Growth Mixture Modelling: A user friendly overview of its application to trauma symptomatology

Cherie Armour, PhD

GMM is largely regarded as an extension of latent growth modelling (LGM) and latent class/profile analyses (LCA/LPA). LCA and LPA (which differ only in their use of categorical or continuous variables respectively; see Shevlin, Armour, Murphy, Houston, & Adamson, 2010; Armour, Elklit & Shevlin, 2011 for examples) are implemented on cross-sectional datasets and assess whether underlying unobserved subpopulations exist in an overarching observed population based on their similarity of responding across a number of indicators (for example, PTSD symptoms or traumatic life events). LGM is a method that assesses longitudinal change across a particular variable whilst assuming that all individuals have a single intercept (baseline score) and a single slope (level of change over time).

In combining these two methods GMM assesses if multiple unobserved latent trajectories are available within an observed overarching group of individuals.  In other words GMM uncovers subgroups of individuals, who report varying levels of change across time, on a particular variable. In order to identify the number of underlying latent trajectories successive models of 1 to 6 (or more) subgroups are specified and estimated (i.e., a model with 2 latent trajectories, a model with 3 latent trajectories and so on). The purpose of comparing models with a differing number of trajectories is to find the model that best approximates the subgroups within the data.  Comparisons are based on a number of fit indices that correspond to each of the models, for example each model will result in a Bayesian Information Criterion (BIC) value. Superior models are regarded as those with lower BIC values (see Nylund et al., 2007).

One application of this within the traumatic stress field pertains to the longitudinal course of PTSD symptomatology (e.g. Armour, Shevlin, Elklit, & Mroczek, 2012). Indeed, the longitudinal course of PTSD symptomatology post-trauma has been a topic of interest for many years. Studies assessing the course of PTSD have reported differential trajectories across a variety of trauma populations. For example, in examining the change in PTSD symptom severity reported by victims of non-sexual assault, Riggs, Rothbaum, and Foa (1995) reported that PTSD symptom severity generally decreased (in the absence of intervention) across 12 weekly assessments. Similar findings of a decrease in PTSD have been reported elsewhere with alternative trauma populations (e.g., Rothbaum, Foa, Riggs, Murdock, & Walsh, 1992; Wu & Cheung, 2006).

However, other studies have reported an increase in PTSD (Clipp & Elder, 1996; Kahana, 1992; Port, Engdahl, & Frazier, 2001), and delayed onset PTSD (Clipp & Elder, 1996; Koren et al., 1999). Notably, epidemiological research clearly demonstrates that not everyone experiences PTSD symptomatology post-trauma exposure. For example, the National Comorbidity Survey; a nationwide probability sample of over 2800 men and 3000 women from the US, reported that trauma exposure outweighed the prevalence of individuals who met PTSD diagnostic criteria (Kessler, Sonnega, Bromet, Huges, & Nelson, 1995).  Similar findings were reported by an epidemiological survey conducted in Australia; the Australian National Survey of Mental Health and Wellbeing (Creamer, Burgess, & McFarlane, 2001).

Therefore, research has demonstrated that different individuals respond to trauma in different ways; some experience symptomatology which 1) gradually decreases over time, 2) increases over time, and 3) has a delayed onset; others experience, 4) relatively low or near pre-trauma exposure levels of symptomatology and therefore appear to be resilient to the effects of the trauma. Pietrzak et al. (2013) notes that “Common trajectories of PTSD symptoms include resistance or resilience (i.e., minimal to no symptoms over time); subsyndromal (i.e., mild to moderate symptoms over time); chronic (i.e., chronically elevated symptoms over time); delayed dysfunction (i.e., increasing symptoms over time); and recovery (i.e., declining symptoms over time)” (p. 2).

It is therefore increasingly apparent that the traditional method of examining change in PTSD symptomatology across time in the form of a single growth trajectory (e.g., LGM) has a strong potential to obscure our knowledge on PTSD’s longitudinal course.  A more formidable alternative is the use of GMM. An additional strength of GMM is that researchers can extend their analysis by investigating which variables influence membership of a particular trajectory group. In doing so, latent class membership (or trajectory group) can be used as the dependant / outcome variable within a number of statistical techniques (e.g. ANOVA, Logistic Regression).  The use of multi-nominal logistic regression is particularly common in GMM studies.

In using multi-nominal logistic regression, one trajectory group is nominated as a reference class (usually the baseline / lowest scores / resilient trajectory), which is then used as a comparison with all other trajectories. If a predictor is significantly associated with a particular trajectory (compared to the reference trajectory) it is interpreted as increasing (odds ratio value over 1) or decreasing (odds ratio under 1) the likelihood with which a person would be placed in that trajectory if they were positive on (categorical) or scored highly on (continuous) the predictor. For example, let’s say we have a situation where the resilient class is nominated as the reference group and the predictor (let’s say social support) is coded so that high scores equalled high levels of social support. We implement our logistic regression and obtain a significant odds ratio of less than 1 (say 0.46) for social support as it relates to a chronic trajectory. In the simplest of terms the interpretation is that an individual high on social support is less likely to be a member of the chronic trajectory as compared to the resilient trajectory.

