This article proposes a new methodology for diagnostic analytics in a logistic regression model with a random intercept motivated by a biological case study. The methodology includes local and global influence techniques. In local influence, a suitable perturbation of the success probability for binary observations is proposed considering their correlation structure when they belong to the same group. This allows us to contrast and complement the results of local influence with global influence by means of case deletion, connecting both techniques. As mentioned, the proposed methodology is applied to a case study with real-world data collected by the authors to show the potential and adequacy of this methodology. The case study corresponds to the reproduction of arachnids reporting how the local and global influence of atypical observations can modify the statistical significance of parameters, and therefore also the biological conclusions. The quality of the model fitting is evaluated through predictive indicators. The proposed methodology is summarized in an algorithm, its computational framework is discussed, and a demo example is implemented in R code to facilitate its application. In order to evaluate the performance of the local and global influence methodology proposed, Monte Carlo simulations are conducted.
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