Thank you for your kind words. It sounds like you'd like to use your thesis to convince more people to consider veganism.
This is a published study that looks similar to what you're envisioning, only they tried to also account for dietary quality of the participants:
The Association between Vegan, Vegetarian, and Omnivore Diet Quality and Depressive Symptoms in Adults: A Cross-Sectional Study - PubMed (nih.gov)
" A cross-sectional online survey utilised the Dietary Screening Tool (DST) and the Centre for Epidemiological Studies of Depression Scale (CESD-20) to measure diet quality and depressive symptoms, respectively."
"This cross-sectional study demonstrates an association between high-quality dietary omnivore, vegan, and vegetarian diets and lower depressive symptoms. It also indicates that vegan and vegetarian dietary patterns were associated with higher diet quality. . . . more frequent intake of fruits, vegetables, nuts, seeds, legumes, whole grains, and water and reduced ultra-processed, refined, and sugary foods, are associated with lower depressive symptoms."
