Participants

Participants were volunteers and answered anonymously. The inclusion criterion was that they should be Argentine citizens (18 years of age or older). The final sample consisted of a total of 2038 Argentine participants. The 51.9 % (n = 1058) were women and 48.1 % (n = 980) were men. The mean age was 40.4 (SD = 14.7), with ages ranging from 18 to 91 years. Regarding marital status, 33.2 % (n= 676) were single, 16.5 % (n = 336) were dating, 26.1 % (n = 531) were married, 20.4 % (n = 416) reported being divorced or separated, while 3.9 % (n = 79) were widowed. Regarding their occupations, 53.4 % (n = 1088) were employed, 18.3 % (n = 374) were not actively working at the time of the survey, 20.1 % (n = 409) reported being self-employed, 0.5 % (n = 11) were unpaid workers, 2.6 % (n = 54) were homemakers, while 5 % (n = 102) were employers. Finally, in relation to socioeconomic level, 2.0 % (n= 40) belonged to a low level, 14.3 % (n = 292) belonged to a medium-low level, 63.5 % (n= 1294) to a medium level, 17.8 % (n = 363) declared belonging to a medium-high level, and 2.4 % (n= 49) of the sample belonged to a high socioeconomic level.

Materials

Big Five Inventory (BFI; ^{John et al., 1991}; Argentine adaptation ^{Castro Solano & Casullo, 2001}). It is a 44-item instrument that assesses the Big Five personality traits (Extraversion, Agreeableness, Conscientiousness, Neuroticism, and Openness to experience). The author of the test demonstrated its validity and reliability in general adult North American population groups. These studies verified the concurrent validity with other recognized instruments that assess personality. Studies carried out in Argentina verified the factorial validity of the instrument for adolescent population, non-consultant adult population and military population (Castro Solano & Casullo, 2001). In all cases, a five-factor model was obtained that explained about 50 % of scores variance. Adequate internal consistency values (ordinal alpha) were obtained for this sample: extraversion = .76; agreeableness = .79; conscientiousness= .82; neuroticism = .74; openness to experience = .69.

Mental Health Continuum-Short Form (MHC-SF; ^{Keyes, 2005}; Argentine adaptation ^{Lupano Perugini et al., 2017}). This 14-item instrument assesses the degree of: a) Emotional well-being, in terms of positive affect and life satisfaction (hedonic well-being), b) Social well-being (including the facets of acceptance, actualization, social contribution, coherence and social integration), c) Personal well-being in terms of ^{Ryff's (1989}) theory (autonomy, control, personal growth, personal relationships, self-acceptance and purpose). The MHC-SF has shown good evidence of internal consistency (> .70) and discriminant validity in samples of adults from various countries. The three-factor structure of the test (emotional, personal and social) has been verified in these studies. Validation studies of this instrument in Argentina have confirmed the factor structure of the instrument and have given evidence of good convergent validity and internal consistency in adult population (Lupano Perugini et al., 2017). The reliability of the subdimensions for this sample were (ordinal alpha): emotional well-being = .80; social well-being = .74; personal well-being = .77.

Positive and negative personality traits

To assess positive and negative personality traits from a psycholexical point of view, the already validated items from High Five Model (HFM; Cosentino & ^{Castro Solano, 2017}) and those derived from the negative trait model (BAM; Cosentino & Castro Solano, 2023) were used:

High Five Model (positive traits) (Cosentino & ^{Castro Solano, 2017}). To assess the positive personality traits, the HFM model was taken into account. The scale is composed of 23 items that assess the five high factors Erudition, Peace, Joviality, Honesty and Tenacity. These factors were obtained through an inductive procedure based on the point of view of common individuals on positive human characteristics. People are asked to respond to each item, for example, "I have patience" on a Likert scale ranging from 1(never) to 7 (always). The higher the score on each subscale, the higher in the factor. Studies on the HFI demonstrated convergent and divergent validity in relation to the Values in Action classification of ^{Peterson and Seligman (2004}) and incremental validity over the factors and facets of the Big Five personality model for the prediction of psychological, emotional and social well-being. Adequate internal consistency values (ordinal alpha) were obtained for this sample: erudition = .84, peace = .86, joviality = .88, honesty = .88, and tenacity = .86.

