The Dependence of Reported Homicide Rates on Reported Non-Motor Vehicle Accident Death Rates in US Young Children and Infants, 1940-2007

doi:10.4236/aasoci.2013.31002

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Advances in Applied Sociology

2013. Vol.3, No.1, 13-19

Published Online March 2013 in SciRes (http://www.scirp.org/journal/aasoci) http://dx.doi.org/10.4236/aasoci.2013.31002

The Dependence of Reported Homicide Rates on Reported

Non-Motor Vehicle Accident Death Rates in US Young Children

and Infants, 1940-2007

Jack E. Riggs1, Gerald R. Hobbs2

1Department of Neurology, West Virginia University, Morgantown, USA

2Department of Statistics, West Virginia University, Morgantown, USA

Email: [email protected]

Received January 24th, 2013; revised February 20th, 2013; accepted March 10th, 2013

An analysis of the relationship between reported homicides and reported non-motor vehicle accident

deaths in young children and infants was performed. Reported young child (aged 1 to less than 5 years)

and infant (aged less than 1 year) homicide and non-motor vehicle accident mortality rates in boys and

girls in the United States from 1940 to 2007 were analyzed using the 4-parameter logistic model. Homi-

cide rate growth over time displayed sigmoid curves with inflection points near 1968 in young children

and near 1984 in infants. Using the maximum and minimum homicide rate asymptotes from those analy-

ses over time, 4-parameter logistic model between homicide rates and non-motor vehicle mortality rates

suggests that 84.2% and 94.2% of the variation in young child homicide rates, in boys and girls respec-

tively, can be explained by variation in the corresponding non-motor vehicle accident mortality rates and

that 69.4% and 66.3% of the variation in infant homicide rates, in boys and girls respectively, was ex-

plained by variation in the corresponding non-motor vehicle accident mortality rates. These findings are

consistent with the thesis that changing propensities in the classification of young child and infant deaths

as either homicides or non-motor vehicle accident deaths, rather than actual changes in societal violence,

may explain a substantial proportion of the reported increases in homicide rates in young children and in-

fants. Moreover, the observation that increases in homicide rates in young children and infants were

separated in time by nearly 16 years further supports this thesis.

Keywords: Accidental Death Rates; Child; Classification; Homicide Rates; Infant; Mutually Exclusive

Events

Introduction

Child abuse and neglect have become the focus of increased

societal attention in recent decades (Cappelleri et al., 1993;

Overpeck et al., 1998; Dubowitz & Bennett, 2007). Many in-

vestigators have suggested that the magnitude of fatal child

abuse has been underestimated (Herman-Giddens et al., 1999;

Crume et al., 2002). Young child and infant homicide are fre-

quently related to child abuse and psychiatric dysfunction in a

parent or custodial adult (Friedman et al., 2005; Jenny & Isaac,

2006; Nielssen et al., 2009). The problem of young child and

infant homicide in the United States began receiving increased

attention in the 1960’s (Adelson, 1961; Kempe et al., 1962).

Low birth weight, young maternal age, and poor prenatal care

are shared risk factors for both infant homicide and accidental

death (Overpeck et al., 1998; Brenner et al., 1999; Jain et al.,

2001). Unnatural deaths in young children or infants, whether

accidental or intentional, frequently involve head injury (Reece

& Sege, 2000; Tung et al., 2006).

Mutually exclusive events, such as reported young child and

infant homicides and non-motor vehicle accident deaths, are in-

herently competitive (Chiang, 1991). It has been suggested that

recent observed increases in reported young child and infant

homicide rates may be related in some competitive manner to

non-motor vehicle accident mortality rates (Riggs & Hobbs,

2011; Riggs & Hobbs, 2012). Growth under competition fre-

quently displays an S-curve or sigmoid curve (Smith, 1952;

Weiss & Kavanau, 1957; Botkin et al., 1972; Southwood &

Comins, 1976; Zeide, 1993; Tsoularis & Wallace, 2002; Powell

et al., 2006). If increases, or growth in young child and infant

homicide rates, are related to competition in some manner, then

the growth of these homicide rates might display an S-curve or

sigmoid curve and conform to logistic dynamics. Moreover, if

young child and infant homicide rates are actually competing

against young child and infant non-motor vehicle accident mor-

tality rates, then plotting young child and infant homicide rates

against corresponding non-motor accident mortality rates might

also illustrate an S-curve or sigmoid curve and conform to lo-

gistic dynamics.

