Bootstrap confidence intervals for generalized linear mixed models in dose-response analysis

Bootstrap methods are widely used for statistical inference in complex models, when obtaining standard errors for parameter estimates presents computational challenges. By leveraging resampling techniques based on the original distribution of the population or the structure of the sample dataset, these methods enable the derivation of inferences and critical information that are often difficult to obtain through analytical means. However, applying bootstrap to data with a hierarchical structure presents specific challenges, such as the need to preserve dependencies between the different levels of the data. In hierarchical data, such as those from agricultural experiments, simple resampling of individual observations can break important relationships between groups, leading to inaccurate inferences. Resampling must, therefore, respect the hierarchical organization of the data to avoid losing variability and structural dependencies, which can compromise the validity of the results. This study proposes a comparison of resampling techniques, with an emphasis on nonparametric bootstrap methods and different approaches, both hierarchical and non-hierarchical. The application of these techniques to fungicidal data, commonly used in agriculture to protect plants from fungal infections, illustrates the need for careful analysis of the data structure, especially when dealing with fixed and random effects in models. Our focus is on evaluating how the hierarchical structure influences the quality of inferences obtained through bootstrap, seeking methodologies that preserve data dependencies during resampling. Our results indicate that resampling that preserves the original characteristics of the experiment–particularly in a hierarchical manner–outperforms other approaches, providing intervals with more reliable coverage rates.