DW stat. 2.06 2.33 1.93 2.43 1.71 2.27
None
Skewness -0.37 0.44 0.16 0.76 0.00 0.03
Excess Kurtosis -0.74 0.11 -0.85 -0.64 -0.07 -0.62
Heterosk. test 0.71 2.82 2.80 0.30 0.50 2.77
DW stat. 2.06 2.41 2.08 2.50 2.42 2.37
Log
Skewness -0.44 0.53 0.23 0.76 0.41 -0.02
Excess Kurtosis -0.60 0.11 -1.10 -0.65 -0.20 -0.62
Heterosk. test 0.56 3.21 1.90 0.30 0.56 2.40
DW stat. 2.00 2.43 2.08 2.43 1.95 2.36
Logit
Skewness -0.43 0.51 0.23 0.76 0.41 -0.01
Excess Kurtosis -0.61 0.11 -1.11 -0.66 -0.20 -0.62
Heterosk. test 0.56 2.96 1.99 0.30 0.56 2.53
DW stat. 2.01 2.43 2.08 2.43 1.95 2.37
M2 None
Skewness -0.08 0.53 0.36 0.76 0.16 0.33
Excess Kurtosis -0.91 1.14 -1.12 -0.62 0.28 0.17
Heterosk. test 0.66 1.91 1.30 0.29 0.42 2.07
DW stat. 2.03 2.05 2.09 2.53 2.25 2.20
M2 Log
Skewness -0.16 0.60 0.30 0.77 0.52 0.28
Excess Kurtosis -0.86 1.17 -1.24 -0.62 -0.13 0.13
Heterosk. test 0.55 1.95 1.00 0.29 0.53 1.54
DW stat. 2.06 2.15 2.07 2.45 1.86 2.39
M2 Logit
Skewness -0.17 0.57 0.32 0.77 0.53 0.29
Excess Kurtosis -0.86 1.18 -1.25 -0.60 -0.11 0.14
Heterosk. test 0.56 1.93 1.01 0.28 0.52 1.63
DW stat. 2.10 2.19 2.09 2.46 1.87 2.39

* - ”Failure to stop after an accident”, ⋆ - Sample size of ISM is adjusted to 19.000.
Bold value - the outcome is outside the confidence interval for the respective statistic.

52

Model
M3

M3

M3⋆

M3⋆

Table 14 – Diagnostic test results for M3 and M4
Transformation/ Breakdowns
Test name Violence Property Vandalism No stop* Other ^Total„
None
Skewness -0.20 0.64 -0.61 0.75 0.14 -0.29
Excess Kurtosis -0.97 0.33 1.08 -0.62 -0.08 -0.44
Heterosk. test 0.77 3.13 4.66 0.29 0.50 4.74
DW stat. 2.00 2.56 1.74 2.51 2.44 2.24
Log
Skewness -0.26 0.56 -0.64 0.77 0.23 0.36
Excess Kurtosis -0.98 0.19 0.95 -0.59 -0.33 -0.52
Heterosk. test 0.69 3.09 3.56 0.27 0.64 2.25
DW stat. 2.08 2.69 1.70 2.47 2.05 2.70
None
Skewness -0.21 0.51 0.13 0.76 0.09 0.01
Excess Kurtosis -0.83 0.23 -0.51 -0.64 0.00 -0.70
Heterosk. test 0.66 2.95 2.98 0.30 0.49 2.90
DW stat. 2.05 2.52 2.04 2.50 2.43 2.36
Log
Skewness -0.26 0.58 0.00 0.76 0.30 0.25
Excess Kurtosis -0.79 0.21 0.54 -0.64 -0.31 -0.48
Heterosk. test 0.55 3.09 2.36 0.29 0.55 2.17
DW stat. 2.04 2.57 1.95 2.44 2.08 2.54
M4 None
Skewness -0.20 0.64 -0.62 0.76 0.09 0.24(-0.44)
Excess Kurtosis -0.97 0.33 1.08 -0.63 0.02 -0.59(0.15)
Heterosk. test 0.77 3.13 4.67 0.29 0.46 3.08(0.29)
DW stat. 2.00 2.56 1.74 2.51 2.48 2.33(2.11)
M4 Log
Skewness -0.26 0.50 -0.37 0.77 0.34 0.88 (-0.39)
Excess Kurtosis -1.05 0.11 0.33 -0.53 -0.21 0.09 (0.33)
Heterosk. test 0.74 3.17 3.03 0.25 0.50 4.02 (0.29)
DW stat. 2.19 2.72 1.80 2.51 2.14 2.51(2.22)
M4⋆ None
Skewness -0.21 0.51 0.13 0.76 0.05 0.28(-0.44)
Excess Kurtosis -0.83 0.23 -0.51 -0.64 0.08 -0.42 (0.15)
Heterosk. test 0.66 2.94 2.98 0.30 0.45 2.64(0.29)
DW stat. 2.05 2.52 2.04 2.51 2.47 2.46(2.11)
M4⋆ Log
Skewness -0.28 0.52 0.13 0.77 0.35 0.81 (-0.38)
Excess Kurtosis -0.88 0.19 -0.73 -0.58 -0.21 -0.03 (0.23)
Heterosk. test 0.63 3.10 2.16 0.27 0.49 3.18 (0.29)
DW stat. 2.15 2.64 2.00 2.48 2.13 2.56(2.14)
* - ”Failure to stop after an accident”, „ - Results for police series are in brackets,
⋆ - Sample size of ISM is adjusted to 19.000.