BAM Model (negative traits) (^{Cosentino & Castro Solano, 2023}). To assess the negative personality traits, the negative trait model was taken into account through the items of the BAM inventory (Brutalism, Arrogance, Malignism). The BAM model is a recently created model that is composed of three factors obtained inductively to evaluate negative personality traits. The inductive procedure followed a psycholexical approach through a corpus of words obtained from ordinary people who reported characteristics considered "negative" and which were socially shared. The brutalism factor is defined by a set of negative individual traits such as being unbearable, careless, unstable, ridiculous; the arrogance factor is defined by a set of negative characteristics such as being arrogant, conceited, arrogant and narcissistic; and the malignism factor is defined by characteristics such as being corrupt, deceitful, immoral, malicious, and despicable, among others. Participants are assessed by asking them to respond to the item, for example, "I am conceited" on a Likert scale ranging from 1 (never) to 7 (always). In a preliminary study (Cosentino & Castro Solano, 2023) the model demonstrated good construct validity and positive associations with psychopathological symptoms and negative associations with life satisfaction. The 22 items of the model are grouped into 3 factors that were confirmed by confirmatory factor analysis techniques that demonstrated a good fit of the model to the data (Robust Weighted Least Squares Estimator (DWLS, robust) χ2 (206) = 323.00, p < .05, fit estimators CFI = .986, SRMR = .060, and RMSEA = .041 (90 % Confidence Interval = .032 - .049). It was decided to include this personality model as a complement to the positive trait model (HFI) in order to further study its predictive validity. Adequate internal consistency values (ordinal alpha) were obtained for this sample: brutalism = .85, arrogance = .91 and malignism = .85.

Procedure

Data were collected by students who were doing a research internship at a private university in the city of Buenos Aires, Argentina. The participants were volunteers and did not receive any compensation for their collaboration. Data were collected during 2021 and 2022. The materials were administered on-line using the SurveyMonkey application. The survey home page requested the participant's consent, assured the anonymity of the data and its exclusive use for research purposes. Data collection was supervised by one of the authors of this article. The research followed international ethical guidelines (APA and NC3R) and those of the National Council for Scientific and Technical Research (Conicet) for ethical behavior in the Social Sciences and Humanities (Resolution No. 2857, 2006) and has the approval of the corresponding ethics committees.

For data analysis, the statistical package Jamovi (2022) was used through the R environment, Version 4.1.2 (R Core Team, 2021) for correlation and logistic regression calculations. For the implementation of machine learning algorithms, the R software (R Core Team, 2021) was used. The packages caret, glmnet, randomForest and e107 were used.

Data Analysis

Different machine learning algorithms were used to validate a model of positive and negative personality traits for the prediction of different types of psychological well-being (research objectives 1 and 2), taking the normal personality trait model as a starting point.

As a first step, the participants were randomly divided into two subsets. The first one was called the training data set (2/3 of the participants, n = 1528), the second subset was called the validation data set (1/3 of the sample, n = 510). All continuous variables were transformed to z-scores.

Different regularization techniques (Lasso regression and Ridge regression) were used to verify the predictive validity of two personality models (normal personality traits vs. negative and positive traits) on psychological well-being. For comparison purposes, a linear regression (ordinary least squares) was carried out in which all predictors of both models (personality variables) were included. The regularization techniques employed are extensions of ordinary least squares regression and include different types of penalties in the regression coefficients with the purpose of improving the interpretation of the models (^{Zou & Hastie, 2005}). Ridge regression is used when there is multicollinearity among the predictors. The advantage of this type of regression is to keep all predictors in the model and the disadvantage is that it does not produce parsimonious models for the reason mentioned above (^{Delgadillo et al., 2020}; ^{Friedman et al., 2010}). Lasso regularization is used in cases where there are several predictors with coefficients close to zero and some with larger coefficients. This type of regression automatically selects the predictors relevant to the model, discards the others, and produces more parsimonious and interpretable models (Zou & Hastie, 2005). The Random Forest algorithm was also used, which is a nonparametric recursive partitioning technique that combines different decision trees in such a way that a random vector depends on each tree and is tested independently. The advantage of this methodology is that it randomly incorporates predictors considered weak, generally ignored in other models, due to the dominance of predictors considered stronger (^{Garge et al., 2013}). Also, this methodology allows the inclusion of a larger number of predictors. It differs from the Lasso and Ridge regularization as it allows working with complex associations and interactions and nonlinear relationships. Lasso and Ridge have two parameters λ (Lambda) and α (alpha). α is arbitrarily set to 1 for Lasso regression and 0 for Ridge. The parameter λ was calculated using the cross-validation technique. The glmnet package (Friedman, et al., 2010) was used to set it.

