Mathematical Analysis of Loan Default Risk in Microfinance Banks in Bauchi State

Microfinance institutions in Bauchi State, North East Nigeria, play a crucial role in extending credit to small-scale traders and artisans excluded from the formal banking system, yet loan default rates persistently undermine institutional sustainability. This study employs logistic regression analysis to model the probability of loan default among 320 borrowers from three licensed microfinance banks operating in Bauchi and Azare towns. Independent variables include loan size, loan tenor, repayment schedule type, borrower age, gender, years in business, collateral type, and group guarantee membership. Binary outcome coding assigns a value of one to loans classified as non-performing after 90 days past due in accordance with Central Bank of Nigeria guidelines. The logistic model achieves an overall classification accuracy of 79 percent on a holdout validation sample, with sensitivity and specificity values of 74 and 83 percent respectively. Statistically significant predictors of default are identified as loan size above 500,000 naira, absence of group guarantee, and loan tenor exceeding 12 months. Group guarantee membership reduces the predicted default probability by 38 percentage points after controlling for other covariates. The study recommends a mandatory group guarantee structure for loans exceeding 300,000 naira as a risk mitigation measure. Findings contribute empirical evidence to credit risk management practices in Nigeria's microfinance sub-sector. Keywords: logistic regression, loan default, microfinance, Bauchi State, credit risk.