ARTICLE REVIEWS CONT

Journal of Criminal Justice 47 (2016) 1–11

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Journal of Criminal Justice

Temporal changes in racial violence, 1980 to 2006: A latent trajectory approach

Karen F. Parker a,⁎, Richard Stansfield b, Patricia L. McCall c a Department of Sociology and Criminal Justice, University of Delaware, Newark, DE 19716, United States b Department of Sociology, Anthropology and Criminal Justice, Rutgers University, 405-7 Cooper Street, Camden, NJ 08102, United States c Department of Sociology and Anthropology, North Carolina State University, 1911 Building 365, Raleigh, NC 27695, United States

⁎ Corresponding author. E-mail addresses: Kparker@udel.edu (K.F. Parker), Rich

(R. Stansfield), Patty_mccall@ncsu.edu (P.L. McCall).

http://dx.doi.org/10.1016/j.jcrimjus.2016.06.001 0047-2352/Published by Elsevier Ltd.

a b s t r a c t

a r t i c l e i n f o

Article history: Received 25 April 2016 Received in revised form 22 June 2016 Accepted 23 June 2016 Available online 1 July 2016

Objectives: The study examines the ability of a latent trajectory approach to advance our understanding of the temporal trends in white and black homicide rates over a critical period, 1980 to 2006. After establishing distinct trajectories that reveal hidden racial heterogeneity, we estimate which of two dominant arguments concerning the changes in homicide rates over time: 1)macrostructural conditions and 2) crime control and drug sales—best explain the latent class race-specific homicide rate memberships at the city level. Methods:Using homicide data from theUniformCrimeReports alongwith decennial U.S. census data across three time periods, we employ both latent trajectory and time series approaches. Results: Our latent trajectory approach identified three unique trends or groupings of cities based on white and black homicide rates, reflecting “high”, “medium” and “low” temporal homicide trends. Time seriesmodels high- light variation in which characteristics contributed to the distinct race-specific homicide trends by trajectory group. Conclusions: Together, this study reveals hidden heterogeneity among American cities with respect to temporal trends that inform the current debate about diversity in the location and magnitude of the crime drop as well as which factors contributed to homicide trends by racial groups. Implications are discussed.

Published by Elsevier Ltd.

Keywords: Racial violence Crime drop Homicide trends Latent trajectory approach Macrostructural approach Crime control strategies Time series analysis

1. Introduction

Major shifts in national crime trends over the last quarter of the 20th century, particularly among African-American males, have prompted criminologists to explore what social, economic and political forces are driving such changes (Blumstein, 1995). Scholars have specifically doc- umented the importance of age composition and gains in the economy (Blumstein & Wallman, 2006; LaFree, 1999; Parker, 2008; Rosenfeld & Messner, 2009) as explanations for declining crime rates since the early 1990s (Gartner & Doob, 2010). Strong evidence that the U.S. crime drop differed in magnitude across locales also led scholars to re- think the crime drop at local levels (Baumer & Wolff, 2014; Messner et al., 2007). These investigations revealed that the economy as well as policy-based factors such as police presence, prison expansion, and receding illicit drug markets might be key to understanding American based declines. The role of each factorwithin cities remains hotly debat- ed however, evidenced by the disagreement surrounding the role of specialized police strategies in New York City (Rosenfeld & Fornango,

ard.stansfield@rutgers.edu

2014; Weisburd, Telep, & Lawton, 2014; Zimring, 2011). We suggest that accounting for racial differences could providemore definitive con- clusions about the role of crime control strategies and structural condi- tions in the American crime drop.

America's enduring problem of violence is not equally dispersed across all cities or all groups. Scholars point to the considerable differ- ences in the average social and economic conditions of racial and ethnic groups, in addition to historic and contemporary differences in criminal justice responses across communities and groups. We examine the ex- tent to which latent trajectory techniques can inform us about the un- derlying factors contributing to race-specific U.S. homicide trends during the latter part of the 20th century and into the early years of the 21st century. Latent trajectory analyses have been applied primarily to individual-level longitudinal cohort data to identify distinct offending trajectories. Few studies have applied this technique to study macro- level crime trends, but there have been notable exceptions at the street or neighborhood level (Boggess & Hipp, 2010; Braga, Hureau, & Papachristos, 2011; Griffiths & Chavez, 2004; Kikuchi & Desmond, 2010; Morris & Slocum, 2012; Weisburd, Bushway, Lum, & Yang, 2004). To date, latent trajectory analysis has rarely been applied to tem- poral trends in city-level homicide (see Hipp, 2011; McCall, Land, & Parker, 2011), despite the predominant focus of the crime drop

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literature on city dynamics. Applying this technique, along with a time series approach, allows us to identify different city-level trajectories with unique white and black homicide rate trends, thus allowing us to capture racial heterogeneity in violence within American cities. Based on extensive research (see e.g., Baumer & Wolff, 2014; Blumstein & Wallman, 2006; Levitt, 2004; Parker, 2008; Zimring, 2007 for in-depth reviews), we know that the crime drop was not universal. For example, Blumstein and Wallman (2006) discuss different patterns across age groups and note that the sharpest decline was for young offenders, while Parker (2008) documents how patterns differ along racial lines. Moreover, macrostructural research has revealed key factors relevant to the temporal trends in homicide rates, and race and ethnicity contin- ue to be among the most important predictors (Hipp, 2011; Peterson & Krivo, 2010; Parker, 2008).With these literatures inmind, this study ex- plores how both macrostructural features of cities and crime control strategies influence race-specific homicide trends overall and by trajec- tory group classification.

2. Racial violence and macrostructural conditions

At its core, economic and social conditions are key structural features of urban areas that receive much attention in the macro-level research on crime. Poverty, unemployment and/or the concentration of these economic disadvantages have been argued to be among the strongest predictors of urban homicide regardless ofwhether the level of aggrega- tion is the community, city, county, or state (Land, McCall, & Cohen, 1990; Phillips, 1997). Family disruption (via divorce) and residential in- stability are two other consistently strong and robust predictors of ag- gregate level crime and violence (see Land et al., 1990; McCall, Land, & Parker, 2010; Pratt & Cullen, 2005; Parker, 2008). For example, Pratt and Cullen's (2005) meta-analysis of structural predictors on crime rates identified family disruption (typically measured as “percent di- vorced”) among the “strongest and most stable” predictors of crime rates out of approximately 1984 effects sizes for ecological predictors in 509 statisticalmodels estimated from 214 differentmacro-level stud- ies (see Pratt & Cullen, 2005: 403). A key advancement in this literature is the racial disparities that exist in macro-structural conditions, which contribute to crime and urban violence (Peterson & Krivo, 2010).

As an example, Sampson and Wilson's (1995) review of the race- criminal violence relations literature highlighted how structurally in- duced disadvantages concentrated in poor black neighborhoods, exac- erbated by high levels of segregation and the development of cognitive landscapes that legitimate crime and violence. The unequal distribution of these conditions all go to the heart of racial differences in crime rates. As scholars have continued to examine the persisting ef- fects of structural differences (and cultural responses) between blacks andwhites, it has become clear that the sources of crime are remarkably invariant across groups (Peterson & Krivo, 2005, 2010). Rather, these groups face different social and economic realities which are the key to understanding the racial gap in crime rates (Hipp, 2011; Ousey, 1999; Parker & McCall, 1999; Parker, 2008). This important aspect of urban violence has been a strong theme in the literature, albeit largely missing from the debate about the crimedrop (see Parker, 2008 for sim- ilar arguments).

