###### Abstract  
Variable selection is important for developing accurate and interpretable prediction models. While classical and penalized methods are widely used, few simulation studies provide meaningful comparisons. This study compares their predictive performance and model complexity in low-dimensional data. Three classical methods (best subset selection, backward elimination, and forward selection) and four penalized methods (nonnegative garrote (NNG), lasso, adaptive lasso (ALASSO), and relaxed lasso (RLASSO)) were compared. Tuning parameters were selected using cross-validation (CV), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Classical methods performed similarly and produced worse predictions than penalized methods in limited-information scenarios (small samples, high correlation, and low signal-to-noise ratio (SNR)), but performed comparably or better in sufficient-information scenarios (large samples, low correlation, and high SNR). Lasso was superior under limited information but was less effective in sufficient-information scenarios. NNG, ALASSO, and RLASSO outperformed lasso in sufficient-information scenarios, with no clear winner among them. AIC and CV produced similar results and outperformed BIC, except in sufficient-information settings, where BIC performed better. Our findings suggest that no single method consistently outperforms others, as performance depends on the amount of information in the data. Lasso is preferred in limited-information settings, whereas classical methods are more suitable in sufficient-information settings, as they also tend to select simpler models. classical variable selection methods; low-dimensional data; initial estimates; model complexity; model selection criterion; penalized regression methods; prediction accuracy; simulation study 2025  
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In this article, we focus only on prediction models, which can be complex as they may include variables with both strong and weak effects, as well as some noise variables, provided the prediction accuracy is not compromised [4; 6]. However, overly complex models may overfit the training data, meaning that the model fits idiosyncrasies in the data rather than generalizable patterns [1; 3]. Consequently, they may generate extreme predictions when applied to new data [3; 7]. Additionally, if the costs of collecting variables are high, these models may not be practically useful and may be quickly forgotten [8]. On the other hand, models with too few covariates may underfit the data, resulting in poor generalization [9; 10]. To strike a balance between overfitting and underfitting, a good variable selection approach that produces a simpler and more accurate model is required [9; 11; 12]. Simpler prediction models are easier to interpret and provide insights into which variables may be important predictors of the outcome [9]. In practice, many variables are often measured, and a more parsimonious model may be preferred. Traditional methods for selecting variables have been in use for over five decades. Although many alternative approaches have been proposed in recent years, meaningful comparisons and a clear understanding of their properties remain limited [4; 13]. [PERSON] et al. [4] reviewed the state of the art in variable and functional form selection in multivariable analysis and categorized variable selection methods into five classes: traditional (classical) methods, change-in-estimate procedures, penalized likelihood approaches, boosting, and resampling-based methods. They concluded that further comparative research is needed to define the state of the art and provide evidence-supported guidance.