Local Influence Analysis in a Gaussian Spatiotemporal Model

Spatiotemporal models are widely used to describe data collected over space and time, where the specification of the covariance structure plays a crucial role in statistical inference. In this work, we extend the local influence methodology to assess the adequacy of the temporal independence assumption in a Gaussian spatial linear model with repeated observations over time. A separable spatiotemporal covariance function is introduced as a structured perturbation of the independence model. Closed‐form expressions are derived for the observed information matrix with respect to the perturbation parameter and for the associated perturbation matrix under this separable scheme, allowing the construction of diagnostic measures based on likelihood displacement. A simulation study is conducted to evaluate the ability of the proposed approach to detect departures from temporal independence. The methodology is further illustrated using a soybean productivity dataset collected at fixed spatial locations over multiple harvest years. The results show that ignoring temporal dependence may affect both model fit and inference on regression coefficients. The proposed framework provides a formal diagnostic tool for assessing covariance structure assumptions in Gaussian spatiotemporal models.