This paper introduces a center-level approach to estimating the effect of center characteristics on outcomes. The proposed method applies to studies where the effect of center characteristics is of primary focus and centers rather than individual patients are entities of interest. Although these studies focus on practices and policies at the center level, it is important to account for the differences in outcomes due to varying patient case-mix. The proposed approach includes two steps. The first step estimates the effect of patient-level characteristics on outcomes so that the variability in patient case-mix can be adjusted prior to estimating the effect of center-level factors. The second step aggregates outcomes (adjusted for patient-level factors) of patients from the same center into a distribution of outcomes representing the response for each center. The outcome distributions are multi-valued responses on which the effects of center-level characteristics are modeled using a symbolic data framework. This method can be used to model the effect of center characteristics on the center-mean outcome as well as the within-center outcome variance. It models the effect of patient characteristics at the patient level and the effect of center characteristics at the center level. The method performs well even when the data come from a classical linear regression model or from a linear mixed effect model. The proposed approach is illustrated using a bone marrow transplant example.