Extending GMM analyses using methods such as logistic regression is particularly useful as both baseline and time-varying factors may be differentially related to trajectories. This is of paramount importance; particularly if factors that are identified as increasing poorer longitudinal outcomes are modifiable and if factors identified as protective can be promoted and enhanced in trauma populations (Bonanno et al., 2012; Pietrzak et al., 2013). For example, Hobfoll et al. (2011) and Karstoft et al. (in press) have reported that a higher level of social support was associated with an improvement in PTSD over time and that people with a higher level of social support were less likely to be found in a chronic PTSD trajectory. Ultimately, this suggests that social support may act as a buffer against worsening PTSD trajectories over time.

Therefore, if interventions to increase social support could be put in place immediately post-trauma (i.e., educating family members, increasing opportunities to build support networks post-military deployment) this may lessen the psychological impact of the trauma on the individual. On that note, GMM is particularly suited for researchers who wish to identify prototypical PTSD trajectories including that of resilience and extend their analysis to further investigate factors that promote ‘Resilience After Trauma.’

To illustrate the application of GMM whilst simultaneously investigating factors of risk and resilience I will summarise two recent studies*; 

1) Pietrzak et al., (2013). Trajectories of PTSD risk and resilience in World Trade Centre responders: an 8-year prospective cohort study. Psychological Medicine, 1-15.

The above study implemented GMM on a sample of 10,835 world trade centre responders (traditional responders [police officers] n = 4,035 and non-traditional responders [e.g., construction workers, security guards, transportation workers] n = 6,800).  PTSD symptomatology was assessed using DSM-IV criteria via the PTSD Checklist Specific-Stressor Version (PCL-S; Weathers et al., 1993) at 3, 6, and 8 years post- 9/11. Several demographics were queried including age, gender, race, marital status and income.

Respondents were also queried in regard to several trauma exposures which were as a direct result of being a responder, such as being exposed to human remains, knowing a Sept 11th injured party, and arriving on site between the 11th and 13th of September (the number of endorsed traumas were summed to create an overall severity score), levels of social support, pre-existing psychiatric and medical conditions, and exposure to life stressors pre- 9/11. GMM was conducted separately on the two groups of responders.

Following standard practice for GMM, successive models through 1 to 6 trajectory classes were assessed and then compared across a number of fit indices including the Bayesian Information Criteria (BIC). Subsequent to this, multi-nominal logistic regression was used to assess the predictors (i.e., demographics, trauma exposures) of the longitudinal trajectories.

The GMM analyses revealed that the number of latent trajectories differed across the two responder groups. The GMM analyses of the traditional police responder group resulted in 4 latent trajectories; Resilient (77.8%), Delayed Onset (8.5%), Recovering (8.4%), and Severe Chronic (5.3%), whereas, the GMM of the non-traditional group resulted in 6 latent trajectories; Resilient (58.0%), Delayed Onset (6.7%), Recovering (12.3%), Severe Chronic (9.5%), Subsyndromal Increasing (7.3%), and Moderate Chronic (6.2%).

Notably, the resilient trajectory comprised the largest proportion of individuals in both groups.  The authors highlighted that there were striking similarities between the prevalence’s of the latent trajectories in their police responders group as compared to that of other studies using similar occupational groups and groups exposed to alternative trauma experiences (e.g., Bonnano et al., 2012; Bowler et al., 2012; Hobfoll et al., 2011). In discussing why the prevalence of individuals in the severe chronic trajectory was greater for non-traditional responders (9.5%) vs. traditional police responders (5.3%) the authors highlighted research which reports the protective role of preparedness in such occupational groups (cf. Goldman et al., 2012).

The multi-nominal logistic regression revealed that several factors were associated with symptomatic PTSD trajectories as compared to the resilient trajectory. In other words, people were more likely to be grouped into a symptomatic trajectory compared to a resilient trajectory if they were female, had lower levels of educational attainment, a greater number of prior life stressors, were of Hispanic ethnicity, had a prior psychiatric history, a more severe world trade centre trauma exposure record, and medical conditions which were related to the world trade centre events. Interestingly, the latter 4 factors were those most predictive of membership in symptomatic trajectories.

Furthermore, level of social support, both support from the family and support from work during the respondent’s time at the site, were negatively associated with membership of a number of symptomatic trajectories (in both groups). Thus, suggesting that social support acts as a buffer against PTSD symptomatology and is perhaps one factor that could be focused on for increasing psychological resilience post-trauma exposure.

