The Influence of Temporal Specification on the Identification of Crime Hot Spots for Program Evaluations: A Test of Longitudinal Stability in Crime Patterns

Abstract

Objectives

Longitudinal studies from the criminology of place suggest crime hot spots are repeatedly found in the same locations within cities over extended periods of time. Program evaluations of hot spots policing interventions often use much shorter temporal windows to define hot spots. This study examines if stability of patterns is still found when using short and intermediate periods of time to measure crime hot spots.

Methods

We examined 765,235 total crime incidents reported to the Cincinnati Police Department from 1997 to 2016. These incidents were geocoded to 13,189 street segments. We created measures of crime hot spots based on varying temporal periods using three different strategies: pooled observations, group-based trajectory modeling, and k-means clustering. These measures were compared using techniques associated with survival analyses to determine the influence of temporal specification on the retrospective identification of crime hot spots.

Results

Our findings suggest regardless of the temporal specification, most street segments identified as crime hot spots remained crime hot spots across the observed follow-up periods. There was still much variability in patterns based upon temporal specifications and the use of additional years of incident report data did not uniformly provide an improved understanding of which street segments remained crime hot spots.

Conclusions

Program evaluations of hot spots policing strategies do not need to use extended periods of time to observe stability in crime hot spots. The criminology of place should provide more attention to the topic of temporal specification and continue exploring the utility of crime hot spots.

Appendices

Appendix 1: Discussion of Outliers & Diagnostics for GBTM

Model S was the first estimated using GBTM to address the influence of outlier crime hot spots. One of the parametric limitations of using GBTM is the truncation of probability distributions. This is even more problematic for research in the criminology of place because these outlier values are the most active crime hot spots which are vital to summarize the distribution of crime at micro-places (see Curman et al. 2015). We found 99 of these street segments were identified using Model S and were excluded from the main analyses for the second measurement strategy to allow for all models to converge. These 99 street segments represented 0.8% of the total street segments but 13.8% of the total crime incidents. The exclusion of these street segments based on findings from Model S helps to eliminate attrition from the GBTM analyses since these locations could be included in the estimation of models with fewer years.

These locations were further examined to determine the number of observations (i.e., 99 street segments × 20 years) which fell below ten incidents a year. Across the 19 group-based trajectory models the threshold of 10 incidents per year often represented the dividing line between crime hot spots and street segments with only moderate patterns. Only 13.1% of the street segments (13 of 99) had one observation below 10 incidents for a given year with only 3.0% of the total observations (60 of 1980) falling below this value. This suggests that even if these outlier street segments were included in the analyses, they would not change the general pattern of findings because almost all these locations would remain crime hot spots over time. In turn, the patterns of cumulative survival rates between measurements would not be drastically changed, the values of cumulative survival rates would just increase uniformly across each of the models since there were almost no failures from these locations (i.e. “a rising tide lifts all boats”). Outside of these analyses providing conservatively lower values of cumulative survival rates, it would not drastically change the general findings from this modeling strategy.

The diagnostics for each model below report most of the models identified less than 4% of locations are crime hot spots. When accounting for the exclusion of the 99 street segments with the most total incidents, these differences do still provide support for the law of crime concentration. Thus, the hot spot population could increase by as much as 0.8% and the incidents up to 13.8% when adding the excluded outliers. By including the outliers and accounting for how GBTM clusters observations, these findings are much closer to fitting the law of crime concentration’s criteria of 4-6% of locations and 50% of incidents. In addition, Models B-F report the lowest percent of locations identified as crime hot spots since the fewer years and number of groups identified made it more difficult.

Model	A	B	C	D	E	F	G
Years	2015–2016	2014–2016	2013–2016	2012–2016	2011–2016	2010–2016	2009–2016
Groups	5	6	6	7	7	8	9
Poly. order	Linear	Linear	Linear	Linear	Quad.	Cubic	Quad.
BIC	− 42,566.22	− 61,508.64	− 81,732.17	− 102,109.34	− 122,913.98	− 143,520.00	− 164,084.09
HS Groups	2	2	2	2	2	2	2
HS Pop.	4.7%	2.5%	3.4%	2.9%	3.2%	3.4%	2.6%
Incidents	36.1%	23.2%	27.2%	24.1%	25.2%	26.1%	22.0%

Model	H	I	J	K	L	M	N
Years	2008–2016	2007–2016	2006–2016	2005–2016	2004–2016	2003–2016	2002–2016
Groups	10	10	10	11	12	12	14
Poly. order	Linear	Quad.	Linear	Cubic	Cubic	Cubic	Cubic
BIC	− 185,296.33	− 206,819.03	− 228,563.90	− 249,330.20	− 271,318.70	− 292,582.00	− 314,212.78
HS groups	3	3	3	3	3	3	3
HS Pop.	4.1%	3.9%	3.8%	4.3%	3.5%	4.2%	3.3%
Incidents	27.7%	27.4%	26.9%	29.6%	25.9%	24.8%	24.8%

Model	O	P	Q	R	S
Years	2001–2016	2000–2016	1999–2016	1998–2016	1997–2016
Groups	16	16	18	18	20
Poly. Order	Cubic	Cubic	Cubic	Cubic	Cubic
BIC	− 335,315.06	− 355,811.7	− 375,503.04	− 397,385.80	− 417,861.9
HS Groups	5	3	4	4	5
HS Pop.	4.9%	3.8%	3.1%	4.2%	4.3%
Incidents	31.0%	24.2%	22.3%	25.4%	28.6%

Appendix 2: Diagnostics for K-Means Clustering & K-Means Clustering Defined Trajectories for Model J

Model	A	B	C	D	E	F	G
Years	2015–2016	2014–2016	2013–2016	2012–2016	2011–2016	2010–2016	2009–2016
Groups	5	5	5	5	5	5	3
Calinski	> 18,000	> 16,000	> 14,000	> 12,500	> 12,000	> 11,000	> 11,000
HS Groups	4	4	4	4	4	4	2
HS Pop.	13.8%	11.9%	11.8%	12.1%	12.3%	11.3%	4.5%
Incidents	67.8%	62.4%	61.0%	61.1%	61.0%	58.5%	38.6%

Model	H	I	J	K	L	M	N
Years	2008–2016	2007–2016	2006–2016	2005–2016	2004–2016	2003–2016	2002–2016
Groups	3	3	4	4	4	3	3
Calinski	> 10,500	> 10,500	> 11,000	> 11,000	> 10,500	> 11,000	> 10,500
HS Groups	2	2	3	3	3	2	2
HS Pop.	6.6%	6.6%	11.2%	11.6%	12.3%	7.8%	7.8%
Incidents	45.8%	45.7%	57.6%	58.2%	59.5%	48.4%	48.3%

Model	O	P	Q	R	S
Years	2001–2016	2000–2016	1999–2016	1998–2016	1997–2016
Groups	3	3	3	3	3
Calinski	> 10,500	> 10,000	> 10,500	> 10,500	> 10,000
HS Groups	2	2	2	2	2
HS Pop.	7.8%	8.0%	7.7%	7.7%	8.0%
Incidents	48.3%	48.7%	47.6%	47.4%	48.3%