Sample Characteristics
Table 1 presents the demographic and life style characteristics of the sample. The sample comprised 249 women and 93 men, with an average age of 35.4 years (median = 33; SD = 11.9). A total of 38.6% of participants reported experiencing childhood adversity. The majority of participants reported low levels of physical exercise (39.8%), cigarette consumption (19.9%), alcohol use (14.9%), and psychoactive drug use (3.2%).
Table 1
Demographics and Life Style Variables for 342 Depressed and Non-depressed Participants
| Overall (N = 342) |
Sex | |
Female | 249 (72.8%) |
Male | 93 (27.2%) |
Age | |
Mean (SD) | 35.4 (11.9) |
Median [Min, Max] | 33.0 [18.0, 86.0] |
Childhood Adversity | 132 (38.6%) |
Physical Excercise | 136 (39.8%) |
Smoking Cigarettes | 68 (19.9%) |
Alcohol Use | 51 (14.9%) |
Psychoactive Substance Use | 11 (3.2%) |
Table 2 presents the IDER trait score, scores for the five cognitive domains, and attributional styles. The IDER score for the sample had a mean score of 21.7 (median = 19; SD = 8.6). For the five cognitive domains, the results showed mean scores of 13.7 (SD = 6.11) for disconnection and rejection, 12.1 (SD = 5.49) for impaired autonomy, 15.2 (SD = 5.72) for impaired limits, 16.3 (SD = 5.63) for Other-Directedness, and 17.6 (SD = 4.74) for Over-Vigilance/Inhibition. Regarding attributional styles, more than half of participants (57.6%) reported Negative Attribution to stressful events, 50.3% reported Unexpected Attribution, and 21.3% reported Out of Control Attribution.
Table 2
IDER, Maladpatative Cognitive Schemas and Cognitive Attibution Scores for 342 Depressed and Non-depressed Participants
| Overall (N = 342) |
IDER Score | |
Mean (SD) | 21.7 (8.66) |
Median [Min, Max] | 19.0 [10.0, 40.0] |
Disconnection and Rejection | |
Mean (SD) | 13.7 (6.11) |
Median [Min, Max] | 13.0 [5.00, 29.0] |
Impaired Autonomy | |
Mean (SD) | 12.1 (5.49) |
Median [Min, Max] | 11.0 [5.00, 26.0] |
Impaired Limits | |
Mean (SD) | 15.2 (5.72) |
Median [Min, Max] | 15.0 [5.00, 30.0] |
Other-Directedness | |
Mean (SD) | 16.3 (5.63) |
Median [Min, Max] | 16.0 [5.00, 30.0] |
Over-Vigilance/Inhibition | |
Mean (SD) | 17.6 (4.74) |
Median [Min, Max] | 18.0 [6.00, 30.0] |
Negative Attribution | 197 (57.6%) |
Unexpected Attribution | 172 (50.3%) |
Out of Control Attribution | 73 (21.3%) |
Higher Scores for the Cognitive Schemas reflect more significant maladaptive schemas. IDER scores: 24–40 High, 17–22 Average, 16 or less Low |
Beta Regression |
The beta regression model results are presented in Table 3.To verify the model’s assumptions, we visually inspected the beta regression using R’s plot function. The generated graphics revealed that all assumptions were well within the acceptable range, the residuals appeared to be randomly distributed around zero, and the Cook’s distance plot did not indicate the presence of influential observations. Therefore, the beta regression model is valid for interpreting our data. The plots are available at the authors GitHub repository and in the appendix.
We also conducted a variance inflation factor (VIF) analysis to detect multicollinearity in the beta regression model. The results indicated that most predictor variables had VIF values below 3.9, indicating a moderate degree of multicollinearity. However, one variable had a VIF of 4.9, which could suggest a stronger correlation with other predictor variables in the model. Nevertheless, since none of the VIF values exceeded the recommended threshold of 5 or 10 [22], we concluded that the collinearity was not severe enough to affect our analysis’s overall findings.
Table 3
Beta Regression for the IDER Score in a Sample of 255 Depressed and Non-depressed Adults
| IDER |
Predictors | Estimates | CI | p |
(Intercept) | 0.16 | 0.07–0.35 | < 0.001 |
Age | 0.99 | 0.98–1.00 | 0.011 |
Disconnection and Rejection | 1.07 | 1.03–1.10 | < 0.001 |
Impaired Autonomy | 1.08 | 1.05–1.12 | < 0.001 |
Impaired Limits | 1.02 | 0.99–1.04 | 0.126 |
Other-Directedness | 1.00 | 0.98–1.03 | 0.939 |
Over-Vigilance/Inhibition | 1.00 | 0.98–1.03 | 0.962 |
Number of Stressful Events | 1.00 | 0.99–1.01 | 0.785 |
Sex [Male] | 1.07 | 0.88–1.31 | 0.477 |
Negative Attribution [No] | 0.66 | 0.53–0.83 | < 0.001 |
Unexpected Attribution [No] | 1.04 | 0.85–1.28 | 0.675 |
Out of Control Attribution [No] | 0.74 | 0.59–0.94 | 0.012 |
Childhood Adversity [No] | 0.71 | 0.59–0.86 | < 0.001 |
Physical Excercise [No] | 1.03 | 0.86–1.23 | 0.773 |
Smoking Cigarettes [No] | 0.75 | 0.60–0.95 | 0.015 |
Alcohol Use [No] | 0.95 | 0.74–1.23 | 0.707 |
Psychoactive Substance Use [No] | 1.43 | 0.86–2.38 | 0.165 |
Observations | 342 |
R2 | 0.596 |
The predictors age, disconnection and rejection, impaired autonomy, negative attribution, out of control attribution, childhood adversity, and smoking cigarettes, are all statistically significant at the 0.05 level, meaning that it is unlikely to have arisen by chance. The negative coefficients for Negative Attribution, Out of Control Attribution, Childhood Adversity, and Smoking Cigarettes suggest that not having these predictors is associated with a decrease in the log odds of experiencing NA (These coefficients are in comparison to the “yes” reference group). In contrast, having these predictors is associated with an increase in the log odds of experiencing NA. Additionally, a negative coefficient for age suggests that as age increases, the odds of experiencing NA decreases.
