We propose a projection-based test to check logistic regression models and apply the test to study telehealth utilization during the COVID-19 pandemic among patients with HIV. The test is shown to be consistent and can detect root- local alternatives. The use of the proposed test to investigate a COVID-19 dataset reveals that the probability of telehealth utilization depends on the following variables: overweight, education, and age and the interaction between age and ethnicity. Specifically, the probability for the Hispanic group decreases with older age, whereas there is no trend between the probability with the age for the group of non-Hispanic. This interaction may be ignored when we apply other goodness-of-fit methods. The simulation studies also show the performance of the proposed method is remarkably attractive compared to its competitors.
Keywords: COVID-19; Consistent test; Goodness-of-fit; Logistic regression; Person living with HIV (PWH); Projection; Telehealth.