Defeat and entrapment: more than meets the eye? Applying network analysis to estimate dimensions of highly correlated constructs

Defeat and entrapment are usually assessed with the Defeat Scale (DS) and the Entrapment Scale (ES), both developed by Gilbert and Allan [1]. The two scales consist of 16 items each using a five-point Likert scale. The DS showed good internal consistency and good convergent and criterion validity in terms of positive relations with depression, hopelessness and suicidality in students, patients, and male prison inmate samples [1, 6, 17‐22]. The ES showed comparable psychometric characteristics in terms of internal consistency and convergent and criterion validity [1, 23]. The ES was originally designed as a two-dimensional instrument, distinguishing between internal and external entrapment [1]. Internal entrapment is measured with six items (e.g., “I would like to escape from my thoughts and feelings” or “I feel trapped inside myself”) and external entrapment with ten items (e.g. “I have a strong desire to escape from things in my life” or “I can see no way out of my current situation”). Gilbert and Allan [1] reported a correlation between both scales of r = .75 but nonetheless argue that they are differentiable facets of the construct. However, subsequent research confirmed the close relation between internal and external entrapment and suggested that entrapment should be best conceptualized as a unidimensional construct [24].

Moreover, a vivid debate is ongoing about the factorial validity of the defeat and entrapment scale. While the two instruments were originally designed and applied as being two separate scales, recent research suggests that they appear to represent the same construct [7, 24, 25]. This implies that the constructs themselves might not be distinct but rather two sides of the same story [24]. Consequently, Griffiths et al. [26] developed the short defeat and entrapment scale (SDES). The SDES consists of eight items, four indicating defeat and four entrapment. The eight items of the SDES were chosen from the 32 items of the original DS and ES by means of a principal-axis exploratory factor analysis (EFA): Griffiths et al. [26] picked the four highest loading items of the DS and the four highest loading items of the ES from the EFA based on data of N = 262 participants from the community. The authors presented then a series of analyses supporting unidimensionality, internal consistency, and validity of this set of eight items building the SDES.

However, within the field of psychometrics, it is known that well established analytic techniques such as exploratory factor analysis (EFA) and Confirmatory Factor Analysis (CFA) might underestimate the number of factors when factors are highly correlated [27]. When Griffith et al. [26] tested a two-factor model of defeat and entrapment, they found that it actually fitted the data better than a one factor model. Yet, because the two factors were highly correlated (r = 0.91), they decided to stay with the one factor model. Within this article, we applied a novel technique based on network modelling that has been found to outperform traditional techniques when data are highly correlated. We will compare the number of identified clusters with the results from standard factor techniques based on data from an online and a clinical sample, and discuss its scientific and clinical relevance.

In the past years, there has been a specific interest in the estimation of network models using psychological data [28]. Network analysis allows to visualize and estimate the association between variables, without assuming any underlying dimensional structure a priori [29]. A network consists of nodes (the items) and the pairwise relation between the items (edges). When two items have a pairwise interaction after conditioning for all other items in the dataset (so-called partial correlation), they are connected via a line (edge). Importantly, the interpretability of a network is highly increased by applying a penalized maximum likelihood estimation called LASSO. After applying LASSO estimation on the partial correlation matrix, non-relevant spurious partial correlations are set to zero, resulting in a network of direct non-spurious relations between nodes [30]. Network modelling has successfully been applied within for example the field of depression research (e.g., [31]), PTSD (e.g., [32]), and recently, suicidology (e.g., [33]).

Although network analysis does not assume any underlying latent structure a priori, researchers and clinicians are still interested in the clustering of nodes. Indeed, Golino and Epskamp [27] argue that clusters in a network are similar to latent variables. The LASSO estimations result in a sparse matrix that is better attuned to identifying clusters in highly correlated data. Next, an algorithm called walktrap can be used to identify numbers of clusters or latent variables within this sparse matrix [29]. In simulation studies, the application of a walktrap algorithm on a sparse matrix was found to outperform traditional methods like parallel analysis and eigenvalue decomposition when analyzing data with multiple strongly correlated latent factors [27]. Confirmatory Factor Analysis can then be applied to test whether the proposed structure fits the data.

The aim of the present study was to estimate the number of dimensions within a network of the 32 items of the DS and ES in an online and a clinical sample using graph techniques and to compare the results with exploratory factor analysis.

Between December 2015 and April 2016, data was collected through an anonymous online survey using the SoSci-server [30]. The study was approved by the Ethics Committee of the Ruhr-Universität Bochum, Germany. Participants were recruited through postings at two universities (Aachen and Bochum) and several psychotherapy outpatient units as well as social media (e.g., Facebook). When surfing on the study website, before the start of the survey, participants were informed about the purpose and content of the survey and provided with useful addresses (i.e., telephone numbers of helplines and contact information for therapy institutions), in case they felt burdened due to the content of the study or had suicidal thoughts in general. They were also provided with contact addresses in case they had any questions. In order to take part in the study, participants had to be at least 18 years old and give their consent to participation at the beginning of the study. Participants could only proceed to the next questionnaire, if they had answered the previous questionnaire completely. It was possible to either take a break (and possibly continue to fill out the rest of the survey later on) or to stop the survey completely (and therefore delete all data) at every time during the survey.

