Abstract
Population heterogeneity and intra-individual change are often overlooked in recidivism research. This study employs latent transition analysis of psychological trauma from intake into a juvenile justice diversion program until termination, followed by modeling of recidivism. A comparison model of a logistic regression without latent variables is also presented, to answer whether the same results would have been achieved without using latent variable modeling. Results indicate that juvenile justice–involved (JJI) youth are assigned into four psychological trauma classes at intake, and three at termination. Latent status membership predicts 6-month recidivism (p = .03). Those who begin in classes that have Depression, Post-Traumatic Stress, and Anger have higher odds of recidivating than those who demonstrate generally high or low trauma symptoms at intake. The comparison regression model found no significant relationship between the five trauma symptom domains and recidivism. Implications for employing latent variable modeling and person-centered analyses for recidivism research are discussed.
Introduction
Population heterogeneity is often overlooked in modeling predictors of recidivism or evaluating the effectiveness of a recidivism reduction program. While we know that overall, diversion programming works in reducing recidivism, it does not work for everyone, even those who may successfully complete a program (Pullmann et al., 2006; Sullivan, Veysey, Hamilton, & Grillo, 2007). This is most likely because there are many patterns of characteristics within one population—known as population heterogeneity (Lubke & Muthén, 2005). Heterogeneous study populations contain subpopulations that share distinct response patterns. Understanding these patterns and subpopulations within a single study population may hold the key to targeting improvements in programming (Swartout & Swartout, 2012).
We cannot account for these patterns with variable-centered statistical analyses alone. In a variable-centered statistical analysis, a linear regression, for example, we focus on the relationships between variables to understand a relationship through aggregate cases (B. O. Muthén & Muthén, 2000). The analysis assumes that the study population is homogeneous. As such, we ignore these underlying patterns of relationships, resulting in analyses that may overestimate or underestimate an effect (B. O. Muthén, 1989). In addition to relying on variable-centered analyses only, many researchers also treat latent variables as observed variables. For the sake of this study, we define an observed variable as a variable we can directly measure and test, such as age or blood pressure. A latent variable (also known as an unobserved or hidden variable) is a variable we cannot directly measure, and instead is measured by more than one observed variable, such as a depression inventory or a victimization questionnaire. In social science research, most variables of interest are not observed variables. For example, because we often cannot directly observe psychological trauma, we employ questionnaires with several items to measure it. This is the case with a questionnaire such as the Trauma Symptom Checklist for Children (TSCC; Briere, 1995; Briere & Lanktree, 1995). Because it cannot be directly measured, psychological trauma is a latent variable. However, many studies treat psychological trauma as an observed variable. This not only introduces unaccounted measurement error but also ignores the underlying relationship between those observed items that produce the latent variable.
Latent variable person-centered analysis addresses these issues. A latent variable person-centered analysis, such as latent class analysis (LCA), identifies subgroups within a population by measuring responses at the individual level initially rather than at the aggregate level (Von Eye & Weidermann, 2015). These subpopulations may then be used in subsequent analyses, both variable-centered and person-centered, to model relationships among variables and persons. It is argued that latent variable person-centered analyses are more applicable for policy, practice, and future research than classic variable-centered statistical approaches (Swartout & Swartout, 2012). These analyses may be able to detect the small population differences within a set of variables previously not noted and apply those results to policy or programming to improve outcomes. Taking it one step further, we can combine person-centered and variable-centered approaches to model complex relationships, such as the one between population patterns of psychological trauma symptoms and later recidivism within juvenile populations (B. O. Muthén & Muthén, 2000). Longitudinally, one may examine changing response patterns of subpopulations over time and how they affect a later outcome, such as recidivism.
Current Study
The current study seeks to answer the following research questions:
We hypothesize that compared with the subpopulation that demonstrates low trauma symptoms from intake to termination, subpopulations that demonstrate more trauma symptomatology from intake to termination will have greater odds of recidivating than those who demonstrate less trauma symptomatology.
To answer these questions, we must combine both types of analyses, first modeling subpopulations (based on psychological trauma responses) using latent variable modeling and person-centered analyses, and then employing these subpopulations as a predictor variable in a logistic regression analysis that models recidivism. Specifically, we seek to illustrate the application of latent variable modeling employing latent transition analysis (LTA) more than 2 times—intake into a juvenile justice diversion program and successful termination from the program—and whether group membership into different psychological trauma symptom populations changes over time, and the impact of this change on later recidivism. We also compare these results with what some might call a “typical” variable-centered and observed variable approach’s results to show that the classical observed variable-centered approach does not detect the heterogeneity of responses that are required to identify the relationship between an intra-individual measure (psychological trauma) and recidivism. We begin by discussing juvenile justice diversion programming, recidivism, and gaps in the literature in addressing recidivism in the juvenile population.