Data

This study utilized publicly accessible data provided by the

National Center for Health Statistics (www.cdc.gov/nchs).

Young child (defined as between one year old and less than five

years old) homicide and non-motor vehicle accident mortality

rates (per 100,000) for boys and girls in the United States for

the years 1940 through 2007 are shown in Table 1. Infant (de-

fined as less than one year old) homicide and non-motor vehicle

accident mortality rates (per 100,000) for boys and girls in the

United States for the years 1940 through 2007 are shown in

Table 2. Annual homicide rates in young child and infant boys

J. E. RIGGS, G. R. HOBBS

Table 1.

Homicide (H) rates and non-motor vehicle accident (A) mortality rates (per 100,000) among young child (aged 1 year to less than 5 years old) boys (b)

and girls (g) in the United States from 1940 through 2007.

Year H(b) H(g) A(b) A(g) Year H(b) H(g) A(b) A(g)

1940 0.6 0.5 42.1 32.2 1974 2.4 2.0 23.7 14.2

1941 0.7 0.4 41.0 30.9 1975 2.8 2.0 20.6 14.6

1942 0.6 0.6 42.7 34.0 1976 2.4 2.5 20.9 13.3

1943 0.5 0.8 48.8 35.7 1977 2.9 2.4 20.4 13.2

1944 0.5 0.6 45.1 33.6 1978 2.7 2.3 21.5 14.1

1945 0.7 0.7 41.2 31.0 1979 2.4 2.6 20.5 12.7

1946 0.7 0.8 38.8 27.7 1980 2.7 2.2 20.2 12.9

1947 0.7 0.5 36.2 24.5 1981 2.7 2.4 19.8 11.8

1948 0.6 0.5 33.7 24.6 1982 3.0 2.5 17.9 11.3

1949 0.8 0.4 30.7 21.9 1983 2.5 2.0 17.3 11.4

1950 0.5 0.7 29.5 20.9 1984 2.4 2.4 16.0 9.8

1951 0.6 0.6 28.0 21.6 1985 2.5 2.4 16.0 9.9

1952 0.8 0.5 28.3 22.2 1986 3.1 2.3 16.1 10.9

1953 0.7 0.7 27.2 20.6 1987 2.2 2.4 16.9 9.9

1954 0.6 0.6 25.5 19.5 1988 2.9 2.3 16.0 9.5

1955 0.5 0.6 25.0 19.0 1989 2.9 2.5 15.0 9.0

1956 0.7 0.7 24.9 18.0 1990 2.7 2.4 13.9 8.1

1957 0.5 0.6 23.6 19.3 1991 3.0 2.6 13.8 9.3

1958 0.7 0.8 24.3 18.5 1992 3.0 2.5 12.9 7.7

1959 0.9 0.8 24.3 17.7 1993 3.4 2.5 13.1 8.3

1960 0.7 0.7 24.3 18.7 1994 3.3 2.7 12.2 7.5

1961 1.0 1.0 23.9 18.3 1995 3.1 2.6 11.2 7.2

1962 0.9 0.9 24.0 18.4 1996 2.7 2.7 10.5 6.5

1963 1.2 1.1 24.7 18.1 1997 2.7 2.2 9.8 6.2

1964 1.3 1.2 24.6 18.2 1998 2.9 2.4 9.5 5.9

1965 1.2 1.1 26.4 17.5 1999 2.5 2.4 9.7 6.5

1966 1.2 1.2 26.7 18.9 2000 2.5 2.1 9.3 5.9

1967 1.1 1.2 26.2 17.6 2001 3.0 2.4 8.8 5.3

1968 1.5 1.5 24.6 17.5 2002 2.9 2.5 8.4 4.8

1969 1.8 1.6 23.9 16.7 2003 2.5 2.3 8.6 5.2

1970 1.9 1.9 23.9 15.9 2004 2.5 2.2 7.6 5.0

1971 2.3 2.0 24.3 15.4 2005 2.6 2.0 8.2 4.6

