The demand for performing data analysis is steadily rising. As a consequence, people of different profiles (i.e., nonexperienced users) have started to analyze their data. However, this is challenging for them. A key step that poses difficulties and determines the success of the analysis is data mining (model/algorithm selection problem). Meta-learning is a technique used for assisting non-expert users in this step. The effectiveness of meta-learning is, however, largely dependent on the description/characterization of datasets (i.e., meta-features used for meta-learning). There is a need for improving the effectiveness of meta-learning by identifying and designing more predictive meta-features. In this work, we use a method from exploratory factor analysis to study the predictive power of different meta-features collected in OpenML, which is a collaborative machine learning platform that is designed to store and organize meta-data about datasets, data mining algorithms, models and their evaluations. We first use the method to extract latent features, which are abstract concepts that group together meta-features with common characteristics. Then, we study and visualize the relationship of the latent features with three different performance measures of four classification algorithms on hundreds of datasets available in OpenML, and we select the latent features with the highest predictive power. Finally, we use the selected latent features to perform meta-learning and we show that our method improves the meta-learning process. Furthermore, we design an easy to use application for retrieving different meta-data from OpenML as the biggest source of data in this domain.