Another important consideration in this line of research is how His- panic population growth in U.S. cities has had profound effects onmany traditional correlates of crime, such as ethnic heterogeneity, local labor market conditions, and even the strength of the family (MacDonald & Sampson, 2012; Martinez, Rosenfeld, & Mares, 2008; Ousey & Kubrin, 2009; Sampson, 2008). Essentially there are ample theoretical reasons to expect shifts in economic, social and demographic characteristics of these areas to have important implications for temporal trends in homi- cide rates (MacDonald & Sampson, 2012; Ousey & Kubrin, 2014; Sampson, 2008; Wadsworth, 2010). Despite the fact that Hispanics often reside in communities that are characterized by a variety of criminogenic factors, research tends to show that the presence of

Hispanic immigrants in urban areas results in either a negligible or neg- ative effect on crime (see, for example MacDonald, Hipp, & Gill, 2013; Ousey & Kubrin, 2014) and may have contributed to the violent crime decline throughout the 1990s (Sampson, 2008; Stowell, Messner, McGeever, & Raffalovic, 2009; Wadsworth, 2010). For that reason, His- panic presence should be taken into consideration for its potential influ- ence on crime rates in general. Accordingly, our research extends these lines of analyses by applying latent trajectory techniques to white and black homicide trends 1980–2006 and then further exploring whether the changes in the composition of American cities, along with shifts in other macrostructural conditions, have contributed to distinct trajecto- ry group membership in homicide rates across racial groups.

3. Crime control and changing drug sale patterns

While differences in homicide rates across racial and ethnic groups have often been attributed to the unequal sorting of economic and social conditions across racial groups (Sampson, 2013), recent attention has focused on theways inwhich racial groupmembership and community may moderate the impact of crime control strategies (Bobo & Thompson, 2006; Borooah, 2011), and the race- and ethnic-specific ways that African Americans or Latinos frame their understanding of police, courts and corrections as result (Unnever & Gabbidon, 2011; Unnever, Barnes, & Cullen, 2016).

There is little doubt that crime control strategies play a role in tem- poral trends in homicide rates. Acknowledging the political and legal changes that occurred as policies shifted to a “get tough on crime” peri- od beginning in the late 1970s, the U.S. has witnessed unprecedented increases in imprisonment rates as well as growing police presence on city streets throughout the 1990s and into the 21st century. In fact, changes in policing and incarceration are the two most commonly de- bated factors associated with changes in American crime trends (Baumer & Wolff, 2014; Blumstein & Wallman, 2006; Levitt, 2004; Rosenfeld, 2016).

Joining others, the accumulation of evidence concerning the role of incarceration and police presence on the U.S. crime drop is quite con- vincing. Scholars have attributed estimates ranging from 10% (Western, 2006), up to a third of the crime decline (Levitt, 2004) to ris- ing imprisonment. Levitt (2004) goes on to also highlight the contribu- tion of policing to the crime decline. While he downplays the role of policing strategies such as the targeting of crime hotspots, he does ac- knowledge the role of the size of the police force on the streets. Claims about the role of crime control strategies like imprisonment and polic- ing on the American crime drop has been bolstered by others (Baumer, 2008; Eck & Maguire, 2000; Garland, 2001; Kubrin, Messner, Deane, McGeever, & Stucky, 2010; Rosenfeld, 2009; Zimring, 2007). Baumer and Lauritsen (2010), using National Crime Victimization Sur- vey data, provide further evidence of the role of policing byfinding a sig- nificant rise in citizen reporting during this time period, which enhanced the ability of police to effectively respond to crime.

The pressure on criminal justice agencies to remove not only violent but drug-related offenders from the streets may also partially explain the declining homicide trend between 1990 and 2000 (Blumstein & Wallman, 2006). Blumstein (1995) links drug markets, specifically the emergence of crack cocaine inmany cities through themid-1980s, to vi- olence in many urban neighborhoods throughout this period. Levitt (2004) also claims that the stabilizing of drug markets during the 1990s resulted in less urban violence. Ousey and Lee (2002) provide ad- ditional evidence that the illicit drug market (especially the crack-co- caine epidemic of this period) that peaked in early 1990s was related to homicide trends during this same time period.

Of course discussions of punishment policies during this time frame have raised concerns over the disproportionate effect of the get tough on drugs era on African Americans, the rates of black incarceration, and a set of law enforcement practices seen as unfair in many African American communities (Bobo & Thompson, 2006; Rosenfeld, 2016;

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Unnever & Gabbidon, 2011). The accumulation of evidence suggests that the criminal justice response through increased police presence and imprisonment, as well as the receding drug markets, are linked to declining rates of violence during the 1990s. Recent research, however, questions whether the criminal justice factors that influence African American offending are similar to those that influence other racial groups. The disproportionate use of these practices may have led to greater divergence in white and black trends. These practices are there- fore pertinent to our examination of homicide trends among racial groups. Furthermore, by incorporating a latent trajectory based ap- proach using separate analyses by racial groups, this study explores whether macrostructural covariates or crime control strategies lead to city-level trajectory placement in high homicide offending groups by race. This research provides additional insights by seeking to under- stand how these two perspectives impact temporal trends in homicides across racial groups. Specifically, we address the following research questions:

1. What is the degree and nature of hidden heterogeneity in temporal homicide trends? That is, are there distinct latent classes or trajecto- ries in city-level temporal trends for white and black homicide rates from 1980 to 2006?

2. Do macrostructural conditions or crime control policies distinguish group classification? How valuable are these two perspectives in ac- counting for the differences in the changes in race-specific homicide rates overall and across latent classes?

4. Data and methods

The homicide rates employed in the trajectory procedure are de- rived from the FBI's Supplemental Homicide File (Fox & Swatt, 2009). Race-specific homicide offenses reported to the police involving single offender-single victims were divided by the city's race-specific popula- tion to calculate thewhite and black offender homicide rates.1 Complete annual homicide data (1980 to 2006) and covariates (for 1980, 1990, 2000, and 2006) are available for 151 large U.S. cities with populations of 100,000 or more.2 The sources for covariates included in the study are: the U.S. Bureau of the Census data (1983, 1994, 2003), American Communities Survey, FBI's Uniform Crime Reports (Crime in America), and the Sourcebook of Criminal Justice Statistics.

4.1. Independent variables

The covariates we employ are based on common measures used in urban homicide studies (Land et al., 1990; Pratt & Cullen, 2005; McCall et al., 2011) and contemporary studies of immigration, crime control policies and changing homicide rates (Baumer & Wolff, 2014; Blumstein & Rosenfeld, 1998; Feldmeyer, 2010; LaFree, 1999; Levitt, 2004; Sampson, 2008). Prior studies have documented that under- standing the contextual basis for race and violence requires race-specif- ic measures of both the dependent variable and key explanatory variables (Phillips, 2002; Sampson &Wilson, 1995). The structuralmea- sures utilized in the present analysis are all race-specific and include: percent of families living below the poverty level, the Gini index (amea- sure of income inequality), percent of children not livingwith both par- ents, racial residential segregation (as measured by index of dissimilarity), the percent of the population of adult males who are di- vorced, and residential mobility (living in a different residence during the past 5 years). To capture industrial restructuring from 1980 to 2000, we include a race-specific ratiomeasure of service tomanufactur- ing industry employment. The percent Hispanic population is also in- cluded to account for the demographic shift occurring in recent decades that added to the population heterogeneity of these cities, as well as the proportion of the population who do not speak English well or not at all, indicating limited English proficiency.

