I'm trying to do a non-linear analysis of covariance (ancova) and can't figure out how to do it with JMP or if it's even possible. Can anyone help me with this issue?
Specifically, I'm trying to test if the difference between multiple non-linear curves is statistically significant. The non-linear curves are in the form of y=aX^b. Additionally, I would also like to test the significance of multiple Explanatory variables on the response variable. I have come close in JMP but I am still missing some steps.
We need more detail about what exactly you are trying to do. Although I hesitate to say anything at all until I have more info, I will note that your non-linear curves can be transformed to linear by taking logs: LogY = Loga + b*LogX. If you did that and assuming you have several such curves with potentially different a and b for each curve, then testing for "differences" would mean testing for differences between slopes and intercepts of the transformed data. This can be done in JMP. There is an example in the JMP sample data called Drug which illustrates the procedure.
I am familiar with transforming the data points to make the data linear and then comparing the slopes and intercepts. However the method of log transformations is known to introduce bias and I was looking to do the same sort of analysis but without making the data linear. My response variable is fecundity and the two explanatory variables are carapace length and location and I want to see if there is a significant difference in fecundity at the different locations after accounting for variation as a result of carapace length. When substituted into the power equation Y=a*X^b, Y represents fecundity and X represents CL. This can be done by comparing the parameter estimates for b. The traditional method of doing this was to transform the equation into LogY = Loga + b*LogX, and test for differences in the transformed data in a GLM. However, I was wondering if I could do the same analysis without transforming the data (keeping it in a nonlinear form).
Using the nonlinear platform in JMP you can estimate parameter pairs (a,b) for multiple locations. JMP will provide confidence intervals for each a and each b. You can estimate the difference between between a1 and a2 or b1 and b2 for locations 1 and 2 and get an estimate of the standard error of the difference. But as far as I can tell, JMP does not supply confidence intervals for the differences in the nonlinear platform.