Permanova with covariate

[alexthomaswolf]

Dear all,


I have designed a permanova analysis with covariate.
It is a 1factorial design
1 Factor: Site (6 levels).
1 Covariate (Algal drymass (g), concrete numbers, 10-150).
1 Depending variable (Organism; abundance data, ranging from 0 (often) to 15 individuals

We are interested whether the covariate plays a role in attracting the organism, which we collected in different algal clumps (count) in 6 different sites (Factor 1: Site).

Depending on the order of terms (DW-> Site or Site-> DW), my results vary a lot.
How can I know which is the correct order?
Both datasets were exp. transformed. The resemblance matrix derives from Modified Gower log 10.

Any help is greatly appreciated.
Alex

[bugman]

A few comments/questions:

1) are you actually interested in site to site differences?
2) what are these concrete numbers in your covariate class?
3) Gowers log10 seems to be a fairly extreme distance measure when you are only dealing with 0-15 individuals. Why have you selected that one?
4) do you only have one organism? Or are you looking at community data? If it is the former I wonder if you would be better modeeling this by fitting an ANCOVA model - unless you have reason to use a distance based method.

[alexthomaswolf]

A few comments/questions:

1) are you actually interested in site to site differences?
yes
2) what are these concrete numbers in your covariate class?
algal weight
3) Gowers log10 seems to be a fairly extreme distance measure when you are only dealing with 0-15 individuals
(the count numbers are that range. Sample size is 70)
Why have you selected that one?
According to my literature, it seems most appropriate when including covariates in the analysis
4) do you only have one organism?
Yes (and then we have different concrete numbers of them)
Or are you looking at community data? - no
If it is the former I wonder if you would be better modeeling this by fitting an ANCOVA model - unless you have reason to use a distance based method.

We have non-parametric data, that is why I chose it.

One more question; We do not necessarily have to transform the data when it is is non-p., right (which I did)? Or, is there a need to even rank it?

Thanks a lot for helping.

[bugman]

We have non-parametric data, that is why I chose it.

One more question; We do not necessarily have to transform the data when it is is non-p., right (which I did)? Or, is there a need to even rank it?

Thanks a lot for helping.

No, not neccesarily. But i still need to understand if you have commnuity data, or are you looking at a single species?

Please answer my listed question before I continue.

[alexthomaswolf]

No, not neccesarily. But i still need to understand if you have commnuity data, or are you looking at a single species?

Please answer my listed question before I continue.

Good morning.

I did, please see the insertions following your questions.

[alexthomaswolf]

yes, a single species. We have counted their numbers on different sites - within an algae; so we include their volume as covariate

[bugman]

I missed that. Excuse me. I am at work, so am just glancing over this right now.

It seems to me, that for a single species you might want to fit a GLM including algal biomass as a covariate (as you inteneded). Have you looked at the distribution of your residuals?

If you have loads of zeros, you might want to look at fitting your GLM with a poisson or negative binomial link.

Also, as for your different results depending on the order which they are included – this shouldn’t matter for balanced designs, and if you design is unbalanced, this will occurer when you use sequential (TYPE 1) sums of squares. Check the defaults in PERMANOVA. TYPE III SS might be a better option for your design, its more conservative and not dependant on the order of terms.

[alexthomaswolf]

I missed that. Excuse me. I am at work, so am just glancing over this right now.

It seems to me, that for a single species you might want to fit a GLM including algal biomass as a covariate (as you inteneded). Have you looked at the distribution of your residuals?

If you have loads of zeros, you might want to look at fitting your GLM with a poisson or negative binomial link.

Also, as for your different results depending on the order which they are included – this shouldn’t matter for balanced designs, and if you design is unbalanced, this will occurer when you use sequential (TYPE 1) sums of squares. Check the defaults in PERMANOVA. TYPE III SS might be a better option for your design, its more conservative and not dependant on the order of terms.

I appreciate your input very much, and give it more thought.
Kind regards.

[alexthomaswolf]

I appreciate your input very much, and give it more thought.
Kind regards.

Dear Sir (or madam),

I think we made quite some progress, considering where I started on saturday, and we are heading the correct way with our analysis. I hope you don't mind that I bother once more to share these thoughts with you?

I was wondering whether an ANCOVA can be compared to permanova at any time? Probably not.
To sum it up: We had a factor, substrate (which had 6 levels), and we took invertebrate counts from algal clumps on these 6 substrates. The invert counts (n=70) had many "0"s (40 in total), quite some 3-6 individuals, and a few 15 individuals max. Having those zeros, we chose (log+1) transformation as most appropriate before creating the resemblence matrix.
Now we added algal dry weight (or volume) as covariate.

1) From an ecological point of view, Bray Curtis distance makes sense, correct. And then, since we have zero's, we need to add a dummy variable. Alternatively, we could use modified Gower log10 (accoriding to the tutorial when using covariates).
R: Both give similar results!!! (great). Which transformation and especially distance measure would you consider most appropriate (BC with dummy variable)?

2) Most striking point, our results vary extremely, when we replace algal dryweight with volume (as covariate), although they are quite similar (regression r2 = 0.8). Is there anything we miss?

3) Is it possible that we have to use the covariate as "nested" within the fixed factor "Substrate"?

Again, your input is really greatly valued. If our manuscript gets accepted, I gladly provide you with a copy. :-)

Have a good day.
Alex

[GretaGarbo]

Permanova is just permutations test on anova (analysis of variance). Ancova is analysis of covariance, that is anova with a covariate = an extra continous explanatory variable (e.g. your algal dry weight). So it is essentially the same thing. (The terms came from a pre-computer era when they split up calculation in separate parts.)

[Historical correction: In the 1930:ies a “computer” was a woman! It was women who made the enormous amounts of calculation by paper and pencil that was needed. Only women could do statistics in those days!]

A traditional method could be, as you suggested to take log(y+1) and run anova on that.

A somewhat more modern method would be to, as Bugman suggest above, to use the original data and use generalized linear model (glm) and specify a Poisson distribution (instead of normal distribution that is implicit in anova) the link function is taken care of by the software so you don’t have to bother by that (but it is usually the log-link for the Poisson) or an other distribution could be negative binomial (which allows for more variation than the Poisson).

If you compare dry weight and volume (and they are very correlated) I guess that one of them have higher numbers, then of course you will get different regression estimates. If that is what you mean by “our results vary extremely”. This is like changing from inch to centimeter. But they will essentially say the same thing.

Sorry I don’t understand the biology that well. (I wish I did.) Are these two the same thing:
“we took invertebrate counts from algal clumps” and “algal dryweight”

Then I would say that there is no meaning to insert algal dryweight as an explanatory factor. It would be like “explaining” the variable with it self, that is, no explanation at all.

Otherwise I don’t think you should insert dryweight as “nested”.