Bold value - the outcome is outside the confidence interval for the respective statistic.

53

Model
Table 15 – Diagnostic test results for M5
Transformation/ Breakdowns
Test name Violence Property Vandalism No stop* ^Total
M5 None
Skewness
-National -0.46 0.52 0.70 0.43 0.18
-Men -0.17 -0.22 0.74 0.36 0.66
-Women -0.69 0.45 0.81 0.22 0.33
Excess Kurtosis
-National -0.78 0.13 -0.37 -1.07 -0.72
-Men -0.38 -0.44 -0.33 -1.42 0.22
-Women 0.19 0.53 0.03 -0.97 0.02
Heterosk. test
National 1.32 4.46 4.19 0.59 4.25
Men 2.97 2.22 2.49 0.76 5.41
Women 0.69 1.87 3.63 0.79 2.62
DW stat.
-National 1.90 2.31 1.74 2.41 2.03
-Men 2.02 1.95 1.33 2.77 1.69
-Women 1.86 2.44 2.17 2.58 2.43
M5⋆ None
Skewness
-National -0.59 0.38 0.72 0.43 0.15
-Men -0.59 -0.25 0.27 0.36 0.05
-Women -0.74 0.26 0.77 0.22 0.33
Excess Kurtosis
-National -0.68 -0.03 -0.20 -1.07 -0.43
-Men -0.50 -0.15 -1.33 -1.42 -0.78
-Women 0.30 0.06 -0.13 -0.97 0.01
Heterosk. test
-National 0.91 4.13 3.36 0.59 3.42
-Men 1.98 2.25 1.28 0.76 3.41
-Women 0.65 1.68 3.42 0.79 2.44
DW stat.
-National 2.11 2.44 2.08 2.41 2.36
-Men 2.23 2.07 1.83 2.77 2.00
-Women 1.84 2.47 2.22 2.58 2.54

* - ”Failure to stop after an accident”, ⋆ - Sample size of ISM is adjusted to 19.000.
Bold value - the outcome is outside the confidence interval for the respective statistic.

54

B

Diagnostic test graphs

55

QQplotinnovationsViolence×normal
2
1
0
-1

0

-2

QQ plot
QQplotinnovationsViolence×normal

-1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
² QQplotinnovationsVandalism×normal

1

-1

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
QQ plot
QQplotinnovationsOther×normal

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

2

0

QQ plot
QQplotinnovationsProperty1×normal

-2
-2 -1 0 1 2

QQ plot
² QQplotinnovationsFailuretostop×normal
1
0
-1

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
² QQplotinnovationsTotal×normal
1
0
-1

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

2
1
0
-1

0

QQ plot
QQplotinnovationsViolence×normal

-1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
QQplotinnovationsVandalism×normal
2

-2
-2 -1 0 1 2

QQ plot
² QQplotinnovationsOther×normal

0

-2
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

2

0

QQ plot
QQplotinnovationsProperty1×normal

-2
-2 -1 0 1 2

QQ plot
² QQplotinnovationsFailuretostop×normal
1
0
-1

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
₂ QQplotinnovationsTotal×normal

0

-1.5 -1 -0.5 0 0.5 1 1.5

(a) M1 None QQ plot (b) M1 ⋆ NoneQQ plot

QQ plot
² QQplotinnovationsViolence×normal
1
0
-1
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
₂ QQplotinnovationsVandalism×normal

