Considering the wide range of personal and social implications related to CP, many efforts have been made to better understand the causes behind this phenomenon and to identify all the factors involved in its development and stability over time. Research conducted in this field has resulted in a long list of dispositional and contextual indicators that may impact the development of CP.

At the child (individual) level, developmental models have listed, based on previous research, some temperamental, personality, and socio-emotional variables with proven influence in the emergence of CP. Among the temperamental variables, widely analyzed in the context of child CP [e.g., (11)], two facets of temperament have demonstrated strong prediction for later maladjustment (12). When present at adaptive levels, emotion regulation, which refers to the ability to regulate emotional experience and expression in favor of adaptive behavior (13), and effortful control, defined as the self-regulatory aspect of temperament that involves attentional and inhibitory control mechanisms (14, 15), have evidenced their role as protective factors that may buffer the development of child CP [e.g., (16)]. Conversely, emotional and behavioral dysregulation would stem from emotional lability, negative affect, and poor effortful control, linked with an increased risk for later CP (12, 17).

Beyond the temperamental influence on child CP, personality traits also play an essential role in the early manifestation and later development of CP. In recent years, there has been an increasing interest in examining traits encompassing interpersonal [e.g., grandiose-deceitful (GD)], affective [e.g., callous-unemotional (CU)], and behavioral features [e.g., impulsive-need for stimulation (INS)] that resemble adult psychopathic personality (18).

Psychopathic traits in childhood have proven their usefulness and predictive value in the prediction of more severe and persistent pathways of CP (19, 20), even when controlling for other relevant risk factors [e.g., (21)]. This influence is particularly noteworthy when all psychopathic dimensions are present, reinforcing the importance of interpersonal (GD) and behavioral (INS) traits beyond the well-known influence of CU traits on child CP (22, 23).

Related to the aforementioned temperamental and personality variables, socioemotional competence has shown a particular ability to promote or restrain child CP based on their adaptive or maladaptive functioning. Deficits in emotion regulation linked to CU traits may drive deficits in the ability to understand and resonate with other's emotions. Empathy has been defined as a multi-component process involving at least affective (i.e., automatic emotional reaction to someone else's emotions) and cognitive domains (i.e., ability to recognize, understand, and share other people's emotions and perspectives), both of them related with multiple forms of CP in childhood and adolescence (24, 25).

Beyond the individual factors, the complexity underlying the CP should be interpreted in the context of the dynamic interplay between the individual and environmental domains. In this regard, individual vulnerabilities unfold in relational contexts, where the child interacts with peers, adults, and systems around them (26).

At early developmental stages, the family constitutes the most proximal context for child development, building social and emotional skills that will support later adjustment (27). Therefore, it is unsurprising that a large set of family variables, with the ability to promote or restrain child adjustment, were repeatedly placed in developmental models of CP (28–30).

From the family context, variables focused on the parent-child relationship have received much attention. The influence of parenting practices, including both positive (e.g., parental responsiveness and warmth) and ineffective parenting (e.g., permissiveness, harsh parenting), in the development of child CP has been extensively recognized in previous research (31). Ineffective and negative parenting, which a difficult child temperament might fuel, is expected to lead to tensions between parents and children, increasing conflictive interactions in the dyad that, in turn, may place the child at risk for CP [e.g., (32)].

Instability in parent-child relationships could also increase the risk for parenting stress, also triggered by an overwhelmed feeling from the multiple challenges and demands required in parenting, which were already related to the emergence and maintenance of CP (33, 34). Additional sources of parental stress (e.g., financial problems, job demands, mental health issues) have also been recognized as potential risk factors for child CP [e.g., (35, 36)]. In this regard, different forms of non-severe psychopathology, including perceived stress, anxiety, and depressive symptoms, have also shown their influence on the development of CP, being considered one of the most relevant early predictors of persistence in the most severe forms of later problematic behavior (37).

