Recommender systems have become crucial in the modern digital landscape, where personalized content, products, and services are essential for enhancing user experience. This paper explores statistical models for recommender systems, focusing on crossed random effects models and factor analysis. We extend the crossed random effects model to include random slopes, enabling the capture of varying covariate effects among users and items. Additionally, we investigate the use of factor analysis in recommender systems, particularly for settings with incomplete data. The paper also discusses scalable solutions using the Expectation Maximization (EM) and variational EM algorithms for parameter estimation, highlighting the application of these models to predict user-item interactions effectively.