At the end of the study, participants had the opportunity to take part in a raffle, where – as an incentive for participation – five Amazon gift cards each valued at 15 euros were raffled. On average, participants spent 15.3 min filling in the questionnaires.

Data of 147 patients who answered the 32 items on defeat and entrapment within 2 weeks after being admitted to German psychiatric hospitals after a suicide attempt or a severe suicidal crisis were used to verify the number of dimensions of the defeat and entrapment scale in a clinical sample. Participants were approached personally while in hospital, informed about the study aims and procedures and gave written informed consent prior to participation. Patients were eligible to participate if they were at least 18 years old, capable to read and communicate in German language and were not suffering from a psychotic disorder or acute substance intoxication. They filled in the ES and DS in a paper-pencil-version together with additional questionnaires reported elsewhere. This is preliminary data that was collected within the scope of a larger ongoing research project called “PRESS: Prediction of the longitudinal development of suicidal thoughts and behaviors - a validation of the interpersonal theory of suicidal behavior” which was approved by the ethics committees of the Ruhr-Universität Bochum, Germany, the Medical Faculty of the RWTH Aachen University, Germany, and the Medical Faculty of the University of Leipzig, Germany.

Descriptive analyses were done using PASW Statistics 20.0.0.

All other analyses were performed with R version 3.3.3. [41].

The outcomes of our exploratory and confirmatory analysis were highly comparable with the analysis of Griffith et al. [26]. One factor explained most of the variance and all items loaded well on the one factor. The graph analysis showed that the items belonged to subtler sub-dimensions. The entrapment items can be thought of as highly related but different from the defeat items, and might even consist of two subscales, internal and external entrapment. Still, when comparing the CFAs, the one factor model as proposed by the EFA was preferred above the three or the four factor structure as proposed by the EGA on the clinical or the online sample. Known as Occam’s Razor, when the fit of two models are highly comparable, the simplest model is preferred [49]. However, no clear answer can be provided what can be considered as the best number of dimensions. The choice of the optimal number of dimensions should be a tradeoff between theory, clinical usefulness, model complexity and fit. The original theory by Gilbert and Allan [1] and more contemporary theories incorporating defeat and entrapment such as the IMV model [12, 13] propose that defeat and entrapment are different constructs. The original theory [1] even suggests that entrapment consists of the sub-dimensions internal and external entrapment. Although replication in larger (clinical) samples is needed our data appear to be in line with these theories and should be interpreted in the light of their assumptions.

On that note, with regard to the Short Defeat and Entrapment Scale of Griffiths et al. [26], we think that a shorter version of the DS and ES can be beneficial for clinical practice. However, it seems that the techniques used to come to the short scale were not able to deal with the highly correlated constructs of defeat and entrapment and their sub-dimensions. We therefore advise researchers not to simply use the short scale, but to select items from a theoretical and clinical perspective. The results of the present investigation may help clinicians and researchers in picking the appropriate items. Still, it is possible that the most informative items will differ from study to study, sample to sample, and perhaps even from patient to patient [50, 51].

From a clinical perspective, it is important to note that the present results support most theoretical clinical models incorporating defeat and entrapment as separate constructs. Most prominent, the IMV [12, 13] proposes that patients in a suicidal crisis develop states of defeat and entrapment consecutively when progressing from suicide ideation to suicide plans and behavior.

Practically, clinicians should be aware that feeling defeated and feeling entrapped most of the times coincide, but, most importantly, can also develop independently from each other. Each of these constructs may entail heightened risk for symptom deterioration or, when referring to suicidology, exacerbate the risk for the development of suicidal thoughts and behavior. Thus, both constructs should be part of a comprehensive risk assessment and should be born in mind when conceptualizing treatment for patients at risk for suicide.

An important limitation is the small sample size of the clinical sample. Although power analysis within network psychometrics is still being discussed, it is argued that to estimate a network of 32 items, at least 32 * (32–1/2) = 496 participants are needed. By this standard, even the online sample was marginally too small. By using bootstrap techniques to estimate our network, we have applied the current state of the art techniques to estimate stable networks. Although rather small, we added the clinical sample to further validate the findings of the online sample and to stimulate researchers with access to a larger clinical sample to use the same techniques and re-run our analyses. To facilitate this, a short online description of the used code was made: https://​derekdebeurs.​shinyapps.​io/​Online_​code/​#section-introduction.

Additionally, the number of dimensions within the online sample differed from the number of dimensions of the clinical sample. Validation in larger samples should investigate whether this differences are real differences between samples or the result of the difference in sample size. Finally, network psychometrics is a rapidly developing field, so new techniques to estimate communities using networks might be developed in the near future.