Genetic studies of psychiatric disorders often deal with phenotypes that are not directly measurable. Instead, researchers rely on multivariate symptom data from questionnaires and surveys like the PTSD Symptom Scale (PSS) and Beck Depression Inventory (BDI) to indirectly assess a latent phenotype of interest. Researchers subsequently collapse such multivariate questionnaire data into a univariate outcome to represent a surrogate for the latent phenotype. However, when a causal variant is only associated with a subset of collapsed symptoms, the effect will be challenging to detect using the univariate outcome. We describe a more powerful strategy for genetic association testing in this situation that jointly analyzes the original multivariate symptom data collectively using a statistical framework that compares similarity in multivariate symptom-scale data from questionnaires to similarity in common genetic variants across a gene. We use simulated data to demonstrate this strategy provides substantially increased power over standard approaches that collapse questionnaire data into a single surrogate outcome. We also illustrate our approach using GWAS data from the Grady Trauma Project and identify genes associated with BDI not identified using standard univariate techniques. The approach is computationally efficient, scales to genome-wide studies, and is applicable to correlated symptom data of arbitrary dimension.