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   Improving Crime Data Project

May 17, 2004 (revised: May 25, 2004); 2003 data posted June 3, 2004

Technical Details: How the City Homicide Rates Were Adjusted

The statistical model used to estimate adjusted homicide rates for the 67 US cities with populations greater than 250,000 was specified as follows:

               Homrate = a + b₁(Disadvan) + b₂(Pop) + b₃(Samres) + b₄(divrate), where  

 Homrate =     Homicides per 100,000 city residents (natural log)

 Disadvan =    A factor representing the level of social and economic disadvantage that

combines five highly intercorrelated variables (factor loadings in

parentheses): the poverty rate (.934), male unemployment rate (.888), %

black (.839), % female-headed families w/own children under 18 (.928),

and median family income (-.862)

Pop =              City population in 2000 Census (natural log)

Samres =         % persons living in same residence 5 or more years

Divrate =         % persons age 15 and over divorced 

The homicide and population data for 2002 are from the FBI’s Crime in the United States 2002 Uniform Crime Report. The homicide data for 2003 are from the FBI's 2003 Preliminary Report. The calculation of each city's homicide rate (rate = homicides/population) used the same population figures for 2002 and 2003.  These are based on the census estimates of each city's 2002 population used by the UCR. All other data are from the 2000 census.

The model was estimated using ordinary least squares on the 2000-2001 average homicide rates for the 67 cities. The parameter estimates from this model were then applied to the 2002 homicide rates. The model explains two-thirds of the variation in homicide rates across the cities. The estimation results are as follows:

Homrate₂₀₀₂ = .061 + .644(Disadvan) + .192(Pop) - .019(Samres) + .048(Divrate)

F_{4, 62} = 35.407;     p < .001;     R² = .696;     N = 67

The residuals from this model (the observed homicide rates minus the homicide rates predicted by the model) represent that component of each city’s homicide rate that is not explained by the variables in the model. The adjusted homicide rankings are based on the standardized residuals from the model. These scores can be compared directly with the standard scores computed from the unadjusted rates ((y - m) / s).

The model was then also estimated on the 2001-2002 average homicide rates for the 67 cities.   The model explains over 70% of the variation in homicide rates across the cities. The parameter estimates from this model were then applied to the 2003 homicide rates. The estimation results are as follows:

Homrate₂₀₀₃ = .485 + .679(Disadvan) + .174(Pop) - .023(Samres) + .047(Divrate)

F_{4, 62;} = 39.237;     p < .001;     R² = .717;     N = 67

The estimations of this model on the 2000-2001 and 2001-2002 data display strong consistency and strong robustness. Given the strength of the model and the consistency of the parameters, then one can attribute the changes in the adjusted rankings between 2002 and 2003 to changes in the number of homicides. 

See Table-1 for a list of the 67 cities arrayed by their homicide rate, standard score of the rate, and the standardized residual from the model; see Table-2 for a list of the cities arrayed by the unadjusted and by the adjusted rankings; see Table-3 for an alphabetical listing of the cities.