The results also show that disconnection and rejection and impaired autonomy are significantly associated with the odds of experiencing NA. Each one unit increase in disconnection and rejection increases the log odds of experiencing NA by 0.06 units, while each one unit increase in impaired autonomy increases the log odds of experiencing NA by 0.08 units (in a scale from 0 to 1).
Table 3 displays the precision results for the mean model, which includes the pseudo R-squared of 0.60 that demonstrates a strong fit for the model as noted by Giselmar and collegues [23]. However, it is important to keep in mind that the pseudo R-squared should not be directly compared to the R-squared of linear regression models. This is because the former only measures how well the model fits the data, and does not estimate the accounted variability.
Regression tree results
Tree-based methods are a type of predictive modeling that seeks to identify similar groups of people based on their outcomes using a series of yes/no questions. These questions are plotted in a graphical format as a tree or bush, with the root representing the initial question and subsequent branches representing subsequent questions. To make predictions for a new person, the tree is traversed from the root to the end of the last branch by answering the yes/no questions. Questions that appear close to the root or frequently throughout the tree are more important for grouping people with similar outcomes.
Tree-based methods can produce very complex trees with small subgroups of people, which can be simplified by pruning or removing certain branches. The optimal amount of pruning is determined by testing different values of the cost complexity parameter (CP) on different parts of the data and choosing the value that results in the best performance on a separate set of data. By simplifying the tree, the model can be made more interpretable and easier to use in practice.
The optimal CP parameter was found to be 0.001, as it produced the highest R-squared value and the lowest root mean square error (RMSE) value among all parameters tested.
Using the value of CP the regression tree model in the testing data achieved an R-squared value of 0.7744057, which measures the proportion of variance in the IDER score that is explained by the predictors selected. A value of 0.7744057 indicates that the model is explaining a significant portion of the variance in the IDER score. Additionally, the RMSE of 4.01031 suggests that the model is providing reasonably accurate predictions for the IDER score.
Figure 1 displays the results of the regression tree analysis. The final decision tree model incorporates nine variables, including three cognitive domains: disconnection and rejection (dyrysq), impaired autonomy (padysq), and impaired limits (seiysq); two attributional styles: negative attribution (is_negative) and out of control attribution (is_no_control); two lifestyle variables: alcohol (is_alcohol) use and smoking cigarettes (is_smoke); and two demographic variables: age and childhood adversity (is_abuse).
The root node of the tree includes 255 observations, with a mean IDER score of 21.88. The sisconnection and rejection variable (dyrysq) is the most critical factor in determining high or low IDER scores, with a cutoff value of 17. The tree also features three other main splits based on impaired autonomy (padysq), childhood adversity (is_abuse), and negative attribution (is_negative). These variables are crucial in determining high or low levels of NA.
The decision tree indicates that a score of at least 35 points in the IDER instrument (split 63 in Fig. 1) is predicted by the interaction of a 16 or higher score in the disconnection and rejection cognitive domain (split 1), a score higher than 13 in the impaired autonomy schema domain (split 3), and not consuming alcohol (split 15) but smoking cigarettes (split 31). On the other hand, lower scores are determined by having low scores in the disconnection and rejection schema, lower scores in the impaired autonomy domain, not interpreting stressful situations as negative, and being 48 years of age or older.
In summary, the decision tree depicts several interactions between cognitive, lifestyle, and demographic variables associated with higher levels of NA. Upon analyzing the results of the beta regression and regression tree, it is apparent that there is a correspondence between the two methods, and they provide complementary information. The beta regression demonstrates that cognitive schemas such as disconnection and rejection, and impaired autonomy significantly increase the likelihood of higher scores in the IDER test (p < 0.001). These two schemas’ effects are evident in the tree as they are the first two splits, indicating their higher importance in estimating higher levels of NA. The regression tree reveals an additional schema that is not significant in the beta regression, impaired autonomy. In combination with high levels of disconnection and rejection, impaired autonomy predicts higher scores in the IDER (split 14).
Furthermore, both methods agree that childhood adversity’s presence or absence is critical in determining high or low levels of NA. The beta regression suggests that not being subjected to childhood adversity decreases the chances of high scores in the IDER, and the tree regression complements this by showing that low scores are possible in the absence of childhood adversity, but this is only achievable with the presence of interpreting stressful events as under control, not consuming alcohol, and lower scores in the disconnection and rejection schema.
In the end, both methods identify the same predictors as crucial in determining the IDER score’s values, but they complement each other by revealing further interactions. Additionally, the tree delves deeper and shows how alcohol consumption may also be relevant in determining the score.