1972 2.0 1.6 25.2 14.6 2006 2.5 2.0 7.3 5.2

1973 2.7 2.3 23.2 15.6 2007 2.5 2.3 8.0 4.5

J. E. RIGGS, G. R. HOBBS

Table 2.

Homicide (H) rates and non-motor vehicle accident (A) mortality rates (per 100,000) among infant (less than one year old) boys (b) and girls (g) in

the United States from 1940 through 2007.

Year H(b) H(g) A(b) A(g) Year H(b) H(g) A(b) A(g)

1940 5.0 4.6 135.3 112.1 1974 5.0 5.9 46.0 34.0

1941 5.4 4.7 132.7 101.2 1975 6.3 4.9 46.0 32.0

1942 4.9 3.8 128.0 103.7 1976 5.5 5.4 37.6 27.1

1943 4.9 4.4 124.9 94.3 1977 5.7 5.1 32.0 24.0

1944 4.4 4.4 123.7 94.9 1978 4.8 4.9 33.3 26.5

1945 5.8 6.3 119.5 94.6 1979 5.9 3.9 28.2 21.8

1946 5.9 5.3 127.3 102.4 1980 6.3 5.6 29.2 22.7

1947 5.4 4.7 107.2 88.4 1981 5.7 6.4 23.1 19.0

1948 4.4 5.1 116.2 92.7 1982 7.5 5.8 26.3 18.2

1949 4.3 3.8 126.4 95.0 1983 4.9 5.7 24.1 17.7

1950 4.5 4.2 119.3 91.9 1984 7.3 5.9 20.2 17.6

1951 3.9 4.6 114.6 92.6 1985 5.6 5.2 20.4 18.1

1952 3.9 3.5 111.1 89.2 1986 8.0 7.0 21.0 18.2

1953 3.1 3.2 105.2 81.5 1987 8.2 6.5 22.5 18.8

1954 4.0 3.3 101.1 78.6 1988 7.9 8.9 21.4 16.8

1955 3.7 3.1 90.1 68.3 1989 8.4 9.0 21.7 18.7

1956 3.1 3.5 93.2 71.5 1990 8.8 8.0 20.3 16.9

1957 3.3 2.8 92.3 73.9 1991 10.1 8.9 22.6 16.5

1958 3.4 3.3 101.1 77.7 1992 8.9 7.4 18.3 14.6

1959 4.2 3.2 95.5 77.9 1993 9.6 7.9 20.3 15.7

1960 4.7 4.9 94.4 75.5 1994 9.9 7.1 20.6 15.5

1961 4.9 4.4 88.8 67.7 1995 8.9 7.2 16.5 15.0

1962 5.6 4.9 89.0 73.2 1996 8.7 8.9 17.6 13.6

1963 5.1 5.0 87.7 71.1 1997 9.4 7.3 17.8 13.7

1964 5.6 5.5 85.7 67.5 1998 8.9 8.1 17.9 13.4

1965 6.4 4.9 88.9 69.3 1999 9.6 7.8 20.4 14.3

1966 6.5 5.3 86.8 67.1 2000 10.4 7.9 21.1 16.3

1967 6.9 6.1 79.3 61.3 2001 9.5 6.9 23.0 18.1

1968 4.7 5.0 70.6 60.0 2002 7.9 7.1 23.5 17.2

1969 5.0 3.8 67.0 53.1 2003 10.0 6.9 22.5 17.4

1970 4.5 4.1 61.1 50.7 2004 8.0 7.9 25.2 19.3

1971 5.0 5.4 60.6 44.1 2005 8.2 6.6 24.0 21.6

1972 5.4 4.9 52.8 36.6 2006 9.4 6.8 28.3 20.3

1973 5.1 5.2 50.3 36.7 2007 9.5 7.0 30.2 24.2

J. E. RIGGS, G. R. HOBBS

and girls were plotted to determine if sigmoid curves were evi-

dent and, if so, whether those curves were well described by

logistic functions. Next young child and infant homicide rates

in boys and girls were plotted against the corresponding non-

motor vehicle accident mortality rates to determine sigmoid

curves were also evident and, if so, whether those curves were

also well described by logistic functions.

