Hi,
I haven't been able to find a lot of resources for this particular issue.
Context:
I am working on insect emergence (after metamorphosis). We are recording the proportion of the initial population emerging over time.
For a group of individuals, this phenomenon always follows a 3-parameter logistic model, but different groups will have different parameters.
We're trying to determine if a treatment will change the parameters of the emergence curve. Any significant changes in one or several of the parameters are relevant
Ex: if I change the ambiant humidity in my rearing space, will the emergence be quicker (impact on inflexion point, growth rate)? Will it come to a cost to the individuals (impact on asymptote)?
To answer this question, we are conducting experiments where n-1 groups receive the n-1 levels of a treatment, and one group is a control. We generate n "emergence curves", each one being described by its 3-parameter vector.
Since we know that we may have cohort or environmental effects, the experiment is replicated m times. Within an experiment (nxm curves generated), each curve is modelled from a fixed sample size (usually about 400 individuals). m is relatively small (<10)
How can we conclude that the factor has an effect on one or several parameters of the curves?
- One option would be to use the "equivalence tests" (parallelism) that are already included in JMP, but they only allow the comparison of two curves at a time. They are described as legacy tests and seem somewhat decried
- Analysing each factor separately (ANOVAs and non-parametric equivalents)? There are some correlations between the parameters of the curves (tested with Pearson's correlation, 2 by 2)
- Using a Manova approach? I'm really not familiar with Manova, so I'd like to know if it would be a valid approach before taking a deep dive in the subject
- Other suggestions?
I can share some sample data if needed (raw emergence data, or a table with parameters)