Understanding child CP in-depth implies considering its complexity, largely represented by the large set of individual and environmental factors spanned in previous research. As occurs with other mental health problems, most of these factors repeatedly emerged in different studies investigating a reduced number of factors or domains at a time, resulting in a vast array of predictors of CP collected in previous literature but with limited information about their relative importance in prediction (38). Also, predictive models of CP have benefited when a cumulative risk perspective was assumed instead of focusing on one or two risk factors [e.g., (39)], suggesting that more complex and varied approaches, allowing to handle a large number of predictors, are needed to improve classification and prediction of child CP.

However, dealing with the multi-factor nature of CP through traditional data-driven approaches (e.g., regression models) has come with several limitations related to mass univariate testing, non-linearity, interaction effects, or overfitting, among others (40, 41), raising the need for new advanced and more sophisticated methodological procedures.

We face several challenges in trying to predict some health topics based on multiple features. As previously mentioned, these aspects of prediction have been traditionally addressed by methods such as regression. In this sense, Machine Learning (ML), still in its infancy in longitudinal data, can provide some valuable advantages (42).

Firstly, incorporating numerous repeated measurements of exposures presents significant challenges because traditional regression models are typically not designed to handle many covariates (43). Secondly, these regression models often assume a linear relationship between each exposure and the outcome, with few or no specified interactions between exposures. However, these assumptions are often unverifiable; if they are incorrect, they can lead to erroneous conclusions. Despite this, these assumptions are frequently overlooked or violated, which can bias the study results (44, 45).

In this sense, ML provides a solution to these limitations of traditional statistical methods because ML can process vast amounts of data with numerous exposures, automatically developing models that accurately predict outcomes and identify the most critical predictive exposures (46, 47). Importantly, ML techniques generally do not assume a specific functional form for the model; instead, they attempt to derive the model directly from the data to maximize prediction accuracy (48).

ML approaches allow for classification and prediction in a multivariate context, projecting data into a multi-dimensional nature space where a classifier can create a decision boundary that optimally separates individuals of different classes within this space, whilst all the factors and their interactions are simultaneously considered (49).

Random Forest (RF), a ML algorithm based on Decision Trees (DT), works under these premises, allowing classification and prediction by handling a large number of predictors that can be distilled based on their relative importance. RF models generate multiple DTs to produce aggregated predictions, detecting interactions and non-linear patterns and reducing overfitting, which overcomes most of the limitations observed in traditional regression models (41).

RF has been increasingly used in the prediction of different mental health problems [e.g., (38, 50)], although its use for predicting and classifying child CP is, to date, limited. Alternative ML classifiers have been used to classify CP children based on parenting practices (51) and emotion recognition abilities (49). At the same time, only one study has included multiple risk factors from multiple domains (i.e., biological, psychological, and social) in predicting child CP over a 2-year period (52). Remarkably, none of the previous studies have addressed the classification of individuals according to levels of CP.

The literature on the application of ML in psychology and healthcare often addresses the idea of explainability (53, 54). According to DARPA's Explainable Artificial Intelligence (XAI) program, explainability refers to an artificial intelligence (AI) system's ability to articulate its reasoning comprehensibly to human users. In recent years, XAI gained relevance within the domains of psychology and psychiatric diagnosis, where decision-making should always be supervised by specialists (55).

In contrast to opaque ML systems, the transparency XAI offers enables health experts to verify AI-assisted classifications, ensuring they are fair, unbiased, and ethically sound. This mitigates misclassification by revealing the most influential factors contributing to a potential diagnosis. Notable applications of explainability and ML include early detection of ADHD (56), schizophrenia diagnosis (57), prediction of anxiety and depression (58, 59), and Alzheimer's disease classification (60). However, to our knowledge, this is the first study addressing the detection of CP using ML with explainability techniques.

Given the multifaceted nature of CP in children, it is essential to explore predictive models that can account for the intricate interplay of its contributing variables. This study leverages a data-driven approach and, based on longitudinal data collected with a 1-year interval, conducts a ML approach for classifying children according to their levels of CP, considering both individual and family predictors.

This study is based on RF, a supervised ML method that combines the results of many different DTs. The longitudinal perspective enables the use of supervised methods, making possible the prediction of future CP using current information about individual and family factors. This also helps improve prediction accuracy by identifying interactions and patterns that traditional statistical models, like linear relationships, cannot capture.