Results Figure 1.

Annual reported young child homicide rates

(per 100,000) in boys (black squares) for the

years 1940 through 2007 are displayed. The

4-parameter logistic (black solid line) best

fitting these data points is also displayed.

Annual (1940 through 2007) homicide rates in young child

boys, young child girls, infant boys, and infant girls are dis-

played in Figures 1-4 respectively. These figures demonstrate

sigmoid curves (better delineated in young child boys and girls)

in which homicide rates increase from a lower plateau to a

higher plateau over a relatively brief period of time. Such sig-

moid curves can frequently be described by a 4-parameter lo-

gistic. The four parameters define the upper plateau or maxi-

mum asymptote, the lower plateau or minimum asymptote, the

slope factor or steepness of the curve, and the midpoint be-

tween the two plateaus or inflection point. The equation de-

scribing the 4-parameter logistic illustrated in Figures 1

through 4 is:

 









HXABA1 expCXD



 



(1)

Figure 2.

Annual reported young child homicide rates

(per 100,000) in girls (black squares) for the

years 1940 through 2007 are displayed. The

4-parameter logistic (black solid line) best

fitting these data points is also displayed.

where H(x) is the homicide rate in year X, A is the upper pla-

teau homicide rate, B is the lower plateau homicide rate, C is

the slope factor which is the slope of the line at the inflection

point of the curve, and D is the year at which the inflection

point occurs.

The 4-parameter logistic describing the data displayed in Fi-

gure 1 (young child boys) shows an upper plateau homicide

rate of 2.77/100,000, a lower plateau homicide rate of 0.64/

100,000, a slope factor of 0.314, and an infection point occur-

ring near 1968 (1968.48). The R-squared value of the logistic

curve displayed in Figure 1 for young child boys was 0.948.

The 4-parameter logistic describing the data displayed in Fig-

ure 2 (young child girls) shows an upper plateau homicide rate

of 2.39/100,000, a lower plateau homicide rate of 0.59/100,000,

a slope factor of 0.277, and an infection point also occurring

near 1968 (1967.72). The R-squared value of the logistic curve

displayed in Figure 2 for young child girls was 0.957. The

4-parameter logistic describing the data displayed in Figure 3

(infant boys) shows an upper plateau homicide rate of 9.29/

100,000, a lower plateau homicide rate of 4.78/100,000, a slope

factor of 0.266, and an infection point occurring near 1984

(1984.13). The R-squared value of the logistic curve displayed

in Figure 3 for infant boys was 0.817. The 4-parameter logistic

describing the data displayed in Figure 4 (infant girls) shows

an upper plateau homicide rate of 7.63/100,000, a lower plateau

homicide rate of 4.50/100,000, a slope factor of 0.406, and an

infection point occurring near 1983 (1982.94). The R-squared

value of the logistic curve displayed in Figure 4 for infant girls

was 0.729.

Figure 3.

Annual reported infant homicide rates (per 100,000) in

boys (black squares) for the years 1940 through 2007 are

displayed. The 4-parameter logistic (black solid line)

best fitting these data points is also displayed.

Homicide rates in young child boys, young child girls, infant

boys, and infant girls versus corresponding non-motor vehicle

accident mortality rates (1940 through 2007) are displayed in

Figures 5-8 respectively. These figures demonstrate much bet-

ter developed sigmoid curves for young child boys and girls

(Figures 5 and 6), in which homicide rates increase from a

lower plateau to a higher plateau as non-motor vehicle accident

Figure 4.

