Partially linear mixed effects model with measurement error in nonparametric part

A partially linear mixed effects model, where the nonparametric part's variable is measured with additive error, is considered in this paper. An estimator of the regression coefficient and a predictor of the random effect parameter are derived by modification of local-likelihood and Henderson methods. We also demonstrate that, under the suitable conditions, the resulting estimator of regression coefficient is asymptotically normal. A Monte Carlo simulation study, together with a Covid-19 data example, is used to evaluate effectiveness of the proposed approach at the end of the paper. Numerical studies support the theoretical findings, revealing comparable rates of measurement error compared to ignoring measurement error in a simulation study. Finite sample and asymptotic distributions of the estimator show agreement, and real data analysis based on the proposed model explores the impact of various factors on Covid-19 deaths. The results conclude that considering measurement error yields smaller MSE and higher R-squared values than ignoring measurement error.