Literature Background
Juvenile justice–involved (JJI) youth report higher rates of behavioral health disorders than the general population of youth (Colins et al., 2010). Although estimates vary, many researchers report between 60% and 70% of JJI youth suffer from some type of mental health or substance use problems (Cocozza & Skowyra, 2000; Shufelt & Cocozza, 2006; Teplin, Abram, McClelland, Dulcan, & Mericle, 2002). Common types of diagnoses among JJI youth include conduct disorder, oppositional defiant disorder, depression, alcohol-related disorders, and post-traumatic stress disorder (PTSD; Arroyo, 2001; Evans Cuellar, McReynolds, & Wasserman, 2006; Teplin et al., 2002). In addition to behavioral health issues, JJI youth experience high levels of trauma (Arroyo, 2001; Ford, Hartman, Hawke, & Chapman, 2008). Abram and colleagues (2004) found that JJI youth reported an average of more than 14 past-year traumatic events. Ford, Grasso, Hawke, and Chapman (2013) found that JJI youth can be classified into three subpopulations of victims: polyvictims, moderate victims, and low victims. Being in the higher victimization classes was associated with psychological trauma and behavioral symptoms. Children who experience victimization are more likely to exhibit symptoms of trauma which may then manifest in delinquent behavior (Cuevas, Finkelhor, Shattuck, Turner, & Hamby, 2013).
Many JJI youth with behavioral health issues do not receive behavioral health treatment prior to involvement with the justice system. While 94% of juvenile justice facilities contain behavioral health treatment for detainees, the services vary widely from facility to facility (Goldstrom, Jaiquan, Henderson, Male, & Manderscheid, 2000). A little over half (56%) conduct full behavioral health evaluations, and 71% offer behavioral health screening. If screening and assessment are offered, these tools are often not standardized, and therefore, it is not known whether the results are valid or generalizable (Hoge, 2002). Even if these youth are screened and assessed for behavioral health issues, the program may not be suited to treat these youth in the manner in which they require (Cocozza & Skowyra, 2000).
In response to the large number of JJI youth with behavioral health disorders, some communities developed programs designed to divert these youth away from incarceration and formal court processing and into behavioral health treatment. A goal of these behavioral health diversion programs is to reduce behavioral health and psychological trauma symptomatology, thus reducing risk for recidivism. To achieve this goal, diversion programming such as the Behavioral Health Juvenile Justice (BHJJ) Initiative, employs in-depth assessment and screening using standardized instruments as well as offers individualized behavioral health treatment (Evans Cuellar, McReynolds, & Wasserman, 2006; Kretschmar, Butcher, Flannery, & Singer, 2014; Kretschmar, Butcher, Kanary, & Devens, 2015). Studies on diversion programming for JJI youth find that generally, recidivism during adolescence following these programs is lower than that in those who are formally processed (Pullmann et al., 2006; Sullivan et al., 2007).
In addition to improvements in recidivism rates, preliminary results from the BHJJ Initiative find that, from treatment intake to termination, those who successfully complete diversion programming report lower psychological trauma symptom scores (Kretschmar et al., 2014). Colwell, Villareal, and Espinosa (2012) reported that problem severity significantly decreased from intake to termination in specialized diversion programming among JJI youths. However, the relationship between problem severity, program participation, and recidivism was not explored. Studies investigating the link between psychological trauma symptomatology and recidivism among youth find that generally, those who recidivate are more likely to have a mental health disorder or psychological symptoms than those who do not. McReynolds, Schwalbe, and Wasserman (2010) found that the impact of mental health disorders on recidivism varied according to mental health disorder type and gender.
The interplay of other covariates, such as gender or race, may play a part in the success of behavioral health diversion programming in regard to reducing recidivism. Dembo, Wareham, Poythress, Meyers, and Schmeidler (2008) employed an LTA of psychosocial functioning, composed of constructs that measure family relationships, peer relationships, education, and mental health issues. They found that there are two subpopulations of youth in a juvenile justice diversion program from intake to termination. They report that older youths were less likely to be members of the few problems category than younger youths. They also performed an ANOVA on 104 cases to measure whether self-reported delinquency at follow-up differed among the subpopulations, and found there to be a statistically significant difference (p = .001). It is not clear whether these youth completed the program successfully or unsuccessfully. Also, while the study includes mental health issues as part of psychosocial functioning, it is only one of four domains. The authors also rely on self-reported delinquency rather than court records.
To our knowledge, there is not a study examining the longitudinal change in psychological trauma symptoms among youth who successfully complete juvenile justice diversion programming. This may be because most diversion programs do not collect variables related to psychological trauma, such as the TSCC (Briere, 1995; Briere & Lanktree, 1995). It may also be because many programs gather only intake data but not termination data. Furthermore, many studies examine psychological trauma and mental health disorders in terms of diagnosis but do not take into account that there may be a change in psychological trauma over time on the symptom level. As trauma symptoms are not experienced equally across all youth who experience violence exposure or other traumatic events, this is an oversight in current research. Recent research found that the construct of trauma symptomatology is not comprised of one factor (Butcher, Kretschmar, Singer, & Flannery, 2015). This suggests that groups of trauma symptoms are not necessarily similarly experienced and that trauma cannot be captured with a binary diagnosis variable but can be thought of as a latent variable. Previous studies employing LCA for mental health diagnosis such as depression or PTSD found several distinct subpopulations. They examined only one diagnosis at a time, not an entire construct of trauma symptomatology such as the TSCC (Breslau, Reboussin, Anthony, & Storr, 2005; Sullivan, Kessler, & Kendler, 1998; Wolf et al., 2012). Furthermore, most diversion programs may not last long enough for a person to change in terms of a psychological diagnosis but may decrease in some symptoms.