Annual reported infant homicide rates (per 100,000) in

girls (black squares) for the years 1940 through 2007 are

displayed. The 4-parameter logistic (black solid line) best

fitting these data points is also displayed.

J. E. RIGGS, G. R. HOBBS

Figure 5.

Annual reported young child homicide rates (per 100,000)

in boys (Y-axis) versus annual reported young child non-

motor vehicle mortality rates (per 100,000) in boys (X-

axis) for the years 1940 through 2007 are displayed (black

squares). The 4-parameter logistic (black solid line) fit-

ting these data points, using the upper and lower plateau

homicide rates determined from the data shown in Figure

1 is also displayed.

Figure 6.

Annual reported young child homicide rates (per 100,000)

in girls (Y-axis) versus annual reported young child non-

motor vehicle mortality rates (per 100,000) in girls (X-

axis) for the years 1940 through 2007 are displayed (black

squares). The 4-parameter logistic (black solid line) fit-

ting these data points, using the upper and lower plateau

homicide rates determined from the data shown in Figure

2 is also displayed.

mortality rates decrease over a relatively narrow span of non-

motor vehicle accident mortality rates, than for infant boys and

girls (Figures 7 and 8). These curves can also described by a 4-

parameter logistic. The equation describing the 4-parameter lo-

gistic illustrated in Figures 5 through 8 is:

 









HZAB A1expCZD



 





(2)

where H(Z) is the homicide rate at non-motor vehicle accident

mortality rate Z, A is the upper plateau homicide rate, B is the

lower plateau homicide rate, C is the slope factor, and D is the

non-motor vehicle accident mortality rate at which the inflec-

tion point occurs. Because Figures 7 and 8 do not display fully

delineated upper plateaus of infant homicide rates for boys and

girls, in the 4-parameter logistic analyses used to analyze the

data in Figures 5 through 8, we set the upper and lower pla-

teaus of young child and infant homicide rates equal to the

values that were determined when using time as the independ-

ent variable in Figures 1 through 4.

The 4-parameter logistic describing the data displayed in

Figure 5 (young child boys) which was set using an upper pla-

teau homicide rate of 2.77/100,000 and a lower plateau homi-

cide rate of 0.64/100,000, shows a slope factor of −0.963 and

an infection point occurring at a non-motor vehicle accident

Figure 7.

Annual reported infant homicide rates (per 100,000) in

boys (Y-axis) versus annual reported infant non-motor

vehicle mortality rates (per 100,000) in boys (X-axis) for

the years 1940 through 2007 are displayed (black squares).

The 4-parameter logistic (black solid line) fitting these

data points, using the upper and lower plateau homicide

rates determined from the data shown in Figure 3 is also

displayed.

Figure 8.

Annual reported infant homicide rates (per 100,000) in

girls (Y-axis) versus annual reported infant non-motor

vehicle mortality rates (per 100,000) in girls (X-axis) for

the years 1940 through 2007 are displayed (black squares).

The 4-parameter logistic (black solid line) fitting these

data points, using the upper and lower plateau homicide

rates determined from the data shown in Figure 4 is also

displayed.

mortality rate of 23.51/100,000. The R-squared of the logistic

curve displayed in Figure 5 for young child boys was 0.842.

The 4-parameter logistic describing the data displayed in Fig-

ure 6 (young child girls) which was set using an upper plateau

homicide rate of 2.39/100,000 and a lower plateau homicide

rate of 0.59/100,000, shows a slope factor of −0.915 and an

infection point occurring at a non-motor vehicle accident mor-

tality rate of 16.75/100,000. The R-squared of the logistic curve

displayed in Figure 6 for young child girls was 0.942. The

4-parameter logistic describing the data displayed in Figure 7

(infant boys) which was set using an upper plateau homicide

rate of 9.29/100,000 and a lower plateau homicide rate of 4.78/

100,000, shows a slope factor of −0.185 and an infection point

occurring at a non-motor vehicle accident mortality rate of

29.22/100,000. The R-squared of the logistic curve displayed in

Figure 7 for infant boys was 0.694. The 4-parameter logistic

describing the data displayed in Figure 8 (infant girls) which

was set using an upper plateau homicide rate of 7.63/100,000

and a lower plateau homicide rate of 4.50/100,000, shows a

slope factor of −0.371 and an infection point occurring at a

non-motor vehicle accident mortality rate of 21.95/100,000.

