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Sunday, August 3, 2003, 6PM

How the City Homicide Rates Were Adjusted

   Improving Crime Data Project

The statistical model used to estimate adjusted homicide rates for the 21 US cities was specified as follows:

                    HomRate = a + b₁(Disadvan) + b₂(Samres), where

HomRate =  Homicides per 100,000 city residents

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

         combines four highly correlated variables (factor loadings in parentheses):

         the poverty rate (.892); male unemployment rate (.953); % black (.947); and

         % female headed families w/own children under 18 (.956)

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

The homicide data are from the FBI’s Preliminary Uniform Crime Report, 2002.  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 21 cities.  The parameter estimates from this model were then applied to the 2002 homicide rates.  The model explains nearly 70% of the variation in homicide rates across the cities.  The estimation results are as follows:

HomRate = 34.607 + 12.520(Disadvan) + -.294(Samres)

     F_{2, 18} = 19.246;     p < .001;     R² = .681;     N = 21

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).  In the table below, the 21 cities are arrayed by their 2002 homicide rate, standard score of the rate, and the standardized residual from the model.

2002 Homicide Rates in 21 Cities and Standard Scores

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