Crime control policies and arrests for drug sales have surfaced as key covariates in the crime drop debate (Baumer &Wolff, 2014; Blumstein, 1995; Levitt, 2004; Kubrin et al., 2010; Zimring, 2007), but also impor- tant indicators leading to the temporal trends in violence over time. Whilemuch of this literature has focused on total homicide rates, we in- clude three measures to capture the relevance of these shifts on white and black homicide trajectories over time. First, the state-level, race- specific imprisonment rates (measured in 1979, 1989, and 1999) are in- cluded as a proxy indicator for the incapacitating effects of “get tough on crime” legislation introduced during these decades. While a state-level proxy measure of imprisonment is far from ideal, incarceration has played a key role in the crime drop debate, even though some studies have reported little to no relationship between changes in incarceration and crime (see Bird & Grattet, 2016; DeFina & Arvanites, 2002; Kovandzic & Vieraities, 2006; Raphael & Winter-Ebmer, 2001; Spelman, 2006, 2009). Because incarceration data at lower levels of ag- gregation are not available, a state level measure is commonly used by scholars examining homicide trends (Devine, Sheley, & Smith, 1988; Marvel & Moody, 1996; McCall, Parker, & MacDonald, 2008; Parker, 2004). Contemporary studies have also pointed to increased police presence as having an impact on homicide rates (Levitt, 2004; Marvel & Moody, 1996; Rosenfeld & Fornango, 2014; Weisburd et al., 2014; Zimring, 2011). Therefore, we include the number of police officers per capita in our models.

To capture the influence of the drug trade on homicides, we include a race-specific adult drug sale/manufacture arrest rate. While the use of arrest data has its limitations, when comparing arrest data with alterna- tive indicators (e.g., Drug Use Forecasting/Arrestee Drug Abuse Moni- toring and/or Drug Abuse Warning Network), research has reported high internal reliability among data sources and that these data sources yield similar estimates of drug activity when compared to drug arrests (Baumer, Lauritsen, Rosenfeld, & Wright, 1998; Rosenfeld & Decker, 1993; Warner & Coomer, 2003). Given that the alternative data sources are limited in sample size, we use drug arrests as a proxy for the level of drug activities across our sample of large urban cities.3 Drug sale arrest data have also commonly used in other longitudinal studies of homicide trends (see Ousey & Kubrin, 2014; Ousey & Lee, 2002; Strom & MacDonald, 2007). Three other covariates of homicide, total population size, percent black and southern region, were used to predict group membership in earlier stages of the latent trajectory estimation proce- dure. Total population size is, however, later re-introduced into the time series analysis estimating the effects of macrostructural conditions and crime control strategies on homicide rates.

Preliminary analyses indicated nonlinear relationships between race-specific homicide rates and the percent Hispanic population vari- able. To adjust for this nonlinearity, we used natural logarithmic trans- formations of the percent Hispanic population. And as commonly practiced in macro-level analysis, principal components analysis was conducted to reduce regressor space shared by these variables that comprised the economic deprivation index (percent family poverty, Gini index, racial residential segregation and percent of children under the age of 18 not living with both parents) and to minimize problems associated with collinearity such as the partialing fallacy. Importantly, racial residential segregation loaded with economic indicators in the black models but remained a separate predictor in the white models; a finding that represents the racial differences in how these measures tend to concentrate in urban communities and a factor loading scheme often found by other scholars (Messner & Golden, 1992; Parker & McCall, 1999; Parker, 2004). Finally, the principal components analysis identified another index that combined the percentHispanic population measure with the percent of residents speaking English either “not well” or “not at all”. These two measures are highly correlated, given that Hispanics comprise the majority of immigration patterns, as well as the population that is more likely to retain language loyalty in the home (Ousey&Kubrin, 2009). Consistentwithmore recent research ex- amining Hispanic immigration (Martinez et al., 2008; Ousey & Kubrin,

Table 1 Time predictors associated with three trajectory group membership for white and black homicide rates from 1980 to 2006. Betas, Z-values (in parentheses) and Wald statistic.

White homicide time model (N = 131)

Lowest Medium Highest Wald

Traj group Traj group

Traj group

Linear −0.0013 −0.1423 −0.2444 35.239⁎⁎

(−0.025) (−3.789) (−4.567) Quadratic −0.1588 −0.3632 −0.5552 61.609⁎⁎

(−1.614) (−5.251) (−5.593) Cubic −0.0114 0.0645 0.1394 14.987⁎⁎

(−0.274) (2.149) (3.210) Quartic −0.0114 0.241 0.3313 73.757⁎⁎

(2.212) (6.000) (5.712) Intercept −10.181 −9.278 −8.402 R2 0.0112 0.0917 0.1433 Overall model R2 0.512⁎

Black homicide time model (N = 144) Linear −0.122 −0.1637 −0.1768 43.141⁎⁎

(−1.169) (−4.447) (−4.186) Quadratic −0.0039 −0.1212 −0.1057 65.358⁎⁎

(−0.099) (−6.490) (−4.719) Cubic 0.0261 0.0564 0.0804 11.122⁎⁎

(0.463) (2.066) (2.512) Intercept −7.554 −7.006 −6.546 R2 0.000 0.2458 0.0926 Overall model R2 0.436

⁎ p b 0.05. ⁎⁎ p b 0.01.

Fig. 1. Display of homicide trajectory groups by race.

4 K.F. Parker et al. / Journal of Criminal Justice 47 (2016) 1–11

2009), this index is referred to as “Hispanic immigration” in ourmodels. All the indexes are computed as the sum of the variables weighted by their respective factor scores (Kim & Mueller, 1978).

We used Latent Gold (version 4.0) statistical package to identify la- tent classes and find evidence of any hidden heterogeneity among the cities with respect to the temporal trends in white and black homicide rates over time. If evidence is found, we can then determine the optimal number of latent groups or classes of cities and the nature of the race- specific trajectories for city groups. For individuals, this technique has been used to identify a set of developmental trajectories typically based on offending patterns and these trends are used to assign individ- uals with like offending patterns to discrete trajectories or classes. For our purposes, the latent trajectory estimation procedure identifies cities that share unique white and black homicide trends into groups or clas- ses. After cities are classified into discrete groupings, we plot the trajec- tories for each racial group for visual comparison. Despite the popularity of trajectory analyses in social science research, there is no agreed upon best method to identify the number of trajectory groupings or assigning observations (in this case, cities) to a specific group. We recognize that different methods used by different researchers could produce differ- ences in the number of trajectories and assignment of cities to trajectory groups (Warren, Luo, Halpern-Manners, Raymo, & Palloni, 2015). Nev- ertheless, this stage of our analysis will allow us to determine if a latent trajectory estimate procedure is useful when identifying distinct race- specific homicide trajectories in our sample of large U.S. cities. By apply- ing this technique, we will learn more about heterogeneity in race-spe- cific homicide temporal trends, as well as whether cities differ in the trajectory classification by racial group between 1980 and 2006.

