The Social Relations Model (SRM) is a conceptual and mathematical model of interpersonal responses in dyads. The SRM permits estimation of responses of one to many (the actor effect) and the responses of many to the one (the partner effect) at the individual level of analysis. The SRM also permits estimation of the unique responses of actors and partners in specific dyadic arrangements (the relationship effect). During the four decades that the SRM has been used empirically, most attention was focused on estimation of variance and covariance of components. More recently, second stage modeling has occurred in which SRM effect estimates are used as variables in multivariate models. Consequently, it has become important to have good predictions of SRM actor, partner, and relationship effects. A method proposed by Warner, Kenny, and Stoto has been used to predict these effects. Here we propose an alternative matrix-based estimation method that predicts the latent SRM random effects from their conditional expected values given observed data. Analytic work and Monte Carlo simulations indicate that our conditional-expectation predictions of SRM effects are more valid and precise than the traditional predictions. They will improve second-stage Social Relations Modeling and also have practical uses as well (in, e.g., determining employee salary raises). (PsycInfo Database Record (c) 2023 APA, all rights reserved).