There is a need in the literature to examine intra-individual level change and its impact on recidivism. Serin, Lloyd, Helmus, Derkzen, and Luong (2013) employed a meta-analysis on individual change scores and recidivism that resulted in a call for more complex statistical models to illustrate the relationship between intra-individual change and multiple measurement periods across time. Also, many of the studies reviewed focused not on psychological change, but on risk factors such as substance use, attitudes about offending, and violent behavior. We focus on psychological trauma symptoms, rather than the aforementioned variables, because our entire sample demonstrates some type of behavioral health issue, and the majority of our sample is exposed to violence or a traumatic event such as the loss of a family member. As BHJJ is a diversion program that seeks to reduce recidivism, we wish to relate the heterogeneous change in psychological trauma throughout a diversion program to recidivism after program termination.
Method
Study Population and Design
The study population consists of 1,217 youth who participated in and successfully completed Ohio’s BHJJ Initiative as of June 30, 2013. BHJJ is a diversion program for JJI youth between 10 and 18 years old with behavioral health issues. In lieu of detention, youth are diverted into community and evidence-based behavioral health treatment. One of BHJJ’s goals is to reduce recidivism by diverting youth into trauma-informed treatment to address their behavioral health problems. Many counties in Ohio participate in the BHJJ program, and while all counties must use an evidence-based or promising practice, counties are able to choose the treatment model(s) that best fits the needs of the youth and families in their area. Examples of treatment types in BHJJ include Multisystemic Therapy, Functional Family Therapy, and Integrated Co-Occurring Treatment. All youth included in the study also had available intake and termination TSCC surveys. All study participants and their legal guardians gave informed assent and consent to participate. The study has institutional review board approval by the study university.
This study is a retrospective observational study design employing secondary data analysis. These data were not collected for the purpose of this study; therefore, aspects such as randomization into the program and sample size and data collection of the unsuccessful completion population are not available for these data. Therefore, while we would like to compare the successful population of completers with the unsuccessful population of completers in terms of their movement from one trauma latent class to another, only 131 cases were unsuccessful and completed the termination TSCC questionnaire. A stable LTA requires a sample size of at least 300 cases (The Methodology Center, The Pennsylvania State University, 2015).
Table 1 gives the demographic composition of the study population. The average participant is about 15 years old, White/Caucasian, and is male. Most of the non-White participants are Black (85%), followed by Multiracial (7.4% of 569), and non-specified Other (6.5% of 569). Most (65.6%) of participants do not recidivate within 6 months. Out of those who do recidivate in 6 months, 42.2% do so once, 24.7% do so twice, 17.1% do so three times, and 15.9% recidivate four or more times. More than 20% of charges are felony charges (20.3%), and about 70% are misdemeanor charges (71.7%). It takes about 265 days to successfully complete BHJJ treatment. During this time, the mean TSCC score changes about 1 to 2 points.
Demographic and Study Characteristics of Participants (N = 1,217)
Note. PTS = post-traumatic stress.
Twenty-three cases (1.9%) were missing on race; therefore, percentages were out of the valid number of cases (n = 1,194).
Percentage of races under the designation “Non-White” is out of the total number of non-White cases (n = 569).
Change in trauma symptom score reflective of total score on that domain at intake minus total score on that domain at termination.
Percentage for felony and misdemeanor is out of number charged (n = 251), not out of the total population, and remaining 8% are missing information.
Measures
TSCC contains 54 questions measuring six domains: anxiety, anger, depression, post-traumatic stress (PTS), dissociation, and sexual concerns (Briere, 1995; Briere & Lanktree, 1995). The “sexual concerns” domain is not used in this study. A recent confirmatory factor analysis (CFA) showed some evidence that the Sexual Concerns sub-scale has weak psychometric properties (Butcher et al., 2015). As such, the remaining 44 items are considered for this analysis. The original questionnaire uses a Likert-type scale of 0 to 4. For the purposes of this analysis, we made each measure dichotomous with a value of 1 to 4 representing yes, and a value of 0 representing no. This is done for two reasons: first, because the cell sizes in the three and four categories are too small for analysis, and second, because a dichotomous variable in LCA is more interpretable than an ordinal one.
To increase interpretability of the latent model, we reduced the number of items per domain to three items that most accurately portrayed that domain, resulting in an abbreviated 15-item measure. Data reduction was employed using a special type of principal components analysis (PCA) for categorical variables in SPSS version 23 (International Business Machines, 2015). PCA identifies which items contribute the most variance to a latent measure. Following the selection of the items, a CFA was conducted in MPlus to confirm that this set of measures was as valid as the original measure in the same population. We found that the abbreviated version of the measure contains a comparative fit index (CFI) of 0.98, whereas the original version contains a CFI of 0.95. A good model typically has a CFI of larger than 0.95 (Hu & Bentler, 1999). The abbreviated version’s root mean square error of approximation (RMSEA) is .056, whereas the original is .046. Generally, a good model should have an RMSEA of .05 or smaller. Keeping these fit statistics in mind, the abbreviated measure fits in general at least as well at the full measure if not better in the study population. External validity testing using Cronbach’s alpha found a coefficient of .89 (.89 standardized) of the short version.
