How do I determine statistical difference in slopes with non-normal data

[#1]

Greeting JMP Community,

I am currently working with a dataset containing a linear responses (r2 ranges from 0.86 to 0.99) of contaminant load in terms of the age of 6 indivuals with sampling over their entire lifetime (lifespans ranging from 2 years to 30+). 4 of the 6 individuals resided in the same region. I plotted the distributions using Log(10), ln, and centered data but I am unable to get a normal distribution for either age or load. Is there a suggested transformation or test to determine if the slopes are statistically different between the 6 individuals and between regions?

I found a post by staff a member suggesting indicator-variable regression with interaction is used to compare slopes of multiple linear fits but I am unsure if this test works with non-normal data. Additonally, the slopes range from 3 to ~500 so I could not use ANCOVA as the slopes are not homogenous. I look forward to hearing from the community and would appreciate any help.

Thanks,

ZW

[#2]

Mark Bailey,

As long as I can state with 95% confidence using ANCOVA that my slopes are statistically different due to location or in this case ID I am very happy with the original model. I have included the age*age, age*age*age, and age*age*age*age just to be sure.

[#3]

I think that your conclusion is sound and defensible even with the slight pattern in the residual plot.

The new analysis with the higher orders should include ID alone and crossed with each of the Age terms. (Sorry I did not make that point clear before now.)

[#4]

Mark Bailey,

I included ID in this last model and received the error "Warning: Ill-conditioned regression problem" and the following output.

Thanks again for you help,

ZW

[#5]

I think that result is because not all of the ID levels have enough data to fit all the higher order terms.

[#6]

Mark Bailey,

There are very few points for 2 of the individuals. If there is an alternative test please let me know. Thanks for all of your help!

ZW

[#7]

Right. I think that the best you can do is to use the reduced model (Age, ID, Age*ID) and the tests that the provide. (We already covered that option.)

[#8]

Mark Bailey,
Perfect! I will proceed with this model. Thanks again!
ZW