Probabilistic Targeted Factor Analysis

We develop Probabilistic Targeted Factor Analysis (PTFA), a likelihood-based framework for constructing latent factors that are explicitly targeted to variables of economic interest. PTFA provides a probabilistic foundation for Partial Least Squares, allowing supervised factor extraction under uncertainty. The model is estimated via a fast expectation maximization algorithm and naturally accommodates missing data, mixed-frequency observations, stochastic volatility, and factor dynamics. Simulation evidence shows that PTFA improves recovery of economically relevant latent factors relative to standard PLS, particularly in noisy environments. Applications to financial conditions indices, macroeconomic forecasting, and equity premium prediction illustrate the measurement and forecasting gains delivered by targeted probabilistic factor extraction.