Specifically, this study aims to focus on the following objectives: (1) To examine and describe the utility and performance of RF models for classifying children with different levels of CP based on individual and family factors; (2) To analyze the interplay of individual and family variables for predicting high CP; (3) To determine which factors, or combination of them, are more relevant for child classification, especially to classify children high on CP; (4) To compare decision-making models based on the presence or absence of a prior measure of CP, analyzing the predictive power of other variables when no prior CP are present.

The sample consisted of 1,352 children (51.2% girls) from the longitudinal ELISA project, which is carried out in Galicia (northwestern Spain). For this study, two waves of the project were utilized: T1 (2022; M_age = 9.20, SD = 1.04, age range = 7–11 years) and T2 (2023; M_age = 10.24, SD = 1.05, age range = 8–12 years). Most of the children were Spanish (~95%).

Regarding the parents' level of education, 11.8% of the mothers and 25.4% of the fathers had attained the highest level of compulsory school education. Additionally, 8.4 and 10% of the mothers and fathers, respectively, had completed a higher level of non-compulsory education. A total of 26.3 and 29.9% had completed vocational training studies, 44.4 and 27.7% had completed university studies, and 8.9 and 6% had completed postgraduate studies. In T1 (2022), 87.1% of mothers and 92.7% of fathers worked outside the home, 5.3 and 2.7% were unemployed or on temporary layoff, 1 and 3.7% were retired/disabled, or unable to work, 0.9 and 0.4% were students, and 5.7 and 0.7% were responsible for domestic duties. In terms of financial well-being, 56.3% of families reported being financially comfortable, 37.4% reported barely getting by, and 6.4% reported having difficulty or serious problems making ends meet. Regarding concern over financial obligations, 39.3% of families reported never worrying, 25.8% worried less than once a month, 31.4% worried at least monthly, and 3.5% worried almost every day.

The longitudinal ELISA project, initiated in 2017, is an ongoing study that has been continuously conducted up to the present day. This study has been approved by the Spanish Ministry of Economy and Competitiveness and by the University of Santiago de Compostela Bioethics Committee. Initially, 126 schools across urban, suburban, and rural areas in the Autonomous Community of Galicia (northwestern Spain) were contacted. Of these, 72 public (79.2%), charter (18.1%), and private (2.8%) schools agreed to participate. Subsequently, the families of the children were invited to participate, with ~25%–50% of families in each school agreeing to take part.

The child's primary caregiver (i.e., mother, father, or primary caregiver) completed a questionnaire at each collection point. Most respondents were mothers (87.3%). School teachers were responsible for supervising the distribution and collection of the questionnaires. Every part involved used a personal keycode to access and identify the questionnaires in order to ensure data confidentiality. Informed consent was obtained from the primary caregiver prior to each data collection. There was no financial compensation for participation.

To the extent possible, an attempt was made to standardize the administration of the questionnaires (from the order of presentation of the scales to the time and place where the questionnaires were administered) across the diverse range of schools included.¹

From the original sample of 1,352 children, discarding all the entries that miss any of the variables required is mandatory. Table 1 describes the final set of 20 variables featured in the analysis. Table 2 includes a definition of each variable extracted from the construction/validation of the instrument.

All the variables have been rescaled from their original ranges to a standard scale (from 1 to 5) to ease the interpretation of the results. As this is a linear transformation, the original information of the rescaled variables remains unaffected.

Once the data set was filtered, the ML algorithm was trained using a 10-fold cross-validation strategy widely used in the literature (71). Following this method, the data set is partitioned into ten equal batches of samples distributed randomly. Then, a ten-step iteration process begins, where nine batches are used to train the model and the remaining one to test the algorithm. On each iteration, the batch is used for testing changes. Once the ten sets have been tested, the results can be assessed.

This study defined two different sets of metrics depending on the aspect being evaluated: regression or classification. For the regression, we chose the Pearson correlation coefficient (PCC) to assess its accuracy regarding the original values of the target variable:

We also observed the Mean Absolute Error (MAE) of the model to understand the magnitude of the errors in the predictions:

For the classification, once the samples were distributed into their corresponding groups according to their predicted score, we could observe the confusion matrix of the model, the global precision and recall, and, in particular, the recall for the group of high CP.

