Accounting for Variation in Youth Homicide Trends Across Cities in the

United States

Kevin J. Strom, RTI International

and

Kirk R. Williams, University of California, Riverside

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The Task:

• To estimate temporal trends in youth homicide rate variation across 91 cities in the United States between 1984 and 2006

• Supplementary Homicide Report (SHR) data were used in the analysis

Three empirical questions were addressed:

1. What is the nature of the temporal trends for homicide rates involving offenders 13-17 and 18-24 years of age?

2. Do the trends differ depending on whether homicide rates are adjusted for missing data?

3. Do the trends vary for different groupings of cities by population size?

The Problem of Missing Data

• The SHR has missing data because of non-reporting or incomplete reporting on offender or victim characteristics (7% to 28% of incidents across all years in the sample of cities – most 15% to 20%)

• Numerous attempts have been made to compensate for the missing data problem (see Wadsworth & Roberts, 2008 for recent review and analysis)

Multiple Imputation (MI)

• Use all incidents of murder and non-negligent manslaughter in the city sample

• Conducted MI with five iterations using the ice command in StataSE 10.1 that included victim characteristics, circumstances of the incidents, and city size

• Used data from first victim (92% to 98% of all incidents from 1984 to 2006 had a single victim)

• After conducting multiple imputation, the data were aggregated to the city level

• Age-specific homicide rates (13-17 and 18-24 years of age) were calculated for each city and each year:

(Age-specific frequency/Age-specific population) * 100,000

Missing Years in the Sample of 100 Cities

• Thirty cities had missing data for one or more years between 1984 and 2006

• Seven were missing for 10 to 14 years; they were dropped from the analysis

• Two additional cities were dropped because no time trend could be estimated

Compensating for Missing Years

• Linear interpolation was used to estimate missing data for the other cities, based on the temporal pattern that best fit the data for each city

• If no temporal relation could be estimated (12 cities for rates involving offenders 13-17 and 8 cities for those 18-24 ), mean substitution was used

Hierarchical Linear Modeling (HLM)

• Compared youth homicide rates based on the raw data, the imputed data, and the imputed-interpolated data

• Estimated fully unconditional models to partition the total variation of these rates between and within cities

• Estimated the temporal trend at level one (within cities) using a third order polynomial model

Rationale for the Third Order Polynomial

• National trend showed:

– A dramatic increase from 1984 to 1993

– A dramatic decrease from 1993 to 2000

– A less dramatic upturn since 2000

• Does this trend occur across the 91 cities?

Results for Homicide Rates Involving Offenders 13-17 Years of Age

 VARIANCE COMPONENTS Raw Imputed Imputed- (UNCONDITIONAL MODEL) Interpolated

Between cities 216.399 419.714 421.377

Within cities 593.015 918.092 902.821

Intra-class correlation .267 .314 .318

POLYNOMIAL MODEL COEFFICIENTS* Time 4.330 13.349 13.170

Time squared -1.036 -1.171 -1.155

Time cubed .025 .028 .027

Intercept 3.838 4.783 5.141

R-squared .195 .162 .161

*Coefficients in bold are statistically significant p<.05

Results for Homicide Rates Involving Offenders 18-24 Years of Age

VARIANCE COMPONENTS Raw Imputed Imputed- (UNCONDITIONAL MODEL) Interpolated

Between cities 631.687 1721.475 1717.022

Within cities 350.359 841.041 832.883

Intra-class correlation .643 .672 .673

POLYNOMIAL MODEL COEFFICIENTS* Time 5.990 8.132 8.263

Time squared -.525 -.593 -.608

Time cubed .013 .013 .013

Intercept 20.514 25.700 25.417

R-squared .074 .092 .095

*Coefficients in bold are statistically significant p<.05

Results for Homicide Rates Involving Offenders 13-17 Years of Age by City Size

HOMICIDE RATES: 13-17* Small1 Medium2 Medium- Large4 Large3

Time 10.410 14.057 15.051 14.946

Time squared -.772 -1.295 -1.373 -1.427

Time cubed .015 .033 .033 .036

Intercept 1.137 3.155 7.582 17.441

R-squared .129 .146 .216 .309

*Estimates in bold are statistically significant p<.051N = 690 annual homicide rates in 30 cities 90,000 to 249,999 in population size2N = 713 annual homicide rates in 31 cities 250,000 to 499,999 in population size3N = 437 annual homicide rates in 19 cities 500,000 to 999,999 in population size4N = 253 annual homicide rates in 11 cities 1,000,000 or larger in population size

Results for Homicide Rates Involving Offenders 18-24 Years of Age by City Size

HOMICIDE RATES: 18-24* Small1 Medium2 Medium- Large4 Large3

Time 4.586 11.138 5.822 14.406

Time squared -.220 -.934 -.360 -1.178

Time cubed .002 .023 .006 .027

Intercept 18.130 23.492 28.501 45.388

R-squared .071 .118 .094 .132

*Estimates in bold are statistically significant p<.051N = 690 annual homicide rates in 30 cities 90,000 to 249,999 in population size2N = 713 annual homicide rates in 31 cities 250,000 to 499,999 in population size3N = 437 annual homicide rates in 19 cities 500,000 to 999,999 in population size4N = 253 annual homicide rates in 11 cities 1,000,000 or larger in population size

Summary of Findings

• The intra-class correlations showed:

– Between city and within city variability was relatively similar across measurement methods

– a substantial amount of the variability was between cities (almost a third for homicide rates involving 13-17 year old offenders and almost two thirds of the variability for rates involving 18-24 year olds)

• the third-order polynomial specification fit the data for both 13-17 and 18-24 year old homicide rates, irrespective of measurement method

• Although the estimated coefficients tended to be slightly greater in magnitude for the imputed and imputed-interpolated rates, the direction and relative strength of the estimated coefficients was similar regardless of the measurement method used.

• the third-order multilevel polynomial model fit the data for all city population groupings for homicide rates involving 13-17 year old offenders, although the fit was increasingly better from smaller to larger cities

• for 18-24 year old homicide rates, the third-order polynomial model fit for medium and large cities but not for small and moderately large cities -- a second-order model fit the data for cities in those two population groupings

Conclusions

• Variability in the temporal trends for homicide rates involving 18-24 year old offenders suggests that using an additional analytical technique that groups cities by differing temporal trends holds promise (e.g., cluster analysis).

• Adjusting for missing data in the SHR makes full use of the data available for measuring lethal violence but has little consequence for estimating temporal trends of youth homicide

• The third order polynomial model fits the data for homicides involving 13-17 and 18-24 year old offenders, but the parameters of the model will vary across cities

• The first parameter captures the accelerating years, the second the decelerating years, and the third the more recent upturn

• The next step is to determine what characteristics of cities account from each of these parameters and whether those that drove the “epidemic” of youth homicide are now driving the recent upturn

• Such findings can help identify cities “at risk” of another “epidemic” and enhance more targeted prevention and intervention efforts

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