0

2

0

-2
2
1
0
-1

QQ plot
QQplotinnovationsProperty1×normal

-1.5 -1 -0.5 0 0.5 1 1.5
QQ plot
QQplotinnovationsFailuretostop×normal

2
1
0
-1

2

0

-2

QQ plot
QQplotinnovationsViolence×normal

-1.0 -0.5 0.0 0.5 1.0 1.5
QQ plot
QQplotinnovationsVandalism×normal

2
0

QQ plot
QQplotinnovationsProperty1×normal

-2
-2 -1 0 1 2

QQ plot
² QQplotinnovationsFailuretostop×normal
1
0
-1

2

-1.5 -1 -0.5 0 0.5 1 1.5
QQ plot
QQplotinnovationsOther×normal

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
₂ QQplotinnovationsTotal×normal ²

-1.5 -1 -0.5 0 0.5 1 1.5
QQ plot
QQplotinnovationsOther×normal

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
₂ QQplotinnovationsTotal×normal

0 ₀ 0 ₀

-2
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
-2
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1 -0.5 0 0.5 1 1.5

(c) M2 None QQ plot (d) M3 None QQ plot

2
1
0
-1

0

QQ plot
QQplotinnovationsViolence×normal

-1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
QQplotinnovationsVandalism×normal
2

-2
-2 -1

QQ plot
² QQplotinnovations
0
×normal
1 2
Other

0

2

0

QQ plot
QQplotinnovationsProperty1×normal

-2
-2 -1 0 1 2

QQ plot
² QQplotinnovationsFailuretostop×normal
1
0
-1

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
₂ QQplotinnovationsTotal×normal

0

QQ plot
² QQplotinnovationsViolence×normal
1
0
-1

2
0
-2

0
-2

-1.0 -0.5 0.0 0.5 1.0 1.5
QQ plot
QQplotinnovationsVandalism×normal

-1.5 -1 -0.5 0 0.5 1 1.5

QQ plot
² QQplotinnovationsOther×normal

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
² QQplotinnovationsPoliceTotal×normal
0

2

QQ plot
QQplotinnovationsProperty1×normal

0
-2
-2 -1 0 1 2

QQ plot
² QQplotinnovationsFailuretostop×normal
1
0
-1

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
QQplotinnovationsTotal×normal
2
0

-1.5 -1 -0.5 0 0.5 1 1.5

-2
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1 -0.5 0 0.5 1 1.5
-2

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

(e) M3 ⋆None QQ plot (f) M4 None QQ plot

QQ plot
² QQplotinnovationsViolence×normal
1
0
-1

-1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
QQplotinnovationsVandalism×normal
2

0
-2
-2 -1

_{QQ plot} 0 1 2
2
0
-2
QQplotinnovationsOther×normal

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
² QQplotinnovationsPoliceTotal×normal
0

2

QQ plot
QQplotinnovationsProperty1×normal

0
-2
-2 -1 0 1 2

QQ plot
² QQplotinnovationsFailuretostop×normal
1
0
-1

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

QQ plot
QQplotinnovationsTotal×normal
2
0

-1.5 -1 -0.5 0 0.5 1 1.5

-2
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

(g) M4 ⋆ None QQ plot

Figure 3: QQ plots for M1- M4

56

C

Smoothed trends and signals
smoothed trend violence data violence smoothed trend property data property

12.5

5.0

15.0
12.5
10.0
7.5
5.0
1.25
1.00
0.75
0.50
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
1.0

1995 2000 2005 2010 ^0.5 1995 2000 2005 2010
smoothed trend other data other smoothed trend total data total

25

20
1995 2000 2005 2010 1995 2000 2005 2010
(a) M1 ⋆ None Smoothed trend

⁶ smoothed signal violence data violence smoothed signal property data property
14

5
13
12
11
1995 2000 2005 2010 1995 2000 2005 2010
2.0
smoothed signal vandalism data vandalism smoothed signal no stop data no stop

1.5
10 ^1.0

1995 2000 2005 2010 ^0.5 1995 2000 2005 2010
_1.0 smoothed signal other data other smoothed signal total data total

27.5

25.0
0.5
1995 2000 2005 2010 1995 2000 2005 2010
(b) M1 ⋆ None Smoothed signal

Figure 6: M1 ⋆ None

59