In the Random Forest algorithm, the parameter to be estimated is the mtry, which is defined by the number of predictors that are randomly assigned to each node. The parameter tuning was performed using the randomForest package (^{Liaw & Wiener, 2002}), through successive iterations, for the selected predictor models.

Next, the models were trained using the training data set. The models were then compared in terms of RMSE (root mean squared error) and R ² in order to select the model with the best goodness of fit. Once this was done, the model was tested on the validation data set and the results obtained on both data sets were compared. Figure 1 summarizes the steps carried out in the data analysis.

Figure 1: Steps in data analysis 

A similar procedure was followed for objective 3. In this case, the Support Vector Machine (SVM) algorithm was used. The SVM is a very robust supervised machine learning algorithm that allows data analysis for both classification and regression purposes (^{Gareth et al., 2013}). Given a set of training data in which a series of predictors are included, being the criterion to be predicted a binary classification, the algorithm allows to establish predictions that are tested on a new sample (validation data set or test set). The algorithm has the task of establishing a hyperplane that separates in the best possible way both binary classes (criteria to be predicted, in this research high and low psychological well-being). The evaluation of the model is done by the ability of the algorithm to be able to predict more accurately the membership of each class. The SVM has 4 parameters (Kernel, Regularization - C -, Gamma and Epsilon) that in this case were estimated using the e1071 package. For comparative purposes, a logistic regression was estimated in which the predictors of both personality models were included as well as the criterion of belonging to the high and low well-being group. The indicators of precision, sensitivity and specificity obtained by logistic regression and by the SVM were then compared. The purpose of this procedure was to establish the predictive capacity of both personality models on psychological well-being.

Predictive Models of Well-Being (Lasso, Ridge and Random Forest algorithms)

First, correlations were calculated between the predictor variables of both models (normal, positive and negative personality traits) and the three types of well-being (emotional, personal, social and total) in the training data set. All correlations obtained between the predictor variables (personality traits) and the criterion variables (well-being types) were significant p < .0001.

Second, the tuned parameters of the three predictive algorithms (Lasso Regression, Ridge and Random Forest) of psychological well-being as a function of normal personality traits and positive and negative personality traits were calculated. Both the parameter λ of the regression models and the mtry of the Random Forest algorithm were tuned using the cross-validation technique.²

Third, the results of the different models are presented, including the linear least squares regression in terms of RMSE (root mean squared error) and R ² (Tables 1 2 3 4). The model with the highest explained variance (highest R ² ) and lowest RMSE is considered as the model selection criterion. The results show that the best predictive model corresponds to the Random Forest algorithm. In the training data set, both for the model of normal personality traits (base model) and for the model of positive and negative traits (model to be tested in this research), the Random Forest algorithm presented the lowest RMSE both for the prediction of total well-being and for emotional, personal and social well-being.

In relation to the variance explained, the model of normal personality traits (base model) explained 32 % of the variance of total well-being, 34 % of personal well-being, 23 % of emotional well-being and 11 % of social well-being. The model of positive and negative traits (model to be tested in this research) reached similar values and in some cases somewhat higher, explaining 34 % of the variance of total well-being, 36 % of personal well-being, 24 % of emotional well-being and 16 % of social well-being.

