title: post-hoc comparisons for GAMs modeling proportion data
body: <p>I’m using GAMs to analyze germination data across a range of 5 constant temperatures. My response variable is total germination proportion (germinated/viable seeds) at the end of the experiment. My experimental variables are the substrate on which seeds are germinating and temperature (I’m linking 5 different temperatures into a continuous variable) to generate a curve for each of the substrates. My experimental question is whether germination on one substrate expands the range of temperatures on which seeds can germinate over another substrate and if so at what portion of the temperature range does this occur (or in other words how does the effect differ at different temperatures)? </p>
  
  <p>I know that is is possible to conduct pair-wise comparisons to determine if the germination response on different substrates differed significantly from each other (analogous to main factor results in glm), but what I want to do is to compare where across the germination curve (x axis = temperatures [5, 10, 15, 20, 25 C] and y axis=cumulative germination proportion at the end of the trial) did germination differ. With my limited understanding, my thinking goes that if I able to splice the data at specific temperature intervals or use loess smoothers with a specific window width (correlated to my temperature profiles) and then get the predicted values for germination within each of those windows or splices, then I could compare them using some sort of post-hoc testing (analogous to Tukey HSD, etc.), but I’m not sure this is possible. </p>
  
  <p>If this is not possible, would it be sufficient for publication and data interpretation to use main effect p-values to first address whether total germination differs among substrates across the continuous temperature range (5-25 C) and then use data visualisation (e.g. plotting the three germination curves next to each other) in order to visually answer the question of where on the curve are differences most pronounced?</p>
  
  <p>I really appreciate any insight you might have into this!</p>