For the comparison logistic regression analysis, we create five psychological trauma change variables by subtracting the termination score from the intake score. The five variables correspond to the five TSCC domains: anxiety, depression, anger, PTS, and dissociation. Table 1 reports the average change in score from intake to termination.
Juvenile recidivism at 6 months following program termination is represented by whether the case was charged with an offense 6 months after program termination. This variable is dichotomous. Six months is chosen as the time period because due to the age of the average successful program completer (M = 15 years at intake; 16.2 years at termination), 12 months would exclude at least 240 participants aged 17 at intake because they would be above the age of 18 by the time 12-month recidivism data are collected.
Gender, age, and race were considered for the logistic regression model. Gender was measured as a dichotomous variable (male, female). Age is a continuous variable. Race was dichotomized into White/Caucasian and non-White because the cell sizes for Multiracial, Asian, Native American, and non-specified Other were too small for individual analysis.
Analysis
To answer Research Question 1—what are the subpopulations or classes of justice-involved youth according to psychological trauma symptoms?—we employ latent modeling methods to identify subpopulations of justice-involved youths according to psychological trauma symptoms. Latent modeling methods allow us to discover distributions of populations according to latent variables. Examples of latent modeling include latent growth analysis, latent class and latent profile analyses, and LTA. Person-oriented analyses such as LCA and its longitudinal sibling, LTA, increase understanding of populations and increase translatability to practice (Swartout & Swartout, 2012). LCA is a cross-sectional latent modeling technique that identifies subpopulations, or classes, according to a latent variable measured by several indicator variables. In our sample, the latent variable being measured is “trauma.” Trauma is measured by 15 indicator variables that are items measured on the TSCC. LCA estimates relationships among individuals according to the latent variable measured and models subpopulations that differ in their responses to the latent variable (McCutcheon, 1987). These subpopulations represent the heterogeneity of the latent variable.
Research Question 2—how do these classes of psychological trauma–exposed youth change from program intake to successful program termination?—employs LTA to measure how these classes change from program intake to program termination. Therefore, the LTA will measure how these trauma classes change from program intake to program termination. Included in this analysis are transition probabilities that estimate the likelihood of moving from one class to another over time as well as the probability of staying in the same class. The transition probability analysis answers Research Question 3—what are the probabilities of transitioning from one class to another class over time?
After performing the LCAs and LTA, we answer Research Question 4—does belonging to a particular latent status (intake class to termination class) increase the odds of recidivating after successful program termination?—by regressing recidivism onto latent status membership, controlling for covariates in the model. To answer Research Question 5—how does the latent transition and subsequent regression analysis compare with a logistic regression analysis without latent variable modeling of psychological trauma?—we employ a similar logistic regression, except we treat psychological trauma as an observed change variable rather than a latent variable with classes. We do this to examine whether employing a classical statistical technique to the same variables will reveal the same relationship between psychological trauma over time and recidivism as the combined latent transition and logistic regression analysis.
LCA intake and LCA termination
Fitting an LCA model involves finding the correct number of classes that best fit the data using fit statistics as well as maintaining interpretability and parsimony (Geiser, 2012). We employed the same fit statistics for the Time 1 and Time 2 LCAs: statistical comparison indices including the Akaike information criterion (AIC), Bayesian information criterion (BIC), and sample size–adjusted BIC (aBIC), as well as the entropy—the measure of classification accuracy—and difference tests such as the bootstrap likelihood ratio (LR) difference test and the adjusted Vuong–Lo–Mendell–Rubin (VLMR) test. In addition to fit statistics, we also considered the interpretability and parsimony of the classes for each model. While a statistical test may favor a higher number of classes, interpretability and parsimony may outweigh that test (Geiser, 2012). We hypothesized that the number of classes for Intake and Termination LCAs would be between three and five; therefore, we ran models with anywhere from one to seven classes. Previous studies of psychological trauma, mainly with PTSD, depression, and one LCA that included mental health disorders, found between two and six latent classes (Breslau et al., 2005; Dembo et al., 2008; Sullivan et al., 1998; Wolf et al., 2012). As this is an exploratory LCA, we cannot hypothesize the composition of the latent classes. The fit statistics for each LCA are organized into Table 2.
Fit Statistics for Intake LCA, Termination LCA, and LTA
Note. LCA = latent class analysis; LTA = latent transition analysis; AIC = Akaike information criterion; BIC = Bayesian information criterion; aBIC = adjusted BIC; LRTB = likelihood ratio test bootstrapped; VLMR = Vuong–Lo–Mendell–Rubin test.
Not estimated in LTA.
Once the number of classes is identified in the LCA, we focus on interpreting the meaning of those classes according to the probability of endorsement (saying yes) to each Trauma item. The distribution of classes is shown in a probability plot, which graphically depicts the distribution by plotting lines on a graph that correspond to the probability of endorsing each item. The process of fitting and interpreting the LCA is conducted twice in this study—once for Intake and once for Termination.
