Thoughts on the Analysis of Group-Based Developmental Trajectories in Criminology

Abstract

Group-based analysis of developmental trajectories has been commonly used to study heterogeneity in criminal offending over the life course. While there have been several critiques of this method, we believe that it is useful in testing hypotheses from theory about the existence of groups and the characteristics and attributes of groups. We present an overview of these issues and close with two points. First, since criminology owes much to description, the group-based method offers one method that permits visualization of data and connection of what we see to the data. Second, although the group-based model is a useful descriptive tool, it is not a mere descriptive tool, as it can be used to test empirical predictions from theory, including the predictions of non-taxonomic criminological theories, as well as other fundamental criminological/criminal justice questions.

Keywords:

• group-based
• trajectories
• longitudinal
• crime

Notes

1. At the outset, we note that we are among those who have used group-based trajectory methods and variations on those methods in our own work.

2. In some of this early work (Blumstein & Moitra, 1980), the weights were assumed a priori rather than estimated. In the contemporary applications of GBT, the weights are estimated based on the observed data.

3. Mixtures and mixing distributions are an important tool in the contemporary criminologist’s toolbox. One of the key insights from nearly 50 years of research on criminal careers is that crime and the tendency to engage in crime exhibits a great deal of heterogeneity. For example, any distribution of criminal offending may actually be comprised of several different distributions (the heterogeneity). Unfortunately, we can never measure all of the sources of this variation or heterogeneity in offending—it is unmeasured and therefore unobserved. Mixtures and mixing distributions provide us with a way to include this variability in our statistical models even though it is unobserved—hence, the term “unobserved heterogeneity.” As with any unobserved quantity, however, our analyses must make some assumptions about the heterogeneity. Different analysts have approached this problem in different ways—some use continuous mixture growth curve models and some use discrete or finite mixture models like those employed in the trajectory framework. Continuous mixture models make assumptions about the shape, mode, and skew of the continuous distribution. Finite mixture models assume that the true mixing distribution is well approximated by a fixed number of discrete groups but are less sensitive to concerns about mode, level, and skew of the mixing distribution.

4. Skardhamar (2010, p. 296) states that Moffitt’s “approach was spurred by the development of semiparametric group-based modeling (SPGM)—a technique that offered a methodological basis to distinguish between groups of individuals with different patterns of offending across time.” In fact, Nagin and Land’s (1993) work cites an early draft of Moffitt’s paper and we have not seen any evidence that Moffitt’s theory was “spurred” by the work of Nagin and Land.

5. In discussing the advantages and disadvantages of GBT, Raudenbush (2005, p. 136, emphasis added) notes: “The scientific question that must be asked is whether the hypothetical existence of “latent” (that is, unobservable) groups helps make better predictions of future behavior than does a model that does not require such groups to exist. An alternative model might be a random effects model (Laird and Ware 1982; see review by Raudenbush 2001) also known as a “latent growth curve model” (see Singer and Willett 2003 for a review) or by a semicontinuous model (Olsen and Schafer 2001). Perhaps we are better off assuming continuously varied growth a priori and therefore never tempting our audience to believe in the key misconception that groups of persons actually exist. We would then not have to warn them strongly against “reification” of the model they have been painstakingly convinced to adopt.”

6. The use of offender types in scientific criminology goes back at least as far as the work of Lombroso (born criminal, insane criminal, and the criminaloid), before that to the early alienists who distinguished moral insanity, total insanity, and imbecility (Rafter, 1997; Gibson & Rafter, 2006), and continues to the present day (Moffitt, 1993; Patterson & Yoerger, 1997). Analytically, offender types serve an important scientific purpose in helping us reduce the complexity in the world. Metaphorically, it serves an important function in separating or differentiating “them” (criminals) from us (Taylor, Walton, & Young, 1973).

7. An anonymous reviewer correctly noted that in some applications theory plays a less prominent role. For example, if a researcher wishes to incorporate GBT into a propensity score matching framework, the interest is in controlling for the developmental history of a particular behavior, and GBT is simply used as a device to obtain those histories in a parsimonious manner. Theory, then, may be applied in later analyses. Similarly, posterior probabilities from GBT may be used as control variables in regression-based analyses without being the main concern. In sum, not all applications of GBT require that every group be interpreted theoretically. If one wishes to make the case that the group is important, that argument must be grounded in theory.

8. We also remind readers that the use of sophisticated quantitative methods (such as GBT), sometimes leads to a devaluation of qualitative techniques that illuminate the empirical world. This is especially true within the developmental/life-course area of criminological research which owes an important debt of gratitude to the early qualitative research by Shaw (The Jack Roller) and the interviews carried out by Laub and Sampson in Shared Beginnings, where some of the interviews produced insights unattainable with advanced quantitative techniques (i.e. the meaning of turning points, zig-zag of criminal careers, notions of human agency). Clearly, a combination of both quantitative and qualitative techniques are important in charting out the entire longitudinal patterning and understanding of criminal activity over the life course.

9. Although we note that Skardhamar (2010) allows that parameter estimates from GBT models can be a useful way to match on pretreatment characteristics in observational studies.

10. We thank an anonymous reviewer for pointing this important issue out.