These results were validated on another dataset (test set) reaching similar values (cross-validation). In this validation subsample, the Random Forest algorithm presented the lowest RMSE for the prediction of total well-being, as well as for emotional, personal and social well-being. Therefore, this algorithm had the best performance to explain the model to be tested in this research (Table 5). To explore the contribution of each specific personality dimension (trait) within the Random Forest technique, the decreasing mean Gini (i.e., IncNodePurity (INP)) was calculated for the positive and negative trait model. This index shows that, for the prediction of total well-being, the most important predictors turned out to be Erudition (INP = 48.48) and Tenacity (INP = 53.68). The results are similar for personal well-being: Tenacity (INP = 57.40) and Erudition (INP = 56.11). For emotional well-being they were Tenacity (INP = 65.66), Peace (INP = 52.34) and Malignism (INP = 51.77) and for social well-being, Erudition (INP = 49.59) and Peace (INP = 49.38).

Predictive Models of High and Low Psychological Well-Being (Support Vector Machine Algorithm)

The Support Vector Machine (SVM) algorithm was used to predict psychological well-being taking as predictors the normal personality models and the positive and negative trait model.

First, two logistic regressions were calculated for both models taking normal personality traits and positive and negative personality traits as predictor variables. In both cases, high/low well-being was considered as a criterion. To form the latter variable, the total well-being variable was converted into a dummy variable (0 = low well-being; 1= high well-being) taking into account the mean (M = 3.05, SD = .86) in the total well-being score for each participant, above the mean was considered high well-being and below the mean was considered low well-being.

The normal personality traits model (base model) was statistically significant, χ2(5,N= 1528) = 431.3.3, p < .001, this indicates that the five predictors composing the model together allow distinguishing between people with high and low psychological well-being. The variance explained was 24.6 % (Cox and Snell's R2). The accuracy of the model (percentage of correct positive predictions) for identifying cases of high well-being was 72 %. Sensitivity (percentage of high well-being cases detected) was 74 % and specificity (percentage of low well-being cases detected) was 69 %. All predictors in the model (personality traits) were significant (p < .001), extraversion and neuroticism recorded the highest values.

The model of positive and negative traits (model to be tested in this research) was statistically significant, χ2 (8, N = 1528) = 414, p < .001, this indicates that the seven predictors that compose the model as a whole allow distinguishing between people with high and low psychological well-being. The variance explained was 24 % (Cox and Snell's R2). The accuracy of the model in identifying cases of high well-being was 71 %. Sensitivity (percentage of high well-being cases detected) was 75 % and specificity (percentage of low well-being cases detected) was 67 %. All model predictors (personality traits) were significant (p < .001), except for two of the negative personality traits (brutalism and arrogance).

The accuracy of both models (base model vs. model to be tested in this research) in predicting high/low psychological well-being was similar, with the normal personality trait model having the best goodness of fit (AIC 1696 vs. 1719).

Second, the SVM algorithm was used to establish the prediction efficiency of both personality models on high/low psychological well-being. The parameters used were SVM of the regression type, Radial Kernel, gamma = .125 and epsilon = .01. The support vectors were 138. The SVM data indicate that the accuracy of both personality models is similar, as well as the indicators of sensitivity and specificity. Sensitivity (percentage of high well-being cases detected) was 75 % and specificity (percentage of low well-being cases detected) was 61 % for both the normal personality trait model and the positive and negative trait model.

Table 1: Fit of Models for Predicting Total Well-Being, according to Positive and Negative Normal Personality Traits (training set: n= 1528 and test set: n= 510) 

Table 2: Fit of Models for Predicting Personal Well-being, according to Positive and Negative Normal Personality Traits (training set: n= 1528 and test set: n= 510) 

Table 3: Fit of Models for Predicting Emotional Well-being, according to Positive and Negative Normal Personality Traits (training set: n= 1528 and test set: n= 510) 

Table 4: Fit of Models for Predicting Social Well-being, according to Positive and Negative Normal Personality Traits (training set: n= 1528 and test set: n= 510) 

Table 5: Summary of Model Fit (R², Random Forest) for the Prediction of Well-Being Types, according to Normal, Positive and Negative Personality Traits (training set: n= 1528 and test set: n= 510)