LTA
The process to fit an LTA is the same as fitting an LCA, with the exception that we do not employ the statistical difference tests. Because our ultimate goal in this study is to examine the change from one class to another over time, we may also use the fit statistics from the LTA to support selection of the classes in the two LCAs in case there is a discrepancy or it is not clear which class solution to select. Another important aspect to fitting the LTA is determining whether we can assume there is measurement invariance from Intake to Termination. We define LTA measurement invariance as whether the same constructs are being measured over time in a population (Collins & Lanza, 2010). Measurement invariance allows us to make some assumptions about the interpretability of the data. However, sometimes, measurement invariance is not realistic or does not fit the data, and we can then estimate using partial measurement invariance. To estimate measurement invariance, we compare the selected LTA model using all freely estimated parameters with the same model except one where all of the parameters are set to equal each other from Time 1 to Time 2. We can calculate the amount that these two agree by conducting a likelihood ratio test (LRT) test, which then gives us a chi-square (χ2) value, degrees of freedom, and the parameters. If the p value is <.05, then we cannot assume measurement invariance and must fit a model that is partially non-invariant by estimating which parameters should be fixed based on theory.
After fitting the LTA model, we interpret the number and percentage of the sample in each class according to Intake or Termination, the number and percentage in each latent status pattern, and the transition probabilities for each latent status pattern. All analyses are conducted in MPlus version 7.11 (Muthén & Muthén, 1998-2015). In addressing missing data, listwise deletion is the default in MPlus if there is missing on all items during either LCA. This was the case for 315 cases for the Time 2 LCA. However, for the LTA, it is a default in MPlus to employ maximum likelihood estimation under missing at random items for cases that are missing either some or all items (Muthén & Muthén, 1998-2015). Due to maximum likelihood estimation, the LTA estimates those cases using the data from the Intake items, allowing for a total of 1,217 cases in the LTA.
Latent variable logistic regression of 6-month juvenile recidivism
After identification of most likely latent status membership, we employed a logistic regression analysis modeling whether latent status membership predicts 6-month recidivism after termination. A preliminary chi-square test between latent status membership and 6-month recidivism found a statistically significant chi-square value of 19.62 (p = .02). After modeling for the main effects of latent status membership, we included race and gender as possible mediators due to their statistically significant relationship to latent status membership or recidivism in chi-square tests. Race is modeled as a binary variable represented by either “White/Caucasian” or “non-White.” Age was not found to be significantly related to neither latent status membership nor recidivism in prior chi-square tests; therefore, it was not included in the logistic regression model.
Due to limited sample size in the latent statuses “Anger Symptoms to High Trauma Symptoms” (n = 4) and “Depression and PTS Symptoms to High Trauma Symptoms” (n = 1), these were combined into a category with “Low Trauma Symptoms to High Trauma Symptoms” (n = 20) to increase computational power. To keep in consideration space and size of the logistic regression model table, we present only comparisons that fall into the 95% confidence range (those that do not include the value of 1) in Table 5. Results include overall Wald test p value at the .05 level, Wald odds ratio, Wald test comparison p value set at the .05 level, and 95% confidence levels. Finally, we provide only the adjusted model (including race and gender) in Table 5.
As a comparison, we also employed a logistic regression to model for the impact of psychological trauma from intake to termination on 6-month recidivism, taking into account the same covariates as the prior logistic regression. We treat change in trauma symptomatology as five variables—anxiety, depression, anger, PTS, and dissociation—calculated as termination score subtracted from intake score. Both logistic regression analyses were performed in SAS 9.4 (SAS Institute, Inc., 2015).
Results
Latent Class Analyses
Table 2 presents the model fit information for the Intake LCA and the Termination LCA. While the fit statistics are slightly more favorable for a five-class model opposed to a four-class model, we found decreased visual interpretability and small class sizes for the five-class model. Furthermore, according to the LTA fit statistics (Table 2), an Intake four-class model fits the latent transition model better than an Intake five-class model. In regard to Termination, we chose the three-class model because it had a higher entropy value (0.84) than higher class models, and a lower AIC, aBIC, and BIC than the two-class model. A Termination three-class model also displays superior fit statistics in the latent transition model compared with two-class and four-class models.
Figure 1 shows the probability plots for the Intake LCA and Termination LCA. In Intake, there are four distinct classes. The first class is demarcated by the high probability of endorsement for the depression items and the PTS items, but a lower endorsement for anxiety, anger, and dissociative items. This class may be considered the “Depression and PTS Symptoms” class. The second class is defined by the highest endorsement probability of all of the items, with a probability of at least .55 (“Feeling Like I’m Not in My Body”) and at most .99 (“Feeling Sad/Unhappy”). This population could be considered the High Trauma Symptoms Class. The third class demonstrates a low probability of endorsing all other items except for the anger items, where it clearly demonstrates a high probability of endorsement (.85-.89). This class is the Anger Symptoms Class. Finally, the fourth class has a low probability of endorsement on all items, ranging from about .25 to nearly 0. This class is the Low Trauma Symptoms Class.

