## 1 Introduction
This allows for the inclusion of covariates, which can then accommodate for confounder effects or exclude any already known mediators of the studied trait. Most of these studies have relied on approaches consisting of the univariate analysis of the association of each SNP with the phenotype. Consequently, the possibility of a correlational and interactional structure between SNPs is not taken into account [3]. This type of approach is not particularly well suited for the detection of small effects [4], which can only become evident in the presence of other causal effects. In univariate approaches, multiple tests are performed independently, making it essential to correct the significance level in order to reduce the probability of type I errors (false positives). Frequently, however, the correction methods (e.g., Bonferroni) are too conservative, meaning it is not possible to detect any significant effects [3], which can consequently lead to a paradoxical increase in type II errors (false negatives) [5]. Another challenge in finding a plausible method to apply to genetic data is due to its high dimensionality; the number of variables (i.e., SNPs) is much higher than the number of individuals (\(n<<p\)). Consequently, models are formed that can adjust data well, but that have poor predictive ability when applied to new data (overfitting and high variability). There are also correlational structures between the predictor variables, which can lead to multicollinearity problems [6]. Furthermore, traditional multivariate regression models were not designed to deal with these problems. Therefore, to apply them to high dimensionality genetic data is not suitable. One way to deal with the above-mentioned problems are penalization techniques, which have already been applied in the context of GWAS [3; 7]. Penalization techniques refer to methods used to introduce a penalty or constraint on the model parameters during the training process. These techniques help to control the complexity of a model, reduce the risk of overfitting, and improve its generalization performance on unseen data. The penalized logistic regression combines traditional logistic regression with this penalty term in order to simultaneously perform classification and gene selection. This technique signifies the choice of a penalty parameter (\(\lambda\)), usually via cross-validation procedures, which define the extent of the predictor coefficient shrinkage. The Least Absolute Shrinkage and Selection Operator (LASSO) method was proposed by [PERSON] [8], and is a penalization technique that imposes an L1--norm penalty. LASSO allows the explicit model simplification and, consequently, the interpretability improvement of the model once the insignificant predictor coefficients are forced to be equal to zero. For these reasons, the LASSO method has become very popular in high-dimensional data. However, this method does have limitations. For example, it cannot select more variables than the sample size. In the context of GWAS, there are high correlations between variables due to linkage disequilibrium or putative group structures. This leads to an instability in the selection of highly correlated variables via the LASSO method, since it arbitrarily only selects up to a few predictors, ignoring the others [5; 9]. Ridge, proposed by [PERSON] and [PERSON] [10], is a penalization technique that uses an L2--norm penalty. In contrast with the LASSO method, Ridge does not have sparse properties in terms of the coefficients estimates as none of them are equal to zero [11]. However, Ridge deals with higher correlations between predictors much better since it shrinks the coefficients of the correlated predictors. To achieve a technique with better performance, [PERSON] and [PERSON] proposed a novel tool that consists of a linear combination of an L1--norm penalty and an L2--norm penalty, which is known as Elastic-Net [12].