The second stage of our analysis allows us to directly examine tem- poral trends in race-specific homicide rates. Using a multilevel pooled cross-sectional time series design, we determine whether race-specific predictors of macrostructural characteristics or crime control strategies contribute to explaining the variation in thewithin-city changes in race- specific homicide rates for the large sample of U.S. cities but also within the highest and within the lowest latent groups. That is, using annual data between 1980 and 2006, we estimate cross-sectional time series models to identify the factors that predict temporal trends for the highest and lowest latent classes, and report the statistically significant differences between them. This allows us to extend prior work showing the value of the trajectory technique (McCall et al., 2011) by (1) assessing the effect of covariates on the distinct white and black homi- cide trends and (2) then determining whether predictors contributing statistically significant variation to those race-specific homicide trends have significantly different effects on higher rate trends vis a vis lower rate homicide trends.

5. Results

5.1. Step one: latent class trajectory analysis

Our research employs a latent trajectory technique on white and black homicide offending rates from 1980 to 2006 in our attempt to es- timate which cities fall into high versus low trajectory groupings while allowing for city compositional difference by the racial group. Table 1 displays parameter estimates generated from the latent trajectory esti- mation procedure for white and black homicide rates. As Bollen and Curran (2006) discuss, approximating functional forms of trajectories is best done on the basis of theory, testing hypothesized forms rather than approximating trends in an exploratoryway. To this end,we tested fourth-order temporal models because the national trend between 1980 and 2006 had four bends in the temporal curve.

The estimates at the top of the Table 1 represent the white model with three latent trajectories and a polynomial of the fourth order in time. The model estimated below it displays those results produced for African Americans, showing three latent trajectories based with a third degree polynomial. The complexity of the polynomial models is

necessitated by turning points in the temporal trends that differ for white and black homicide rates across the decades included in the anal- ysis (see Fig. 1a and b). Simply put the fitted curves or functions that best fit the data are different by racial group. That is, the quartic (4th order polynomial) function was significant for all white trajectory groups and thus the quartic specification was chosen—adding a slight increase in homicide rates for whites for the early years of 2000 that

5K.F. Parker et al. / Journal of Criminal Justice 47 (2016) 1–11

was not found for the black homicide trajectories. Therefore, the cubic model was chosen for the black homicide trajectory groups given the distribution of a polynomial in the 3rd order. A three latent class model was chosen for both racial groups because of the fit to the data using BIC scores as a criterion (Raftery, 1995).4 Other more parsimoni- ousmodels were considered, but the nuances of variation in the tempo- ral trends were lost with simpler model specifications. Covariates were used in this estimationprocedure to establish thebaseline, including the measures of total population size, percent black and a regional code of South.

Fig. 1a and b display the predicted trends in white and black homi- cide rates for the three classes of trajectories identified in Table 1—showing white homicide rate trajectories and black homicide rate trajectories, respectively – in addition to the overall white and black ho- micide trends for comparison. Based on sample percentages of cities classified in each group displayed in Fig. 1a, 45% of cities would be con- sidered in the low white homicide rate group, 35% are classified as me- dium and 25% of cities are found within the high white homicide rate group trajectory. In Fig. 1b, 38% of the cities are found in the low black homicide trajectory group, followed by 36% as medium and 26% cites in the high black homicide trajectory group.

The graphs also display the relative variation in patterns for these trajectories across racial groups. That is, there are differences among the trajectories in the degree of fluctuations, the curves, and themagni- tude of the homicide rates characterizing each class. From the predicted trends displayed in Fig. 1a, we see that, by and large, a steeper decreas- ing slope is associated with the highest white homicide rate trajectory group throughout the 1980s compared to the average white homicide trend during that time, with a slight increase beginning around 1987. In 1993 begins a steady continuous decline for this group through the end of the 1990s and into the 2000s with an upward turn around 2003. The magnitude of homicide rates characterizing the medium white group more closely mirror the average white homicide rate for all cities. In terms of fluctuation, however, the medium and low groups are parallel, by and large, with muted variation when compared to the high rate group.

Examining the trends displayed in Fig. 1b, we see a marked contrast with the trajectories for thewhite homicide rates, driven by a higher av- erage black homicide rate showing amore noticeable incline during the 1980s, and decline throughout the 1990s. The high and medium black homicide rate trajectories exhibit this same pattern over time. Both the high and medium trajectory groups show a steep incline in homi- cides during the 1980s, followed by a steady decline beginning around 1988, throughout the 1990s and into themid-2000s. The low trajectory

Table 2 Descriptive statistics with sample means (and standard deviations) by trajectory group memb

White models Traj group 1 (low)

Economic disadvantage index⁎ −16.93 (9.54) Racial segregation (index of diss.)⁎ 50.82 (15.05) Industrial restructuring⁎ 0.846 (0.345) Divorced males⁎ 8.19 (1.49) Hispanic immigration index⁎ 8.09 (6.91) Incarceration rate⁎ 0.460 (0.145) Drug sales arrest rate⁎ 40.03 (37.11) Police presence 196.55 (58.87) Total pop size 217,595 (126,725)

Black models Traj group 1 (low) Economic disadvantage index⁎ 44.64 (26.53) Industrial restructuring⁎ 1.27 (1.29) Divorced males⁎ 9.64 (2.59) Hispanic immigration index⁎ 15.34 (16.24) Incarceration rate⁎ 0.41 (0.148) Drug sales arrest rate⁎ 36.21 (57.74) Police presence 177.88 (57.06) Total pop size 187,749 (116,734)

group, on the other hand, exhibits a steady trend until 1988 and a slight yet continuous decline over the remaining period. An interesting point of comparisonwith thewhite high group is the timingwhen the decline during the 1990s begins; that is, the white high rate group begins their “crimedecline” in 1993whereas the black high andmedium rate groups begin their “crime decline” in 1988 (Messner, Deane, Anselin, & Pearson-Nelson, 2005). Overall, the black homicide trends are higher than white homicide trends. For example, low-rate black homicide tra- jectory is still higher in magnitude than the white homicide rate in the highest trajectory class.

We list the U. S. cities comprising the “low”, “medium” and “high” white and black homicide trajectory classifications in Appendix 1. Ex- amining the cities of each classification for commonalities is a difficult task given the race-specific nature of the analysis, but similarities are found in a large number of the cities that form the trajectory classes across racial groups. First “university towns” tend to cluster in the low homicide rate trajectory groups more so than in medium or high groups. McCall et al. (2011)study also found a relatively large propor- tion of “university towns” cluster in the low homicide rate groups.

In terms of the high homicide trajectories, there are commonalities in the cities that comprise this classification as well. Cities such as Los Angeles, Atlanta, Chicago, Gary, New Orleans, Detroit, Las Vegas and NewarkNJ are found in this trajectory across the racial groups. These cit- ies have garnered significant attention in criminological and economic/ urban sociology literatures, as they are places that have experienced sig- nificant racial composition and economic shifts over time. Los Angeles comprises the largest Hispanic (largely Mexican) population, wherein 9% of the entire U.S. population who identifies as Hispanic (foreign but largely U.S. born) resides (Rytina, 2009). Detroit and Gary are cities where the removal of manufacturing jobs has contributed to significant unemployment and economic declines, while New Orleans and Las Vegas have experienced significant population and economic fluctua- tion in recent decades. Given the dramatic changes to the urban econo- my, aswell as the influx of populations, these cities aremore likely to be found in higher homicide trajectory groups than their counterparts.

