We use variational inference (VI), a technique from the machine learning literature, to estimate a mortality-based Bayesian model of nursing home quality accounting for selection. We demonstrate how one can use VI to quickly and flexibly estimate a high-dimensional economic model with large datasets. Using our facility quality estimates, we examine the correlates of quality and find that public report cards have near-zero correlation. We then show that in contrast to prior literature, higher quality nursing homes fared better during the pandemic: a one standard deviation increase in quality corresponds to 2.5% fewer Covid-19 cases.