In conclusion the study provides further evidence of the heterogeneous nature of PTSD across time, and highlights the lower likelihood of negative symptom trajectories in traditional responders as compared to non-traditional responders, suggesting that non-traditional responders may carry a certain degree of vulnerability in such situations. Further, the authors highlighted the protective role of social support and the risk posed by a number of factors such as prior psychiatric history and Hispanic race.

2) Karstoft, K. I., Armour, C., Elklit, A., Solomon, Z. (in press). Long term trajectories of PTSD in veterans: the role of social resources. Journal of Clinical Psychiatry.

The above study implemented GMM on a sample of 675 male Israeli combat veterans (a clinical group of 369 veterans who were diagnosed with a Combat Stress Reaction (CSR) and a control group of 306 veterans without a CSR). PTSD symptomatology was assessed using DSM-III criteria (given the timing of initial data collection) via The PTSD Inventory (Solomon, Weisenberg, Schwarzwald, & Mikulincer, 1987). Data was collected across three time points spanning 20 years: 1 year (T1), 2 years (T2), and 20 years (T3) years post war. Respondents were queried in regard to demographics, subjective combat exposure, multiple psychological factors, and multiple social factors. This particular study chose to focus on subjective combat exposure and the social factors of  military unit support, family relations, social network support, and social re-integration post-deployment; all of which are indicative of social support more generally.

GMM was conducted on both the CSR and non-CSR groups. Again, following standard practice for GMM, successive models through 1 to 6 trajectory classes were estimated and then compared across a number of fit indices, including the Bayesian Information Criteria (BIC).  Subsequent to this multi-nominal logistic regression was used to assess the subjective combat exposure and social support indicators as predictors of the longitudinal trajectories.

The GMM analyses revealed that 4 latent trajectories best represented the underlying heterogeneity of the two groups however the prevalence of individuals differed within trajectories; Resilience (CSR = 34.4% vs. non-CSR = 76.5%), Recovery (CSR = 36.3% vs. non-CSR = 10.5%), Delayed Onset (CSR = 5.4% vs. non-CSR = 6.9%), and Chronicity (CSR = 20.9% vs. non-CSR = 6.2%). The authors highlight that these results demonstrate that early trauma responses such as a CSR may be predictive of chronic outcomes. The multi-nominal logistic regression revealed that if respondents perceived the war as life threatening this predicted membership of all symptomatic trajectories for the CSR group and of the chronic and recovering trajectory for the non-CSR group; as compared to the resilient trajectories.

Respondents reporting higher levels of social support in the CSR group were less likely to be grouped into the chronic and recovering trajectories compared to the resilient trajectory, however there were no significant effects of social support on trajectories for the non-CSR group. Furthermore, less exclusion from society when returning home post-deployment decreased the likelihood with which respondents would be grouped into the chronic and recovering trajectories in the non-CSR group, and all symptomatic trajectories in the CSR group. In an attempt to differentiate the chronic trajectory group from other trajectories the multi-nominal logistic regression was conducted using the chronic trajectory as the reference/comparison group.

In the non-CSR group only the perception of war threat was able to significantly differentiate the chronic trajectory from the delayed onset trajectory, with respondents being less likely to be in the recovery group in they had a high perception of threat. In the CSR group, the chronic trajectory was differentiated from both the recovery and delayed onset trajectory with less exclusion at homecoming being predictive of membership in recovery and delayed onset trajectories. 

In conclusion, the authors confirmed the heterogeneous nature of PTSD across time whilst confirming 4 latent trajectories that correspond with a number of other studies (cf. Bonanno et al., 2012). Moreover, social support was once again highlighted as buffering against symptomatic trajectories of PTSD post-trauma; this time however social support was investigated across multiple levels adding further weight to its protective role. 

Future studies implementing GMM will clarify the longitudinal course of PTSD and further highlight both risk and resilience factors for heterogeneous trauma responses. Ultimately, this line of work will be imperative in the development of intervention and treatment programmes. Indeed, knowledge in relation to factors which promote resilience will enhance endeavours to prevent the development of PTSD post-trauma exposure.

*Please note that these studies are simply a selection from many possible alternatives.

About the Author

Cherie Armour, PhD, CPsychol, is a lecturer in psychology based at the University of Ulster, Coleraine Campus, Northern Ireland. Cherie lectures on abnormal and clinical psychology, health psychology, and quantitative research methods. Currently she supervises PhD and MSc students. Prior to this appointment, she held a postdoctoral position at the National Centre of Psychotraumatology based at the University of Southern Denmark with professor Ask Elklit. Cherie's current research interests primarily relate to PTSD symptom structure and comorbidity, PTSD longitudinal course, and teenage dating violence.

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