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Level I

Linear mixed model - assumption of homoscedasticity violated

Hi JMP users

I am trying to assess the infuence of sex (nominal), altitude (nominal) and latitude (nominal) on corrected wing size (continuous; residual of wing size by body mass) of an animal species. I considered altitude as a nominal factor given the fact that this particular species is mainly distributed at the extremes (low and high) of steep elevational gradients in my study area. I also considered latitude as a nominal fixed factor given the fact that I have sampled individuals only at three main latitudinal levels (north, center and south).

I have been suggested to use Linear Mixed Model for this analysis. Specifically, considering sex, altitude, latitude, sex:latitude, sex:altitude, and altitude:latitude as fixed factors, and collection site (nominal) as the random effect. The latter given the clustered distribution of the collection sites. However, I noticed that despite the corrected wing size follow a normal distribution, it violates the assumption of homoscedasticity among some altitudinal/latitudinal groups. Can I still use linear mixed model in jmp? If not, what other option can I pursue to analize my data?

Thanks in advance for your kind attention.

Super User

Re: Linear mixed model - assumption of homoscedasticity violated

First, welcome to the community.  Here are my initial thoughts (Analysis should always follow this order: Practical>Graphical>Quantitative):

1. Plot the data.  You can use Graph Builder or Multivariate Methods>Multivariate to get scatter plot matrices.

2. Plot the data.  Determine if the variation in the response of practical value (did it vary enough?)

3. Plot the data. Quantitative analysis is used to support the conclusions from the graphical analysis.  There are no required assumptions to plot the data.

"All models are wrong, some are useful" G.E.P. Box
Level VII

Re: Linear mixed model - assumption of homoscedasticity violated

Adding to @statmans helpful suggestions,

I like the variability plot,

and also like to look at random data (where no effect should be found).

The script below will generate that data.

And follow the path from simple analysis (e.g. distribution and also fit y by x) to complex (mixed model analysis).



Names Default To Here( 1 );

// Generate a data table with random data
doe_obj = DOE(
	Full Factorial Design,
	{Add Response( Maximize, "size", ., ., . ), Add Factor( Categorical, {"m", "f"}, "sex", 0 ), Add Factor(
		{"north", "center", "south"},
	), Add Factor( Categorical, {"low", "high"}, "altitude", 0 ), Set Random Seed( 35445577 ), Make Design, Replicates( 10 ), Simulate Responses( 0 ),
	Set Run Order( Randomize )}
dt = doe_obj << Make Table;
doe_obj << close window;
// generate random response
dt:size << set Formula( Random Normal() );

// Variability chart
dt << Variability Chart( Y( :size ), X( :sex, :latitude, :altitude ) )