LCA Intake and Termination Probability Plots
There are three distinct classes at Termination. As shown in Figure 1, the Anger Symptoms and Depression and PTS Symptoms Classes from Intake have changed. Most likely, these classes have merged to form the first class of Termination, which is marked by the higher endorsement on anger and depression items and a low endorsement on other items. We call this class the Anger and Depression Symptoms Class. The second class demonstrates low endorsement on all items, most of the probabilities close to or at zero. This is the Low Trauma Symptoms Class. Finally, the third class demonstrates generally high endorsement on all items, the highest of all classes. This is the High Trauma Symptoms Class. As shown in both of the plots, there tends to be a generally lower endorsement of dissociative items (“Feeling Like Things are Not Real,” “Feeling Like I’m Not in My Body,” and “My Mind Going Blank”). It may be that this sample does not demonstrate variable dissociative symptomatology.
LTA
Table 2 presents the fit statistics for the LTA. As stated previously, the Intake four-class Termination three-class model shows the best fit in terms of entropy (0.79). Also, compared with other Intake four-class possibilities, the three-class model demonstrates the best AIC, aBIC, and BIC. In our model, we found partial measurement invariance (χ2 = 9.655, df = 9, p = .62) when we held Classes 4 (Intake) and 3 (Termination) invariant, Classes 1 (Intake) and 2 (Termination), and the first and second anxiety items, depression items, and dissociative items regardless of class. The structure of the anger items and anger distinctive class changed over time; therefore, theoretically it is sound to allow these to vary freely from Intake to Termination.
The results of the LTA show the final class counts and proportions based on Intake and Termination (Table 3). The highest proportion of the sample in Intake is in the Low Trauma Symptoms Class (41.2%). The lowest proportion of the sample is in the Anger Symptoms Class (7.7%). The highest proportion of the sample in Termination is in the Anger and Depression Symptoms Class (48.4%). The lowest proportion of the sample is in the High Trauma Symptoms Class (13.2%).
Number and Percentage of Population in Each Class Dependent on Time Period a
Note. PTS = post-traumatic stress.
Number and percentage rounded, and percentage is out of total population in time period.
To explain the movement from Intake to Termination, Table 4 shows the final counts and proportions for each latent status based on likely class membership—a status being a combination of Intake and Termination class membership. As seen, about 22% of the sample stayed in the Low Trauma Symptoms Class from Intake to Termination. The same amount moved from the Depression and PTS Symptoms Class to the Anger and Depression Symptoms Class. About 16.8% of the sample moved from the Low Trauma Symptoms Class to the Anger and Depression Symptoms Class. Few (10% of the sample) stayed in the High Trauma Symptoms Class from Intake to Termination. Also, the lowest percentages were those that moved from a lower trauma class to the High Trauma Symptoms Class.
Number and Percentage of Population in Each Latent Status Pattern Based on Their Most Likely Latent Class Pattern
Note. PTS = post-traumatic stress.
Number and percentage rounded; percentage is based on number in Time 1 latent class, not on population total.
The transition probabilities for the movement from one class to another are demonstrated in Figure 2. These transition probabilities support Table 4, where the lowest probabilities are from a different class into the High Trauma Symptoms Class. The highest transition probabilities are those from the Anger Symptoms Class and Depression and PTS Symptoms Class into the Anger and Depression Symptoms Class (.891 and .737). This most likely demonstrates that the Termination 2 Anger and Depression Symptoms Class is a compilation of the Intake Anger Symptoms Class and Depression and PTS Symptoms Class.

Transition Probabilities Intake to Termination Based on Estimated Latent Transition Model
Logistic Regression Analysis of Recidivism using Psychological Trauma Latent Statuses
Table 5 presents abbreviated results of the logistic regression analysis modeling the odds of recidivating 6 months after Termination from the BHJJ program given latent status membership. As shown in previous studies of the same population (Kretschmar et al., 2014), race is a significant predictor of recidivism following treatment. Those who are non-White demonstrate 42% increased odds of recidivating than their White/Caucasian counterparts, controlling for latent status membership and gender.
Logistic Regression Analysis Modeling the Odds of 6-Month Juvenile Recidivism Following Program Termination (n = 722)
Note. OR = odds ratio; CI = confidence interval; PTS = post-traumatic stress.
Overall p value of latent status membership is .03.
The analysis revealed five comparisons that contained effect sizes precise enough to not contain the value of 1. The first comparison is using the Low Trauma Symptoms to Low Trauma Symptoms latent status (n = 333) as the reference category and the Depression and PTS Symptoms to Anger and Depression Symptoms latent status (n = 280) as the comparison category. We find that those who move from the Depression and PTS Symptoms Class to the Anger and Depression Symptoms Class have 65% more the odds of recidivating than those who remain in the Low Trauma Symptoms category.
