New Modified Estimators for the Spatial Lag Model with Randomly Missing Data in Dependent Variable: Methods and Simulation Study

Accurately estimating the spatial lag model (SLM) in the presence of randomly missing data in the dependent variable poses a significant challenge. We introduce some modifications to the two-stage least squares with imputation (I2SLS) estimator previously proposed by Izaguirre [1] and Wang and Lee [2]. Our key contributions include (1) introducing the generalized nonlinear least squares (GNLS) estimator as an alternative imputation method to the previously used nonlinear least squares (NLS) approach in the literature, (2) incorporating additional instrument matrices (IM), and (3) implementing both partial and total imputations for all modified estimators. Through a Monte Carlo simulation (MCS) study, we evaluate the performance of these estimators across various scenarios of sample size, spatial weights matrix densities, and missingness rate. Results are compared in terms of coefficient bias and root mean squares errors (RMSE) for both the parameters and model fit. The findings indicate that all estimators demonstrate relatively strong performance in the context of estimator coefficients bias and RMSE. However, our modified estimators demonstrate slightly better performance compared to those previously documented in the literature in terms of overall RMSE. While both total and partial imputation approaches tend to produce similar results, partial imputation demonstrated superior performance in certain scenarios. Additionally, the estimators proved robust, maintaining their reliability across varying levels of spatial connectivity. However, higher missing data rates led to slightly increased bias and RMSE.