Estimation of Binary Logistic Regression Using Three Links Function (Logit, Probit, and Complementary Log Log) In Accessing the Factor That Influence HIV

Human Immunodeficiency Virus (HIV) remains one of the major public health concerns globally, with sub-Saharan Africa accounting for a significant proportion of the global burden of the infection (Kharsany & Karim, 2016). According to UNAIDS (2024), millions of people continue to live with HIV, with new infections occurring daily due to persistent demographic and behavioral factors. In Nigeria, the HIV epidemic exhibits geographic and demographic variation, influenced by age, sex, socioeconomic status, risk behaviors, and accessibility to healthcare services (Obeagu & Obeagu, 2022). Understanding the determinants of HIV infection is crucial for effective prevention, early detection, and policy formation. Statistical modeling plays a vital role in identifying and quantifying the effect of such determinants. This study applies binary logistic regression using logit, probit, and complementary log–log (cloglog) link functions to assess the influence of age, sex, and year on HIV infection among patients tested at General Hospital Takum, Taraba State, Nigeria, between 2018 and 2023. The objective is to identify significant demographic determinants of HIV infection and determine the best-fitting link function for the data. Model performance was evaluated using goodness-of-fit statistics (Deviance, Pearson chi-square, and Hosmer–Lemeshow tests) and model selection criteria (Akaike Information Criterion and Bayesian Information Criterion). Results indicate a consistent decline in HIV odds across the years, significantly higher odds among females, and substantially increased odds among adults aged 30–49 and 50 years and above. Among the three models, the complementary log–log link function demonstrated the best overall fit, exhibiting the lowest AIC and BIC values and non-significant goodness-of-fit tests. The study concludes that age, sex, and year are significant predictors of HIV infection, and that the complementary log–log model provides the most reliable framework for predicting HIV status in this population. The findings are expected to contribute to improved model selection in epidemiological research and inform localized HIV prevention strategies.