We find that compared with the High Trauma Symptoms to Low Trauma Symptoms latent status (n = 194), there are four latent statuses that have effect sizes greater than 2. The first is the same latent status as the last comparison: Depression and PTS Symptoms to Anger and Depression Symptoms (n = 280), with an odds ratio of 2.5 compared with the High Trauma Symptoms to Low Trauma Symptoms category. The second is the Low Trauma Symptoms to Anger and Depression Symptoms (n = 143), where those who are in this latent status have at least 2 times the odds (2.39) of recidivating 6 months after successful program termination than those who move from High Trauma Symptoms to Low Trauma Symptoms. The third is the Anger Symptoms to Low Trauma Symptoms (n = 13); those in this category have 4.33 times the odds of recidivating than the referent category. Finally, those in the Depression and PTS Symptoms to Low Trauma Symptoms demonstrated nearly 3 times the odds (2.96) of recidivating than those in the High Trauma Symptoms to Low Trauma Symptoms latent status.
Comparison Logistic Regression using Psychological Trauma as Observed Change Variables
As a comparison between standard statistical analysis and latent variable modeling, we performed the same logistic regression but with psychological trauma as five observed change variables, controlling for gender and race. The results indicate that a change in depression (p = .051), anxiety (p = .201), anger (p = .767), PTS (p = .186), or dissociation (p = .272) does not significantly affect 6-month recidivism.
Discussion
Change in Psychological Trauma Symptomatology Classes
Many (29.3%) of our sample moved from the Intake Anger Symptoms Class (n = 77) or Depression and PTS Symptoms (n = 280) Class into the Anger and Depression Symptoms Class. The Anger Symptoms Class was a small class (n = 94) to begin with, so this may be why we see a change in the composition of classes at Termination. An increased sample size may see a more distinctive Anger Symptoms Class at Termination. It may also be that anger and PTS are addressed in the diversion program more so than depression, resulting in lower endorsement probabilities that do not create decisive patterning.
The Anger Symptoms and Depression and PTS Symptoms Intake Classes and the Anger and Depression Symptoms Termination Class may represent subpopulations of our sample that demonstrate similar symptomatology to that of what D’Andrea, Ford, Stolbach, Spinazzola, and van der Kolk (2012) describe as a complex type of PTSD or developmental trauma disorder. Although not discussed explicitly in this article, the BHJJ sample demonstrates a high level of victimization or exposure to violence (Kretschmar et al., 2014); therefore, the symptomatology described by D’Andrea and colleagues may apply to these subpopulations.
Dembo and colleagues (2008) reported four psychosocial latent statuses over time in their latent profile transition analysis of juvenile diversion program completers—those who remain in the few problems class from intake to termination, those who remain in the many problems class, those who move from few to many, and those who move from many to fewer problems. Comparison between that study and this one is difficult, mainly because Dembo et al.’s study used a mean score of mental health problems as one of five indicators, and this study focused only on psychological trauma using 15 indicators. However, similar to our study, Dembo et al. see more movement from the high to low problems statuses than low to high problems.
Psychological Trauma Change and Recidivism
We are surprised to find that even among those who might “improve” from Intake to Termination, such as those originating in the Anger Symptoms Intake Class, still have greater odds of recidivating than those who originated in the High Trauma Symptoms Intake Class. This may be because those who are in the High Trauma Symptoms Intake Class highly endorsed every item regardless of the item, and they may be generally psychologically traumatized, but those who endorse very specific items and symptoms such as anger, depression, and PTS have very specific and high intensity issues that may not be addressed during a short period treatment time.
Although race is not a surprising predictor of recidivism given that is a predictor in a previous study with the same population (Kretschmar et al., 2014), we suspect that race may moderate the relationship between latent status membership and recidivism. While race is not statistically associated with latent status membership (χ2 = 5.94, p = 0.75), when race is added into the regression equation between latent status membership and recidivism, the strength of association decreases from a chi-square value of 19.17 to 10.20 between latent status membership and recidivism. We hypothesize that the change in psychological trauma may have a larger effect on recidivism in one racial category more than another. Finding a differential effect of mental health status and recidivism based on race is not a new concept. Researchers such as Weirson and Forehand (1995) found that this relationship was different based on race. An examination of recidivism, race, gender, and mental health problems in incarcerated juvenile offenders found similar results (Becker and Kerig, 2011). Unfortunately, we cannot address this hypothesis further in this article due to small cell sizes in some of the latent statuses. A future study with more participants can examine the racial differences in the effect of psychological trauma change on recidivism.
We find it interesting that gender did not predict 6-month recidivism; however, it did weaken the association between latent status membership and recidivism. This lack of association may be because these are among only successful completers, or because a direct relationship between gender and recidivism does not exist in the BHJJ program sample. Kretschmar and colleagues (2014) did not find gender to be a predictive factor in a logistic regression model of 12-month recidivism. A more complex relationship between latent status membership, recidivism, and gender may exist, and may possibly involve race as well. Preliminary analyses with a limited sample size point in that direction; however, more analyses with a larger sample size need to be conducted.
Comparing the Latent Variable Regression Model with the Observed Variable Regression Model
We failed to find a statistically significant relationship between any of the independent variables and 6-month recidivism, without the gender or race covariates and with them included in the model. None of the trauma symptoms were significantly associated with recidivism nor did they have an effect on recidivism.
If we had conducted this analysis using psychological trauma as five observed change variables rather than modeling it as a latent change variable to understand the relationship between psychological trauma change and 6-month recidivism, we would not have found the relationship that we did. This comparison supports the argument that latent variable modeling and person-centered analyses can find the population-level heterogeneity needed to model important relationships that observed variable-centered statistical analyses cannot on their own.
