An ANOVA-based test for random effects in a nonlinear mixed model using a Monte Carlo permutation procedure

Nonlinear mixed models are essential for data analysis due to their versatility and adaptability to many research objectives and data formats. Testing misspecification is crucial to selecting a working nonlinear model. A useful and simpler model is often chosen using variance component tests. Nonlinear models are rarely studied in the literature, unlike linear models, which have numerous successful test development attempts. The latter test requires linearity between the answer and the explanatory factors. Thus, we use an existing linearization technique to build a linear model using pseudo-responses. If random effects were needed in the original nonlinear mixed model, the pseudo-responses vector inherits a mixed linear model representation. Simulation experiments and an application to a real-world bioassay data set evaluate this permutation test.