Where to Start

We have multiple options to proceed, namely:

1. Start with a GAM because the data exploration shows non-linear patterns.

2. Apply linear mixed effects models to allow for correlation between observations from the same batch.

3. Apply additive mixed modelling because we saw non-linear patterns and may have correlation over time, or between observations from the same batch.

4. Start with a basic linear regression model, see where we get stuck, and slowly improve the model step by step.

The first three approaches can be followed if you are familiar with GAMs and linear mixed effects models. But for pedagogical reasons, we will start with the last approach. After all, a linear regression model is so much easier to work with.

Therefore, we start with linear regression, followed by a section on GAM, and then generalised additive mixed modelling (GAMM). Each method is based on a series of assumptions, that all need to be verified, or else we cannot trust the inferences from the models. This verification process is also called the model validation. We will see how the failure of the model validation process of one model leads into another, more complicated model. Each approach contains a lot of numerical (anova tables, t-values and p-values) and graphical output. However, we only present these for the final model.

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