A set of widely used ML models were tested to find the most accurate. Both performance and interpretability were taken into account.

We conducted these tests two times:

With these cases, we expect to conclude the real relevance of having previously measured CP for prediction of later CP scores.

Among the variables used for model training, some stand out for predicting future CP, considering their positions in the tree structures. A first noteworthy result is that individual factors play a more decisive role than family factors, regardless of whether previous CP are considered. This is consistent with findings from other studies that compared factors from different domains to predict mental health outcomes in youth (38).

This pattern of findings can also be considered in the light of broad theoretical frameworks in behavioral sciences like Bronfenbrenner's (76, 77) Bioecological Model. According to this model, human development results from several intertwining layers of influence, including the individual and progressively larger systems (e.g., family, community, cultural values, etc.); despite the powerful influence of the family contexts, individual characteristics are more directly related to behavior, and, ultimately, filter the experiences and interactions with the other layers.

Within the individual factors, our results highlight the role of temperament and psychopathic traits in the pathways to children's CP. Particularly, the results reinforce the role of effortful control (attentional focusing and, especially, inhibitory control), in alignment with other studies (78), that highlight self-regulatory dispositions as predictors of behavioral disturbances. Our results also point to emotional reactivity (lability/negativity) as a significant contributor to the prediction of CP. This result is consistent with a strong line of research on the role of negative affect (79), emotional instability (80), and irritability (81) in the configuration of the children's most common CP. Thus, RF models endorsed both the tendency to display intense emotionality and the difficulties for self-control as key factors in the prediction of CP.

Our results also bolster the role of the so-called psychopathic traits (82) for the identification of children at risk of high CP. The significance of psychopathic traits remains evident, regardless of whether prior CP are included as a predictor. Results show that CU, often considered the core of psychopathic personality (83), is located within the highest positions in the decision trees. Thus, emotional coldness, lack of guilt, and insensitivity to other needs, which define the concept of CU, are corroborated as powerful aspects for the detection of risk for high CP. However, results indicate that other psychopathic variables are also important. GD ranks even higher than CU both in Case A and Case B; it seems that interpersonal components of the psychopathic domain (e.g., arrogance, manipulativeness, disposition to cheat or lie for the own benefit) play a standing role in the prediction of CP. Also, at least in Case B, the behavioral facets of the psychopathic traits (INS), encompassing impulsivity, irresponsibility, and need for stimulation, are part of the most influential predictors. Therefore, results bring support for a burgeoning research line claiming that, besides CU traits, interpersonal and behavioral psychopathic traits should be considered for a more precise account and prognosis of high CP (21, 22).

In the family realm, results underscore the role of conflict in the relations between parents and children. This result is in keeping with previous research showing how developmental outcomes are strongly influenced by the family atmosphere, family strain, and difficult interactions between parents and children [e.g., (84, 85)]. In our study, although some other family variables (e.g., parenting stress) seem decisive in the highest nodes, conflict stands out among the other family factors in both Case A and B. The power of this dimension may respond to the fact that conflictive relations can inherently reflect other relevant family aspects, like ineffective parenting and a compromised emotional connection among the family members (86, 87), thus being an efficient indicator of broader dysfunction in the family setting. Therefore, we found that the most important variables align with findings from previous literature on CP. The RF models underscore a specific set of predictors, both at the individual and family levels, that have been emphasized in psychological research and theory. This convergence between computational findings and existing research is noteworthy, as it not only validates the identified predictors, but also reinforces some previous advances in developmental psychopathology. At the same time, the RF models offer valuable insights for further exploration. Future research should keep expanding beyond the central focus on CU traits when studying psychopathic tendencies at early ages, and place greater emphasis on the core role of parent-child conflict among the various family factors typically considered in the development of CP.

In addition to studying the most relevant variables for prediction of CP, we also sought to identify clusters of variables that tend to act together, in an attempt to capture the interaction patterns that emerge from the RF analyses. Both the most frequent and the most successful combinations were analyzed, and similar combinations were identified in both approaches. Some sets of variables bring together different kinds of individual factors. Specifically, psychopathic and temperamental predictors tend to appear together in a relatively high number of samples and are also part of the most accurate paths. For example, GD and lability/negativity align together frequently and successfully. Some other times, several psychopathic traits are combined with lability/negativity.