Last, Table 2 furthers our examination of the U.S. city based classes identified in the latent trait analysis by providing descriptive statistical information for each trajectory group by race. The statistical information is displayed for whites at the top of the table, followed by African Amer- icans. For both racial groups, the high trajectory group comprises cities with the greatest economic deprivation, family disruption and industri- al restructuring, relative to the low and medium trajectory groups. The high trajectory groups are also the most residentially segregated cities racially and have the largest percentage of Hispanics facing language

ership for racial groups.

Traj group 2 (medium) Traj group 3 (high)

−9.83 (8.98) −5.66 (10.95) 59.66 (15.10) 63.32 (12.32) 0.835 (0.273) 0.922 (0.492) 9.27 (1.83) 9.28 (2.33)

17.62 (17.83) 27.46 (18.35) 0.447 (0.132) 0.382 (0.108) 62.23 (64.31) 71.94 (55.33)

229.44 (81.38) 259.64 (102.30) 347,754 (288,995) 966,355 (1,559,522)

Traj group 2 (medium) Traj group 3 (high) 77.98 (16.40) 77.56 (21.07) 1.44 (0.649) 1.64 (1.14) 9.7 (2.19) 10.74 (2.56)

12.76 (12.44) 17.65 (17.81) 0.45 (0.153) 0.41 (0.173)

70.69 (87.40) 125.49 (160.94) 227.51 (64.81) 259.38 (108.87)

459,389 (1,027,725) 592,180 (708,385)

Table 3 Multilevel mixed effects cross-sectional pooled time series regression estimates with [Z scores] and (Robust standard errors) for white homicide rates within large U.S. cities, within high and within low latent trajectory classification.

All cities High Traj class

Low Traj class

Coefficient comparison test high vs. low

Macrostructural conditions Economic disadvantage indexa

0.022⁎⁎ 0.021⁎⁎ 0.007⁎⁎

[8.06] [6.60] [3.02] 3.88⁎⁎

(0.002) (0.003) (0.002) Racial segregationa 0.012⁎⁎ 0.024⁎⁎ 0.002

[9.76] [6.29] [0.67] 4.92⁎⁎

(0.001) (0.004) (0.002) Industrial restructuringa

−0.166⁎⁎ −0.124 −0.237⁎⁎

[−4.30] [−1.81] [−3.84] 1.20 (0.039) (0.069) (0.064)

Divorced malesa 0.092⁎⁎ 0.148⁎⁎ 0.061⁎⁎

[14.68] [10.83] [5.02] 4.72⁎⁎

(0.006) (0.014) (0.012) Residential mobility

−0.003⁎ −0.013⁎⁎ −0.001 [−2.26] [−3.34] [−0.05] −3.33⁎⁎

(0.001) (0.003) (0.002) Hispanic immigration index

0.032⁎⁎ 0.034⁎⁎ 0.007 [30.52] [20.13] [1.84] 6.04⁎⁎

(0.001) (0.002) (0.004) Crime control and arrest for drug sales Incarceration ratea −0.025 0.396⁎ −0.300

[−0.24] [1.87] [−1.80] 2.58⁎⁎

(0.102) (0.212) (0.167) Drug sales arrest ratea

−0.001 −0.001 0.001 [−1.22] [−1.62] [0.82] (0.001) (0.001) (0.001)

Police presence 0.001 −0.001⁎ 0.001 [0.51] [−2.02] [0.49] −1.41 (0.002) (0.001) (0.001)

Population size (log)

0.109⁎⁎ −0.053 −0.022 [5.39] [1.65] [−0.50] (0.020) (0.032) (0.045)

Log likelihood −2205.29 −280.13 −803.55 N 2335/131 446/26 867/59

⁎⁎ p b 0.01. ⁎ p b 0.05. a Denotes measure is race-specific.

6 K.F. Parker et al. / Journal of Criminal Justice 47 (2016) 1–11

barriers. These cities comprise some of the largest population sizes in our sample, such as Los Angeles and Chicago, and also represent some of the largest percentages of police officers per capita. Arrests for drug sales are among the highest for this trajectory group regardless of race, but the incarceration rate is lower than most other trajectory groupings. A quick comparison of the means across racial groups sup- ports previous findings that African Americans face much higher levels of disadvantage relative to whites (Krivo & Peterson, 2000; Parker & McCall, 1999; Sampson & Wilson, 1995), supporting the need for a race-specific investigation of homicide trends (see also Phillips, 2002).

Thus, with regard to our first research question, we find that the group based trajectory approach produces evidence of unique homicide trajectories that characterize relatively homogeneous groups of U.S. cit- ies with respect to trends in homicide rates for the period 1980 to 2006, as well as evidence of heterogeneity among the entire set of cities with respect to temporal trends by racial groups. In addition, the fact that the grouping of cities displays relatively different temporal trends by race over the time period requires additional research into which macro- level forces are influencing these classifications of homicide trajectories revealed in our latent trait analyses. Given evidence of heterogeneity and significant variation in race-specific homicides, we further investi- gate these perspectives using a time series approach.

5.2. Step two: multilevel time series analysis

In this stage of the analysis,we usemultilevelmodels in a time series cross-sectional (TSCS) analysis to determine if eithermacrostructural or crime control strategies contribute to the within city changes in race- specific homicide rates over time. This method is applicable to the pres- ent research questions given the temporal hierarchy in the data, where measurement occasions are nestedwithin cities (Beck & Katz, 2007). As Beck and Katz (2007) show, multilevel/random effects models perform better with TSCS data than alternative models, as they allow for the es- timation of city-level time-invariant parameters, in addition to observed time-variant characteristics. After performing time series analysis of the changes in black and white homicide rates for the large sample of U.S. cities as a baseline model, we further our investigation by estimating cross-sectional time seriesmodels for thehighest and also for the lowest trajectory classes by racial group. This additional analysis allows us to more closely examine our central research question by identifying the factors that predict temporal patterns within latent groups and observe any differences by race. Before discussing the results displayed in Tables 3 and 4, we strengthen our estimation by accounting for two important statistical issues.

First, we test for the presence of unit roots (or non-stationarity) in our panel data set. Although there are several tests we could have used, we chose to use the Harris and Tzavalis (1999) test because our time dimension is small (21 years, from 1980 to 2000), and we have a relatively large number of cases in our panel (N = 151). Using the xtunitroot command in Stata (version 13), we test the null hypothesis that panels contain unit roots against the alternative hypothesis that panels are stationary. Cross-sectional means were removed to control for contemporaneous correlation using the demean option. Statistically significant results of the HT test lead us to reject the null hypothesis and conclude that neither the black nor white homicide series contain unit roots.5 As such there are no obvious non-stationarity issues in either the black or white homicide trajectories. Second, we provide a formal test for statistically significant differences between the high and low la- tent trajectory classes to further our research aimof establishinghetero- geneity. Using the formula by Paternoster et al. (1998), we calculate and report the coefficient comparison test of differential impact of predic- tors on high versus low trajectory classification by racial group. This sta- tistical test is ideal given the assumption of independent samples.

