###### Abstract
Among seven key issues they identified for further investigation, issue 1 is the \"Investigation and comparison of the properties of variable selection strategies.\" To address this gap, [PERSON] and [PERSON] [12] designed a simulation study in the context of linear regression to compare selected traditional and penalized variable selection procedures, with a particular focus on the role of shrinkage in model selection and prediction--a key component of penalized likelihood approaches. The study was designed following the principles of neutral comparison studies, which aim to provide objective insights into the properties of methods without favoring any specific approach [14]. The simulation design borrowed information from published simulation studies with related investigations to inform its structure and gain insight into the weaknesses and strengths of alternative designs, as summarized in their Supplementary Materials (Figures S1-S8). In addition, they published their study protocol prior to conducting the analysis to mitigate potential issues of publication bias. To ensure the reproducibility of our results, we will make the programs available. We focus on evaluating prediction models for continuous outcomes in the context of low-dimensional data, assuming linear effects for all signal variables and no interactions. We consider three classical variable selection methods (best subset selection (BSS), backward elimination (BE), and forward selection (FS)) and four penalized regression methods: nonnegative garrote (NNG) [9], lasso [11], adaptive lasso (ALASSO) [15], and relaxed lasso (RLASSO) [16]. The prediction accuracy and model complexity of NNG and ALASSO depend on the choice of initial estimates [15; 17; 18; 19]. Therefore, our first objective (O1) is to evaluate the effect of three initial estimates on prediction accuracy and model complexity: those from ordinary least squares (OLS), ridge [20], and lasso. The tuning parameters of ridge and lasso are selected via a cross-validation scheme aimed at optimizing prediction performance. Our second objective (O2) is to compare the prediction accuracy and model complexity of NNG and ALASSO against the models that generated the initial estimates. Despite some criticism [3], classical variable selection methods are still popular and remain practically useful. They either retain or drop covariates from the model based on certain criteria, rather than gradually shrinking their coefficients to zero [11]. This discrete process can be problematic, as even slight changes in the data may lead to different models, resulting in unstable predictions [10; 11; 21; 22; 23]. Penalized regression methods are alternative techniques for variable selection that continuously shrink regression coefficients towards zero, while setting some coefficients exactly to zero [3; 9; 11]. They differ based on the penalty function. According to [PERSON] and [PERSON] [23], an ideal penalty function should (i) produce nearly unbiased estimates for large coefficients to avoid estimation bias, (ii) exhibit continuous shrinkage to avoid instability in model predictions, and (iii) perform variable selection by forcing some regression coefficients to be exactly zero. The penalty functions of the NNG and ALASSO possess these properties, as they shrink small and large coefficients differently, while the lasso penalty may produce biased estimates for large coefficients, which may increase prediction errors, especially in situations where minimal shrinkage is required [15]. To reduce over-shrinkage of large coefficients and achieve good prediction accuracy, the lasso, when tuned via cross-validation for optimal prediction, often selects many variables, leading to a relatively high rate of false positives [24; 25]. The continuous process of shrinking regression coefficients by penalized methods can lead to more stable predictions than classical methods, due to the bias-variance trade-off, especially in situations with small sample sizes or low signal-to-noise ratio (SNR) [11; 21; 23].