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Contents of Homicide trends in the U.S.

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Homicide trends in the U.S.

Weighting and Imputation Procedures for the 1976-2005 Cumulative Data File

by James Alan Fox, The Lipman Family Professor

      of Criminal Justice, Northeastern University

        and

      Marianne W. Zawitz, BJS Statistician

Most of the data used in Homicide Trends in the United States are from the FBI's Supplementary Homicide Reports (SHR) which provides detailed, incident-level data on nearly all murders and nonnegligent manslaughters in the United States. These reports include information on the month and year of an offense, on the reporting agency and its residential population, county and Metropolitan Statistical Area (MSA) codes, geographic division, and population group, on the age, race, and sex of victims and offenders, and on the victim-offender relationship, weapon use and circumstance of the crime. Except for some slight modification in 1980, the record layout and variable definitions in the SHR data have remained unchanged since 1976 when the reporting format underwent a major revision.

This document describes adjustments used in this analysis for handling missing data in the SHR that result from agency failure to file reports and incomplete records that are missing certain information about the incident, victim or offender.

Correcting for Missing Records

Law enforcement agencies voluntarily report both Uniform Crime Reports (UCR) summary data and SHR incident data to the FBI on a monthly basis. The offense data in the UCR includes counts of murder and nonnegligent manslaughter as well as seven other Index crimes. The number of murders and nonnegligent manslaughters is based on the number of victims. For the most part, each month agencies report a total number of offenses in each Index crime category. In some instances agencies may not report each month or may not report at all which results in missing data when aggregating to the State or national level. After imputing for missing data, the FBI publishes estimates for the Nation as a whole as well as for individual States for all Index offenses, including murder and nonnegligent manslaughter. (For additional information on the imputation methods used by the FBI, see "Bridging Gaps in Police Crime Data" by Michael Maltz, 10/99, NCJ 176365, http://www.ojp.usdoj.gov/bjs/abstract/bgpcd.htm.) These annual UCR State and national estimates of homicide volumes are used as benchmarks for assessing the completeness of the SHR data file and to adjust SHR victim or offender counts as needed.

Not all of the murders and nonnegligent manslaughters reported in the UCR are included in the SHR. The SHR file appears to be just over 90% complete, although, as shown in Table 1, the level of completeness of the SHR has generally diminished in recent years. To correct for missing SHR records, the national and regional totals have been benchmarked to the UCR estimates. Specifically, SHR records were weighted so that State and national total counts matched UCR estimates for murder and nonnegligent manslaughter. This weighting process assumes that the missing records are not systematically different from those available in the file. While the systematic exclusions for certain years of a State like Florida or a city like Washington, D.C. may cause some concern, the fact that missingness occurs in both large and small jurisdictions lends support for applying these benchmark weights.

Correcting for Incomplete Records

Even for the 90% of SHR records that are available for analysis, certain variables have nontrivial rates of missingness. At one extreme, characteristics of an agency (e.g., region, population group) are always complete. Victim data, though sometimes missing, are absent at such a low rate that standard approaches for handling missing data (specifically, listwise deletion) hardly bias analyses of patterns and trends in victimization. Specifically, as shown in the top panel of Table 2, victim age is missing in 1.72% of homicides, race in 1.04% and sex in 0.14%. Overall, 2.49% are missing on at least one of these measures.

At the other extreme, the percentage of missing data is greater for homicide offenders than victims. A significant problem in using SHR data to analyze offender characteristics is the sizable and growing number of unsolved homicides contained in the data file. Overall, 26 percent of the SHR offender records describe the perpetrator as unknown (based on situation codes), and this percentage has grown from just under 20 percent in 1976 to nearly 30 percent by the mid-1990s. Even when the offender is known to the police, not all characteristics about the offender may be reported. Table 2 shows specifically that as many as 26.48% of offender records contain no information about the perpetrators, and 31.6% of records are not complete in terms of the assailant's age, race and sex.

Ignoring unsolved homicides and missing offender data seriously understates calculated rates of offending overall and by particular subgroups of the population, distorts trends over time among these same subgroups, and biases observed patterns of offending to the extent that the likelihood of missingness of offender data is associated with offender characteristics.

While it is not possible to determine directly whether case solution and thus missingness in offender data are associated with offender characteristics themselves, some indication about the pattern of missingness can be derived from examining the extent to which the likelihood of case solution is related to victim and incident variables. As shown in Table 3, case solution rates are lowest for homicides against young adult victims as well as for elderly victims. Solution rates are also lower for incidents involving black or male victims. As expected, solution rates decrease with increasing population size and urbanness. In part as a consequence of urbanicity differences, solution rates in the South are much higher than other regions. Finally, whether or not a gun is used to commit the homicide does not appear to impact upon rates of case solution.

A weighting strategy based on available information about the victims (age, race and sex) murdered in both solved and unsolved homicides is used to adjust for missing offender data in Homicide Trends in the United States. Through this imputation algorithm, the demographic characteristics of unidentified offenders are inferred on the basis of similar homicide cases--similar in terms of the victim and incident profile--that had been solved. In other words, offender profiles for unsolved crimes are estimated based on the offender profiles in solved cases matched on victim age, sex and race, region, urbanness, weapon and circumstances.

The weighting procedure is accomplished by establishing adjustment groups within a large, multidirectional cross tabulation. For each cell, we tally the number of offenders (N_c) and the number having complete offender data (n_c), and use as a weight the inverse proportion of complete cases:

Next these adjustment cell weights are applied to the offender records based on their cell membership (i.e., based on victim age, race, sex, location type, weapon and circumstances) and whether or not the offender information is complete. That is,

Finally, the weights are adjusted or "raked" post-stratification so that marginal weighted counts by year and State match fixed values.

This weighting approach is applied to the entire offender record so that cases with missing offender age, race or sex are excluded by virtue of their zero case weights. As a consequence, partial offender information is discarded, causing some slight inefficiency in the approach. While it would be possible to retain partial offender information, this would require separate weights for each offender characteristic. Finally, all non-zero weights are further increased slightly to account for the small percentage of cases unassigned to any adjustment cell because of their being missing on one or more victim characteristic.

In any analysis of weighted data, offenders with incomplete age, race or sex information are dropped due to assigned zero weights. Offenders with complete age, race and sex information all have weights at or above 1.0, and become proxies for excluded cases, matched on victim characteristics, State, and year. Thus, for example, an offender with an imputation weight of 2.0 would count in any analysis as if he/she were two offenders. The entire distribution of the weighting variable is shown in Table 4.

Table 5 demonstrates the impact of applying the imputation weights by comparing the distribution of offender characteristics (age, race and sex) using the adjustment weights with those using listwise deletion of missing data. The approach boosts the abundance of youthful offenders; offenders under the age of 25 represent 47.5% of the imputed distribution, compared to 45.0% for the distribution using listwise deletion. The percentage of black offenders grows to 52.2%, compared to 51.2% without weighting. The sex distribution, which by any measure overwhelmingly favors male perpetrators, shifts slightly from 88.2% to 88.8% (clearly indicating a ceiling effect governing this percentage).

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Page last revised on July 11, 2007