A Poisson-modified quasi-lindley regression approach for multicollinear data using Kibria–Lukman Estimator

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Count regression models based on the Poisson distribution are widely used for non‑negative integer responses but often perform poorly when data exhibit overdispersion and multicollinearity, leading to inflated variances and unstable maximum likelihood estimates. Building on the flexibility of the Poisson‑modification of the quasi‑Lindley regression model (PMQL‑RM) for overdispersed counts, this paper proposes a new ridge‑type shrinkage estimator for PMQL‑RM based on the Kibria–Lukman (KL) biasing scheme. The resulting Poisson‑modified quasi‑Lindley Kibria–Lukman estimator (PMQL‑KL) combines ridge and Liu structures within the PMQL‑RM framework. We derive its bias, variance–covariance matrix, and matrix mean squared error (MMSE), and establish MMSE‑based theoretical comparisons with the PMQL maximum likelihood estimator (PMQL‑MLE), ridge estimator (PMQL‑RRE), Liu estimator (PMQL‑LE), and Liu‑type estimator (PMQL‑LTE). Sufficient conditions are obtained under which PMQL‑KL dominates these competitors in the sense of a smaller MSE matrix, and a data‑driven rule for selecting the KL biasing parameter is proposed. A comprehensive Monte Carlo simulation study is conducted over a range of sample sizes, numbers of predictors, correlation levels, and dispersion parameter settings. The results indicate that PMQL‑KL consistently attains the smallest scalar MSE, with especially marked gains over PMQL‑MLE and existing shrinkage estimators under severe multicollinearity. An empirical application to overdispersed Swedish football score data confirms that PMQL‑KL produces more stable coefficient estimates and the lowest empirical MSE while preserving the substantive interpretation of covariate effects. These findings suggest that PMQL‑KL is a robust and efficient alternative for modeling overdispersed count data with multicollinearity in the PMQL regression framework.