In Table 3, the panel results show how changes in macrostructural and crime control strategies are related to the changes in white homi- cide rates. The results for the full sample of cities are displayed in

Model 1, followed by cross-sectional time series estimates identifying the factors that contribute to changes in white homicide rates for those cities within the high rate trajectory (Model 2) and low rate tra- jectory placements (Model 3). Examining Model 1, we find changes in all six macrostructural conditions are significantly related to changes in white homicide rates from 1980 to 2006, whereas none of the crime control indicators reach statistical significance. Turning attention toward the latent class specific analyses, we find in Model 2 that most macrostructural conditions and crime control are significantly related to changes in white homicide rates within the high rate trajectory class, with the exception of industrial restructuring and drug sales ar- rest. On the other hand, in Model 3 only a few structural conditions (economic disadvantage, industrial restructuring and family disruption) are related to changes in white homicide rates among those cities in the low rate trajectory, and crime control and drug sales arrest are unrelat- ed to changes in white homicide rates in this trajectory. The coefficient comparison test shows further evidence of the significant differences in the predictors onwhite homicide rates in the high versus low trajectory groups. Almost all themacrostructural conditionswere significantly dif- ferent and had a stronger effect in the high rate model than the low rate model, and the incarceration rate also had a stronger effect on the high rate trajectorymodel. This formal test reveals greater evidence of statis- tically significant differences in macrostructural conditions than among the crime control and drug sales indicators. For white homicide trends, the vast majority of the predictors are among the macrostructural con- ditions vis-a-vis the crime control and drug sales arrest indicators.

Table 4 Multilevel mixed effects cross-sectional pooled time series regression estimates with [Z scores] and (Robust Standard Errors) for black homicide rateswithin large U.S. cities,with- in high and within low latent trajectory classification.

All cities High Traj class

Low Traj class

Coefficient comparison test high vs. low

Macrostructural conditions Economic disadvantage indexa b

0.002⁎ 0.002 −0.000 [2.22] [0.16] [−0.16] (0.001) (0.001) (0.002)

Industrial restructuringa

−0.081⁎⁎ −0.072⁎⁎ −0.015 [−4.41] [−3.20] [−0.32] −1.09 (0.018) (0.022) (0.047)

Divorced malesa 0.045⁎⁎ 0.025⁎ −0.001 [7.03] [1.90] [−0.18] 1.53 (0.007) (0.013) (0.011)

Residential mobility

0.004⁎ 0.010⁎⁎ 0.001 [2.27] [3.57] [0.035] 2.12⁎⁎

(0.002) (0.003) (0.003) Hispanic immigration index

−0.001 −0.002 0.002 [−0.12] [−1.21] [1.41] (0.001) (0.002) (0.002)

Crime control and arrest for drug sales Incarceration ratea −0.519⁎⁎ −0.362⁎ −2.00⁎⁎

[−4.36] [−1.96] [−7.79] 5.09⁎⁎

(0.119) (0.194) (0.257) Drug sales arrest ratea

0.001⁎⁎ −0.000 0.001⁎⁎

[3.22] [−0.18] [3.05] 1.00 (0.000) (0.000) (0.000)

Police presence 0.001⁎⁎ 0.001⁎⁎ −0.002⁎⁎

[3.38] [2.18] [−2.35] 3.00⁎⁎

(0.000) (0.000) (0.001) Population size (log)

0.070⁎⁎ 0.035 −0.339⁎⁎

[3.58] [1.03] [−4.88] 4.97⁎⁎

(0.019) (0.030) (0.069) Log likelihood −2021.92 −460.55 −650.88 N 2089/144 630/37 616/55

⁎⁎ p b 0.01. ⁎ p b 0.05. a Denotes measure is race-specific. b Racial residential segregation is included in economic deprivation index.

7K.F. Parker et al. / Journal of Criminal Justice 47 (2016) 1–11

In Table 4, threemodels are provided in our investigation of changes in black homicide rates. Similar to the white models, Model 1 displays the cross-sectional time series results for the total sample, while the tra- jectory specific results are shown in Models 2 and 3. In Model 1, all but one of the macrostructural conditions and all of the crime control and drug sales arrest indicators are related to changes in black homicide rates. The only exception is Hispanic immigration which exhibits a null effect on black homicide rates. Among those cities found in the high trajectory class (Model 2), we continue to find macrostructural conditions and crime control predictors exhibit significant influence on black homicide trends, although drug sales arrest, economic disad- vantage and Hispanic immigration do not reach statistical significance. Finally, in Model 3, none of the structural predictors have a significant effect, whereas the crime control and drug sale indicators are related to changes in black homicide rates over time. The formal test for statis- tical significant differences in the predictors for high versus low trajec- tory classifications reveal few differences, especially relative to the tests conducted for differences between the two white models. Specifi- cally, residential mobility, the incarceration rate and police presence had a stronger effect in the high black homicide rate model than in the low rate model. Moreover, differences between the high and low ratemodels were found for crime control versusmacrostructural condi- tions in the blackmodels. That is, a greater proportion of the crime con- trol and drug sales predictors predicted black homicide trends than did the macrostructural conditions.

Overall, there are some themes or general patterns in the findings based on the time series model results. First, our results illustrate the

important role of macrostructural conditions and crime control strategies as they contribute to race-specific temporal trends in homicide rates. There is significant heterogeneity among American cities in homicide trends by racial groups and city trajectories. For example, while these findings suggest macrostructural conditions are generally more relevant to changes in homicide rates over time than crime control strategies and drug sales arrests, crime control and drug sales indicators are more relevant to our understanding of homicide trends in high trajectory than low trajectory placement and to black homicide than white homicide. That is, crime control strategies and drug sales arrest are most relevant to homicide trends in cities within the highest trajectory classification and for blacks as compared to whites. Another important theme revealed in this work are the findings concerning Hispanic immigration. Hispanic immi- gration is significantly related to changes in white homicide rates in the time series analyses of overall and high rate trajectory models but unrelated to changes in black homicide rates regardless of trajectory classification. The implications of these findings are addressed in the concluding remarks below.

6. Conclusion

As race remains one of the most robust correlates of homicide and violence in the U.S., we examined the underlying factors accounting for the racial differences in U.S. homicide trends during the latter part of the 20th century and into the early years of the 21st century. Firstly, we determined if a latent trait approach could advance our understand- ing of temporal trends in homicide rates during a critical period of time, 1980 to 2006.Moreover, we examinedwhether distinct latent classes or trajectories in city-level temporal trends differed for white and black homicide rates. With this objective in mind, we utilized a latent trajec- tory approach on the temporal trends in city-level race-specific homi- cide rates from 1980 to 2006. The result of that analysis revealed three distinct trajectory groups for each racial group studied here, suggesting a group-based approach was appropriate for identifying hidden hetero- geneity for race-specific homicide trends at the city-level. This finding also highlights the benefit of this approach as distinct trends or trajecto- ries would not be readily apparent using other statistical methods (see Brame, Paternoster, & Piquero, 2012 for other arguments on the useful- ness of this particular technique). Additionally, the general shape and slope of the trajectories emphasize the complexities underlying the crime drop, especially the stark differences of homicide trends for each racial group.

In terms of these complexities, for example, the latent trajectory ap- proach reveals that in our sample of large U.S. cities, a relatively large proportion of cities fit within the low trajectory classification, where no evidence of a dramatic “crime drop” of the 1990s was found. In fact, almost half of the cities were in the white low rate group and over a third in the African American low homicide rate trajectory. These lower homicide rate classes, accordingly, were associated with relatively lower levels of racial isolation, economic disadvantage, family disruption, and Hispanic immigration when compared to city member- ship in higher rate trajectories.