Also, the tandem of GD and social competence (emotional regulation) can be identified, particularly when CP are also included as predictors. These results suggest the need for further studying the interactions between psychopathic and affective/self-regulatory traits [see, for example, (88, 89)] for a better depiction of the psychological mechanisms underlying high CP.

The analysis of predictor combinations also points to some individual and family factors working together in the classification task. For example, inhibitory control and parents' stress show up as a common and accurate cluster, a pattern of results that reflects the relevance of studying the interactions between temperament and family, as several previous research lines have suggested (27, 90). Also, our results show that psychopathic traits and family dimensions repeatedly appear as sets of intertwined variables. Specifically, interactions identified by the RF models highlight the predictive power of high levels of parent-child conflict when combined with CU or INS. Additionally, the coexistence of high GD, parent-child conflict, and stress in the parental role defines a particularly risky setting for the development of CP. As previous research has shown, psychopathic factors could trigger family dysfunction (91), or, conversely, the family dynamics could affect the development of psychopathic traits (92); psychopathic traits could also moderate the impact of family factors on developmental outcomes (93). Our results suggest that the dynamics of psychopathic traits and family relations (particularly, the strained relations between parents and children) should be a prioritized research field, so that the predictive and etiological processes underlying CP can be fully understood.

Results from RF can provide valuable orientations for theory building and refinement in the field of early CP. The findings on individual dispositions (temperament and psychopathic traits) suggest that models on CP should account not only for these factors but also for their joint effect and their interaction with family variables. Emotional reactivity and self-regulatory skills are highlighted as two main axes of temperamental influence; both axes have already been present in classical models on “difficult temperament” (94) and in theoretical models specifically designed for antisocial behavior [e.g., (95)]. Results from RF corroborate the impact of such dimensions and support their utility in the design of broader models of CP. Also, psychopathic traits should occupy a significant space in theories on stability, chronicity, and severity of CP; within this framework, not only does affective insensitivity (CU) seem relevant, but behavioral traits (INS) and, especially, the interpersonal aspects (GD; manipulativeness, narcissism, dishonest charm) should also be considered (21, 82). These dispositions should be addressed in interaction with the family function; particularly, according to our results, and in line with coercion theory (66) conflictive interactions between parents and children, possibly within a psychosocially stressed family, may be a key factor for etiological models of children's CP.

Additionally, insights from RF provide support to the developmental heterogeneity of CP (96). As shown by our results, CP can be predicted on the basis of different combinations of factors; in some of the trees, individual factors (e.g., GD and lability/negativity) seem to be dominant, while in others, both individual and family factors play a pivotal role in prediction roots (e.g., family conflict, GD and CU). In this sense, RF models can be a useful way to explore the variety and complexity of pathways leading to CP, resonating with the principles of equifinality and multifinality proposed by developmental psychopathology (97).

On a practical level, our results can help in the early identification of at-risk children by recognizing the main predictive variables, the more powerful clusters of factors, the thresholds and the itineraries for making classificatory decisions. Beyond the previous levels of CP, individual and family factors can aid in distinguishing children who may present future behavioral difficulties. This can guide social and health policies so that targeted interventions can be designed to curb the problematic pathways. Additionally, our results yield meaningful information for guiding prevention programs by highlighting major domains for intervention like interpersonal sensitivity, coping with frustration and negative emotions, executive functioning skills, and parent-child relational patterns. Some interventions targeting these factors have demonstrated their efficacy for prevention of CP, thereby reinforcing the relevance of these predictors as key contributors to the development of CP. For instance, some interventions have built on the child's individual characteristics to promote cognitive flexibility and constructive coping strategies [e.g., Problem-Solving Skills Training (PSST)] (98). Other interventions, like the Triple P-Positive Parenting Program (99) have focused on family dysfunction, and have shown significant success in addressing CP. Moreover, the combined influence of individual and familial predictors in CP prediction further supports the need for a multicomponent approach that targets a broader range of risk factors. Such an approach may be particularly beneficial in CP treatment, as demonstrated by programs like Incredible Years (100), which have shown strong short- and long-term efficacy. Based on our results, further research should advance in the design of individual- and family-oriented programs that consider the diversity of needs of CP children. In particular, modular programs [e.g., (101)], matching the intervention components to the strengths and difficulties of each child, would show promise for dealing with the heterogeneity of pathways in children's CP.