The R-squared of the logistic curve displayed in Figure 8 for

infant girls was 0.663.

Discussion

The observation that reported young child and infant homi-

J. E. RIGGS, G. R. HOBBS

cide rates displayed sigmoid curves rising from a lower plateau

to an upper plateau (Figures 1 through 4) is consistent with the

thesis that some competitive influence may be driving the

growth of these reported homicide rates (Smith, 1952; Weiss &

Kavanau, 1957; Botkin et al., 1972; Southwood & Comins,

1976; Zeide, 1993; Tsoularis & Wallace, 2002; Powell et al.,

2006). The observation that increases in reported homicide

rates in young children (Figures 1 and 2) and infants (Figures

3 and 4) were separated in time by nearly 16 years argues

against any suggestion that increased societal violence directed

against young children and infants was responsible since it

seems rather unlikely that societal violence against young chil-

dren would have increased in the late 1960’s and then, about 16

years later, that societal violence against infants would have

distinctly and separately increased in the early 1980’s. Figures

5 through 8 are consistent with the thesis that decreasing re-

ported non-motor vehicle accident mortality rates in young chil-

dren and infants were the competitive factor responsible for the

observed increases in corresponding reported homicide rates.

The regressions performed on the data displayed in Figures 5

through 8 suggest that 84.2% and 94.2% of the variation in

young child homicide rates was explained by variation in cor-

responding non-motor vehicle accident mortality rates in boys

and girls respectively, and that 69.4% and 66.3% of the varia-

tion in infant homicide rates was explained by variation in cor-

responding non-motor vehicle accident mortality rates in boys

and girls respectively.

When classifying two mutually exclusive events, their rela-

tive frequency may be important. For example, if event A and

event B are potentially difficult to distinguish and event A is

much more frequent, then there may be a tendency to bias clas-

sification towards event A (Riggs & Hobbs, 2011; Riggs &

Hobbs, 2012). However, if event A becomes less frequent and

sensitivity to recognizing event B is increasing, there may be a

tendency to bias classification towards event B (Riggs & Hobbs,

2011; Riggs & Hobbs, 2012). Thus, when reported young child

and infant non-motor vehicle accident mortality rates were both

absolutely and relatively high compared to reported young child

and infant homicide rates, under ascertainment of homicides

was understandable, and perhaps even predictable. However,

when reported young child and infant non-motor vehicle acci-

dent mortality rates absolutely and relatively declined com-

pared to reported young child and infant homicide rates, and

these changing frequencies were coupled with the increased so-

cietal sensitivity to the problem of child abuse, a change in the

propensity to assign a homicide classification over a non-motor

vehicle accidental death classification as a cause of unnatural

death in a young child or an infant became conversely under-

standable, and perhaps even also predictable (Riggs & Hobbs,

2011; Riggs & Hobbs, 2012).

These findings are consistent with the thesis that changing

propensities in the classification of young child and infant

deaths as either homicides or non-motor vehicle accident deaths,

rather than actual changes in societal violence, may explain a

substantial proportion of the reported increases in homicide

rates in these two groups. Moreover, the observation that in-

creases in homicide rates in young children and infants were

separated in time by nearly 16 years further supports this thesis.

This analysis deals with the inherent competitive nature of

classifying two mutually exclusive events, homicides and non-

motor vehicle accident deaths, in young children and infants.

This analysis does not prove that misclassification of these two

mutually exclusive events actually occurred in any specific in-

stance. Nevertheless, this analysis does demonstrate that homi-

cide rates have been substantially dependent upon non-motor

vehicle accident death rates in young children and infants.

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