Institutional classification systems, such as the Carnegie Classifications, are used to delineate groups of institutions with similar characteristics and by administrators to guide policy decisions. However, the Carnegie Classifications themselves are neither well-documented nor easily reproduced. Using the 2015 data set from the Carnegie Classifications for Doctoral granting institutions, we propose an alternative method of classification that relies on Structural Equation Modeling rather than the Principal Components Analysis-based approach currently used. Rather than modeling two indices of institutional performance, as in the Carnegie method, we propose a single index created from two latent factors: one pertaining to STEM research outcomes and the other to non-STEM outcomes. Classifications can then be made using a univariate mixture model as opposed to subjective determination of groups, as is done in the Carnegie method. To explore the two classification methods, we created two R-Shiny applications that allow a user to change the underlying variables on which universities are measured and assess the resulting changes in group membership.