Another complexity revealed by the latent trajectory approach is the different shapes andmagnitudes of the fitted curves across the trajecto- ries for each racial group. As detailed earlier, the primary distinction within the race-specific group trajectories is the steepness of the slopes, but the contrasting trends are striking as well. For the two higher black homicide rate trajectories, we find an increase at the beginning of the series and then a steady, continuous decline in homicides from the late 1980s to 2006 (with the decline for the low rate group beginning in 1983). On the other hand, we discover a vacillating trend for the white trajectories—first declining until around 1986, upward until 1994when it begins a “crime decline” and then increasing again around 2003. This finding provides support for those claims that the crime drop should be examined more closely at the local level, and efforts to

8 K.F. Parker et al. / Journal of Criminal Justice 47 (2016) 1–11

understand the nature of the crime drop in one locale as compared to others warrants attention (Baumer & Wolff, 2014; Zimring, 2007). It also raises the possibility that some arguments for the crime decline may better explain trends by racial group (such as enhanced penalties for crack cocaine related crimes). The application of this research fur- thers the current crime drop literature by identifying differences that appear across racial groups even though the high trajectory groups comprise a similar percentage of the city sample (about a quarter of the cities) and a number of the same cities (e.g., Los Angeles, Atlanta, Chicago, Detroit and Dallas).

This finding led us to investigate further the reasons for these temporal trends by estimating cross-sectional time series models to identify the factors that predict temporal patterns within latent groups and to observe any differences by race. That is, in this paper, we not only reveal hidden heterogeneity in city homicide trends by race, but we used a time series approach to address the questions: Do macrostructural conditions or crime control policies contribute to racial homicide trends? Do these perspectives ex- plain cities being placed within the highest trajectory classifica- tion? Do they show important differences by racial group? Significant effects for both macrostructural conditions and crime control strategies on trajectory placement were found, with some interesting caveats.

First, while it is well established that economic disadvantage is one of the strongest and most consistent predictors of homicide rates (Land et al., 1990;McCall et al., 2010; Phillips, 2006) and trajec- tory group membership (Griffiths & Chavez, 2004; McCall et al., 2011; Stults, 2010), there are significant racial differences in the im- pact of economic disadvantage on homicide trends once trajectory membership is accounted for. The economic disadvantage index had a significant impact on the changes in white homicide rates across the three models, while this index did not contribute to the change in black homicide rates within trajectory classification (only significant in the total model). Another indicator of economic instability, industrial restructuring, had a statistically significant, inverse effect on the changes in racial homicide trends in both the white and black total models, but statistical significance varied across trajectory and racial groups. That is, industrial restructuring was inversely related to the change in white homicide rates in the low trajectory group, but not related to black homicide rates within this classification. Rather, it contributed to the changes in black homicide rates for cities placed within a higher trajectory class. These findings reflect the multiple disadvantages within U.S. cities that directly limit the socioeconomic wellbeing and resources facing African Americans, leading to challenges for this group in the form of heightened violence, but also increasing the probabilities that cities will be placed within low or high homicide trajectory groups.

For whites, economic disadvantage, racial segregation and industrial restructuring were each strongly related to homicide trends. Further- more, based on the coefficient comparison test, these indicators signifi- cantly distinguished city classification across the trajectory groups. On the other hand, while economic disadvantage influenced black homi- cide rates overall (Model 1), industrial restructuring had amore delete- rious impact for African Americans than whites, contributing to cities being placed in the highest trajectory classification (Wilson, 1987; Parker, 2008). Hispanic immigration, on the other hand, contributed to the change in white homicide trends overall, in addition to white ho- micides in the highest trajectory group. The Hispanic immigration index was not related to black homicide trends in any of the three models. While a finding of racial differences in the estimated effect of Hispanic population growth is consistent with some recent work (Parker & Stansfield, 2015), previous studies also lead us to be cautious when interpreting this claim as we discuss in more detail below (Steffensmeier, Feldmeyer, Harris, & Ulmer, 2011).

A second major finding is that macrostructural conditions are more strongly associated with white homicide trends overall and by

trajectory group placement than crime control strategies, yet both perspectives are equally important in addressing black homicide trends. In the white models, our measures of incarceration rates, drug sales arrests and police presence did not reach statistical signif- icance, with the limited exception of two significant predictors in the highest trajectory groupmodel only. On the other hand, indicators of crime control and drug sales had statistically significant effects on black homicide trends in the overall models and based on trajecto- ries. The findings, or lack thereof, concerning crime control and drug sale policies on white homicide trends mirrors cautions in pre- vious work about a deterrent effect of criminal justice interventions (Nagin, 2013; Baumer & Wolff, 2014). Our research does suggest, however, significant racial differences, which have been neglected in previous studies. While a number of studies report little to no re- lationship exists between prison growth and crime trends (see DeFina & Arvanites, 2002; Kovandzic & Vieraities, 2006; Raphael & Winter-Ebmer, 2001; Spelman, 2006, 2009), such a claim might only be true for whites. Police presence and drug sales arrests were positively related to black homicide trends overall and by city trajec- tory group. These findings are consistent with the notion that cities with heavy drug trafficking and drug turf wars had high homicide rates during the 1980s and early 1990s (Blumstein & Wallman, 2006; Ousey & Lee, 2002). Additionally, we find general evidence that greater police presence influences black, but not white, homi- cide trends. We surmise that the influence of police presence in the black models is reflective of the disproportionate police attention received by low-income and minority communities (Bobo & Thompson, 2006), however our measure of police presence does not capture police activity directly. As research on crime trends con- tinues to expand (including more recent debates about the role of de-policing activity following Ferguson and other controversial po- lice use of force incidents) and limitations on existing data are ad- dressed, more definitive conclusions may emerge about the role of race in crime control strategies (Rosenfeld, 2016).

There are some limitations to this study, in addition to those mentioned above. First, our measures of the covariates of homicide are summary measures only and intercensal measures are derived by interpolation. Nevertheless, this provides general levels of social and economic factors that we find to be corroborated for the most part in this analysis. The purpose is to predict classification of cities into trajectories with relatively distinct homicide rates for racial groups and these summary measures serve that purpose. A second data limitation involves the missing data issues associated with SHR homicide counts and the inability to distinguish between of- fenders (or victims) as Hispanic or non-Hispanic. As mentioned above, we caution against strong conclusions regarding Hispanic im- migration because it appears the large influx of immigrants in recent decades may be confounded in the white models as an increasing number of Hispanics are identified as white in homicide statistics.6

Furthermore, as Hispanic migration increased during this time frame in many American cities, this could have contributed to con- founded census estimates of the declining average economic levels of whites, thereby increasing the odds of those cities being found within the higher trajectory group.

We also acknowledge our inability to separate out homicide trajec- tories by age. Data reveal that the crime declines experienced since the early 1990s included very different patterns in youth violence trends specifically (Blumstein & Wallman, 2006). Disentangling the story of city-variations in race-specific homicides by age would be a complex, yet fruitful endeavor for future research. In addition to age, there are a number of important ways of disaggregating homicide trends that might be important for future work. Given the importance of young people in shaping crime patterns in the US, it is also notable that this study could not capture youth engagement with conventional institutions such as higher education and employment among race-spe- cific groups.

