Employee engagement is increasingly important, as it can become a competitive advantage for companies, helping them increase productivity, attract talent and improve customer satisfaction. Numerous works have studied the drivers that encourage employee engagement and have developed models to identify them. However, the existing models have limitations, and the literature demands more research on the subject since the precision of the models still needs to improve. This paper presents a computational model that can estimate the drivers of employee engagement accurately. A sample of 205 Spanish employees was used, allowing us to consider a wide sectorial heterogeneity. Different methods have been applied to the sample under study to achieve a high-precision model, selecting drivers using the Multilayer Perceptron Classifier and quantifying the impact of the drivers with Sensitivity Analysis. The results obtained in this research present important implications for the managerial improvement of human resources departments by facilitating the design of strategies and policies that foster employee engagement, which significantly influences corporate results.