The latent variable person-centered approach answers different questions than the observed change variable-centered approach. Person-centered approaches are interested in defining subpopulations that may be used in subsequent analyses, whereas variable-centered approaches treat a sample as homogeneous and instead focus only on relationships between variables. Furthermore, it may be essential to combine multiple techniques including variable-centered and person-centered statistical analyses to answer complex research questions such as the ones posited here (Muthén & Muthén, 2000).
Limitations
This study is not without limitations. First, those who are in BHJJ are not randomly assigned into BHJJ. Those who successfully complete may have some sort of self-selection bias for which we cannot account. Also, we do not have a control group in two ways: We do not have a group who do not go into BHJJ at all, and we do not have an unsuccessful treatment completion group. This means that we cannot make comparisons between not attending BHJJ or unsuccessfully completing BHJJ and successfully completing BHJJ. Perhaps in the future, as we increase the number of people into BHJJ, we may be able to gain a large enough unsuccessful completion group for analysis.
Second, we could not measure the true effect of latent status membership on an outcome such as recidivism, but rather had to rely on the estimations from the latent transition membership classification to group people into these 12 initial categories, then 10 categories based on sample size restrictions, and regress that onto recidivism. As a result, there may be some misclassification of some cases into a latent status by about 21% (entropy = 0.792). We had no choice but to do this because the cell sizes were too small for distal outcome estimation. In a future study, with a larger population, we should be able to employ distal outcome estimation, a more accurate estimation analysis.
Third, we encountered sample size issues in a number of ways in regard to the logistic regression model. We were forced to combine three latent status membership categories into one because cell sizes were too small for a meaningful estimation. Also, we could not add as many covariates as we would have liked because cell sizes were already very small as it is. Finally, we could not stratify by gender or race because the cell sizes in some latent status categories were too small to estimate. Stratification or other methods may assist in understanding the relationship between race, gender, psychological trauma change, and recidivism after completion of diversion programming. An increased sample size would make this possible.
Conclusion
Even among those who successfully complete a juvenile justice behavioral health diversion program, there are those that go on to recidivate a year following termination from the program. This study finds that specific subpopulations, particularly those who have the specific endorsement of depression or anger symptoms at Intake, are more likely to recidivate later than those who have generally low trauma or even have generally high trauma symptoms, even if they move to an improved latent class at Termination. This interesting finding suggests that behavioral health diversion programming may need to target treatment to these specific subpopulations of those youth who demonstrate high symptomatology in depression or anger. When depression and anger symptoms are not successfully addressed during the treatment period, youth are at the highest risk for recidivating.
Future research and evaluation should focus on targeting youth who demonstrate anger and depression symptoms at Intake, and what the diversion programs are that may require better services to reduce anger and depression. Although many of these youth may demonstrate developmental trauma disorder (D’Andrea et al., 2012), as seen in this study, the youth in the high trauma symptoms class, who may also demonstrate the characteristics of developmental trauma disorder, demonstrate other internalizing symptoms that are different from the anger and depression class. This may make them not only more amenable to the treatment modalities offered, but it may be that the treatment offered is able to reduce their symptomatology enough that they are more successful than youth who are very angry and depressed. Providing treatment to youth who display more externalizing symptoms, such as anger, should be considered for therapeutic interventions to address emotional numbing, as well as behavior management programming (Ford, Steinberg, Hawke, Levine, & Zhang, 2012; Kerig, Bennett, Thompson, & Becker, 2012).
Not treating psychological trauma change as a latent variable results in an underestimation of effects on recidivism. It also does not reveal any of the population heterogeneity that we identified through LCA and LTA. Intra-individual change’s effects on recidivism, such as change in mental health issues, are rarely studied (Serin et al., 2013). Furthermore, Serin and colleagues call for more sophisticated modeling techniques to measure intra-individual change as a construct rather than an observed variable. We address this gap in the literature by modeling psychological trauma change as a latent categorical variable that manifests as subpopulations.
We now know that in our population of successful juvenile diversion participants, there are four distinct subpopulations that display psychological trauma symptoms at intake, and then three subpopulations at termination. Certain subpopulations are at higher odds of recidivating than others, a finding that only a latent class and transition analysis would have found. Understanding these constellations of symptoms within these subpopulations may be the first step to identifying improvements in diversion programming to reduce recidivism even further within this population. Further person-centered analyses are needed to identify these youth, perhaps using a developmental trauma disorder–informed focus as suggested in D’Andrea and colleagues (2012).
In addition, the field needs further research that focuses on the relationship between victimization and psychological trauma in the context of diversion programming and recidivism prevention. The authors plan to expand their research to model the effects of victimization and exposure to violence on psychological trauma over time within the behavioral health diversion programming population. This study is one of many that will employ person-centered research to explore the complex relationship between victimization, psychological trauma, and later recidivism. Future research should also focus on replicating these results within a larger and different sample to confirm the findings.
Footnotes
This research was supported in part by grants from the Ohio Department of Youth Services and the Ohio Department of Mental Health & Addiction Services.