9K.F. Parker et al. / Journal of Criminal Justice 47 (2016) 1–11

These limitations aside, the present city-level study demon- strates that a latent trajectory approach, which illustrates the relative uniqueness in temporal trends by revealing hidden hetero- geneity among race-specific homicide trends in a larger sample of U.S. cities, can play an instrumental role in future research on tem- poral crime patterns and the racial nature of violence in American cities specifically. Through revealing hidden heterogeneity in homicide rates over time by place and racial group, these findings

Appendix 1 List of U.S. cities by trajectory membership for racial groups sorted alphabetically by state and

White trajectory model cities (N = 131)

Low (N = 59) Medium (N = 46) High (N = 26) Huntsville Mobile Birmingham Anchorage Tucson Phoenix Tempe Little Rock Fresno Berkeley Anaheim Long Beach Concord Bakersfield Los Angeles Fremont Oxnard Oakland Fullerton Pasadena Sacramento Glendale Riverside San Bernardino Modesto San Diego Santa Ana Sunnyvale San Francisco Stockton Aurora San Jose Bridgeport Colorado Spring Denver Hartford New Haven Louisville Atlanta Stamford Baltimore Chicago Waterbury Springfield Gary Columbus Flint New Orleans Savannah Jackson Detroit Evansville Kansas City Las Vegas Fort Wayne St. Louis Newark Indianapolis city Reno Paterson South Bend Elizabeth New York Cedar Rapids Jersey City Columbus city Des Moines Albuquerque Dallas Lexington-Fayette Rochester Fort Worth Baton Rouge Cleveland Houston Shreveport Dayton San Antonio Boston Oklahoma City Worcester Tulsa Ann Arbor Allentown Grand Rapids Philadelphia Lansing Providence Minneapolis Chattanooga St. Paul Knoxville Springfield Memphis Lincoln Nashville-Davidson Buffalo Amarillo Syracuse Austin Yonkers Beaumont Charlotte Corpus Christi Greensboro El Paso Raleigh Lubbock Winston-Salem Waco Cincinnati Portsmouth Toledo Richmond Portland Tacoma Erie Milwaukee Pittsburgh Arlington Garland Irving Alexandria Chesapeake Hampton Newport News Norfolk Virginia Beach Seattle Spokane Madison

highlight the challenges that must be acknowledged in managing the future direction of crime trends, as some groups in some cities will undoubtedly continue on a high criminal trajectory, while others experience stabilization or declines. Combining trajectory based procedures with time series analysis in this systematic study proved to be fruitful to understanding how changes in urban contexts account for distinct patterns of racial differences in homicide trends.

city within state.

Black trajectory model cities (N = 144)

Low (N = 55) Medium (N = 52) High (N = 37) Huntsville Birmingham Phoenix Anchorage Mobile Little Rock Mesa Tucson Bakersfield Tempe Berkeley Long Beach Anaheim Fresno Los Angeles Concord Modesto Oakland Fremont Pasadena San Bernardino Fullerton Riverside San Francisco Garden Grove Sacramento Santa Ana Glendale San Diego Stockton Huntington Beach Aurora Atlanta Oxnard Colorado Spring Honolulu San Jose Denver Chicago Sunnyvale Bridgeport Gary Torrance Hartford New Orleans Lakewood Savannah Baltimore New Haven Fort Wayne Detroit Stamford Indianapolis city Flint Waterbury South Bend Warren Columbus Louisville Minneapolis Boise City Baton Rouge Kansas City Evansville Shreveport St. Louis Cedar Rapids Boston Las Vegas Des Moines Grand Rapids Newark Lexington-Fayette Lansing Albuquerque Springfield St. Paul Columbus city Worcester Jackson Philadelphia Ann Arbor Elizabeth Knoxville Sterling Heights Jersey City Amarillo Independence Buffalo Dallas Springfield New York Fort Worth Lincoln Rochester San Antonio Reno Charlotte Salt Lake City Paterson Winston-Salem Richmond Syracuse Cleveland Spokane Yonkers Dayton Tacoma Greensboro Toledo Milwaukee Raleigh Oklahoma City Cincinnati Tulsa Eugene Portland Allentown Pittsburgh Erie Providence Arlington Chattanooga Austin Memphis Beaumont Nashville-Davidson Corpus Christi Houston El Paso Lubbock Garland Waco Irving Newport News Pasadena Norfolk Alexandria Portsmouth Chesapeake Seattle Hampton Virginia Beach Madison

10 K.F. Parker et al. / Journal of Criminal Justice 47 (2016) 1–11

Notes

1 Previous research on race-specific homicide rates has acknowledged some problems with race-specific homicide data from the SHR, including limitations arising from homi- cide cases where the offender(s) is unknown and from those SHR data which are submit- ted at early stages of investigation thereby based on incomplete or inaccurate information (Messner & Golden, 1992). Given that our homicide counts are disaggregated by race of the offender, data with multiple imputations was preferred to address item missingness on offender characteristics. Fox and Swatt (2009) specifically implemented amultiple im- putation approach based on a log-linear model for incomplete categorical data. Our data represent the average annual race-specific homicide counts across 5 different imputations generated by Fox and Swatt (2009). Although our analyses proceed with single offender/ single victim data with imputed offender characteristics, a recent study addressing the quality and use of race-specific SHR data has concluded that empirical findings and con- clusions about city-level covariates of race-specific offending rates are less sensitive to the selection of a specific data source (Messner, Beaulieu, Isles, & Mitchell, 2014).

2 In preparation for estimating a multilevel mixed effects pooled time series analysis used in this study, annual estimates ofmacro structural predictors and crime control mea- sures were generated using linear interpolation between 1980, 1990, and 2000 (e.g. Xie, Lauritsen, & Heimer, 2012).

3 There are few ideal measures for capturing the drug trade that became associated with the dramatic rise in homicides during the late 1980s and early 1990s. Nevertheless, this measure is one of the best available for this phenomenon. We include all drug sale/ manufacture arrests because the period covers more than just the 1980s when crack-co- caine was introduced to the drug market. See Ousey and Lee (2002: 81) for a discussion of the strengths and weaknesses of using drug arrest rates.

4 We worked with a number of model specifications, making comparisons across models as to the percent reduction in the BIC statistic as the numbers of classes were in- creased. In other words, we explored the gain or improvement in model fit provided by models with larger numbers of classes for purposes of assessing whether amore parsimo- nious model (fewer classes) could be identified. The model specification shown here was the best fit to the data.

5 Significant Harris-Tsavalis test statistics reveal that we do not have unit roots in ei- ther the black homicide series (rho = 0.07, p b 0.001) or white homicide series (rho = 0.51, p b 0.001). As suggested by Pesaran (2012), we tested each time series individually.

6 The possibility that Hispanic immigration has confounded white homicide statistics was established in the work of Steffensmeier et al. (2011) who found evidence of a “His- panic effect” in Uniform Crime Report (UCR) and National Crime Victimization Survey (NCVS) data,wherein the growth in theHispanic population leadwhite estimates of crime (as compared to black) to be confounded with Hispanic offenders. Specifically, they state, “Hispanic offenders are typically classified in national databases as “white” (approximate- ly 93%)” (Steffensmeier et al., 2011: 233).

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