The results of this study should be viewed in light of some limitations. First, despite the longitudinal nature of the design, which enables prospective predictions not attainable by cross-sectional research, the follow-up (1 year) was relatively short. We analyzed data from children across the elementary school years, a critical period for the development of the most stable patterns of CP; however, prediction through a longer time frame, including the preschool years, would be particularly useful for identifying the earliest predictors and informing preventive practices in early childhood.

Second, while the ELISA sample was relatively large and reasonably heterogeneous, it was community-based and drawn from a specific sociocultural setting, which may restrict full generalizability to other samples and settings. Additionally, in studies like ours, the likelihood of involving children with very high CP is moderate unless there is an oversampling of participants exhibiting significant difficulties at baseline. Therefore, caution is advised, as the results might not be fully applicable to other groups. Further studies in diverse populations and social backgrounds are needed to evaluate the robustness and generalizability of our findings. Such research will help clarify which predictors of CP are consistent across different contexts and provide a more refined perspective on CP prediction. It is also worth noting that in this study, we excluded children who missed any data collection points. Additionally, previous studies associated with the ELISA project (32, 102), as well as existing literature (103), have shown that children with incomplete assessments typically have a lower socioeconomic status (SES) compared to those with complete data. This may introduce bias and limit the generalizability of the findings to children from lower SES backgrounds. Therefore, it is recommended that future studies place a stronger emphasis on retaining participants from disadvantaged backgrounds, as they are more likely to drop out of community-based longitudinal studies.

Third, our selection of family variables prioritized malleable factors, which are particularly useful for informing the design of preventive interventions. Consequently, certain variables, such as socioeconomic background, parental education level, and the presence of serious mental disorders in parents, were not included in the model. Research has shown that these factors can significantly affect developmental outcomes, including CP, often indirectly [e.g., (104)]. Incorporating such variables into future models could help further elucidate their role within a more comprehensive framework of risk factors.

Future research should address these limitations. As suggested above, applying RF to long-term longitudinal data will enhance the opportunity for predictions across extended periods of the lifespan. Additionally, examining predictors measured at different ages (e.g., preschool and primary school) could help identify which factors are more significant at different developmental stages and depict how the pathways to CP unfold through time. This approach would enhance prediction and theory building and improve prevention by highlighting critical ages for timely intervention and indicating which factors should be addressed at different developmental times.

Future investigations should also refine the RF models by incorporating a wider range of potential predictors. While individual and family factors are recognized as fundamental domains underlying CP [e.g., (105)], other variables from the community, school and peer contexts could boost the predictive power of the RF and provide new insights on the interactions that drive CP.

Also, RF models in this field can be fine-tuned by considering how the pathways to CP may be conditioned by gender. Higher prevalences of CP in boys are commonly found (106), although when CP are developed in girls, the behavioral difficulties may be particularly detrimental [i.e., the “gender paradox”; (107)]. Nevertheless, the differential factors involved in the development of CP in boys and girls are poorly understood (108). Longitudinal studies with RF can be a useful tool to unravel the distinctive routes to CP across genders.

This study illustrates how explainable ML can integrate predictive accuracy with psychological understanding, elucidating not only the key variables, but also the ways in which they interact across multiple levels of influence to contribute to maladaptative developmental trajectories. Data-driven models based on RF algorithms represent a promising approach to address the complexities of predicting and explaining CP. Our results emphasize the influence of individual and family factors and demonstrate how these elements are intricately combined to shape heterogeneous pathways. Moreover, findings from this longitudinal study can inform more effective screening processes and tailored interventions; they also highlight the value of bridging psychological insights and advanced computational methods to better address one of the most prevalent and impairing challenges in children's mental health.