Detroit Homicide Data for 1961-1973

The data set Detroit was used extensively in the book by Miller (2002) on subset regression. The data are unusual in that a subset of three predictors can be found which gives a very much better fit to the data than the subsets found from the Efroymson stepwise algorithm, or from forward selection or backward elimination. They are also unusual in that, as time series data, the assumption of independence is patently violated, and the data suffer from problems of high collinearity.

As well, ridge regression reveals somewhat paradoxical paths of shrinkage in univariate ridge trace plots, that are more comprehensible in multivariate views.

Format

A data frame with 13 observations on the following 14 variables.

Police: Full-time police per 100,000 population
Unemp: Percent unemployed in the population
MfgWrk: Number of manufacturing workers in thousands
GunLic: Number of handgun licences per 100,000 population
GunReg: Number of handgun registrations per 100,000 population
HClear: Percent of homicides cleared by arrests
WhMale: Number of white males in the population
NmfgWrk: Number of non-manufacturing workers in thousands
GovWrk: Number of government workers in thousands
HrEarn: Average hourly earnings
WkEarn: Average weekly earnings
Accident: Death rate in accidents per 100,000 population
Assaults: Number of assaults per 100,000 population
Homicide: Number of homicides per 100,000 of population

Source

https://lib.stat.cmu.edu/datasets/detroit

Details

The data were originally collected and discussed by Fisher (1976) but the complete dataset first appeared in Gunst and Mason (1980, Appendix A). Miller (2002) discusses this dataset throughout his book, but doesn't state clearly which variables he used as predictors and which is the dependent variable. (Homicide was the dependent variable, and the predictors were Police ... WkEarn.) The data were obtained from StatLib.

A similar version of this data set, with different variable names appears in the bestglm package.

References

Fisher, J.C. (1976). Homicide in Detroit: The Role of Firearms. Criminology, 14, 387–400.

Gunst, R.F. and Mason, R.L. (1980). Regression analysis and its application: A data-oriented approach. Marcel Dekker.

Miller, A. J. (2002). Subset Selection in Regression. 2nd Ed. Chapman & Hall/CRC. Boca Raton.

Examples


data(Detroit)

# Work with a subset of predictors, from Miller (2002, Table 3.14),
# the "best" 6 variable model
#    Variables: Police, Unemp, GunLic, HClear, WhMale, WkEarn
# Scale these for comparison with other methods

Det <- as.data.frame(scale(Detroit[,c(1,2,4,6,7,11)]))
Det <- cbind(Det, Homicide=Detroit[,"Homicide"])

# use the formula interface; specify ridge constants in terms
# of equivalent degrees of freedom
dridge <- ridge(Homicide ~ ., data=Det, df=seq(6,4,-.5))

# univariate trace plots are seemingly paradoxical in that
# some coefficients "shrink" *away* from 0
traceplot(dridge, X="df")

vif(dridge)
#> Variance inflaction factors:
#>             Police  Unemp  GunLic  HClear  WhMale  WkEarn
#> 0.00000000  24.813  4.857  19.272  46.923  56.711  54.717
#> 0.03901941  20.119  3.870  11.362  33.072  35.390  31.883
#> 0.10082082  15.415  2.971   6.432  21.289  20.776  17.353
#> 0.20585744  10.776  2.208   3.597  12.171  11.258   8.750
#> 0.40331592   6.534  1.623   2.128   5.996   5.503   4.113
pairs(dridge, radius=0.5)


# \donttest{
plot3d(dridge, radius=0.5, labels=dridge$df)

# transform to PCA/SVD space
dpridge <- pca(dridge)

# not so paradoxical in PCA space
traceplot(dpridge, X="df")

biplot(dpridge, radius=0.5, labels=dpridge$df)

#> Vector scale factor set to  2.844486 

# show PCA vectors in variable space
biplot(dridge, radius=0.5, labels=dridge$df)

#> Vector scale factor set to  0.8573165 
# }