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Thread: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

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    Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help




    Hello all,

    I am trying to run a nested ANOVA in JMP on some ecological field data - I'm trying to measure whether fish biomass is different in and out of a marine reserve. The data has the following heirarchical structure:

    Protection (Reserve, Non-Reserve)
    Site (Site 1, Site 2, Site 3, Site 4)
    Transect (1, 2, 3, 4, 5, 6, within each site)
    Fish biomass (of each fish, within each transect)


    My guess is that I would run an ANOVA using the following terms:

    Protection
    Site[Protection] (site nested within protection)

    OR am I supposed to average the transects due to potential for pseudo replication? or does the nested feature account for this?

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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    Questions:

    1) do you have four sites in reserve/non reserve?
    2) how many samples did you collect along each transect?
    3) are these count dataa? or did you actually collect the fish?
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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    Thanks for the reply. These are technically count data yes. More specifically they are length data that have been transformed into biomass. So they are essentially counts within each particular length class.

    Here is a better description:

    Diver swims along 6 transects at each site and counts all of the fish and places them within a particular size category.

    Does this at 4 reserve sites, and 4 non-reserve sites (the "treatment," I presume)

    So the statistical question is are there significant differences between total biomass of fish between each of the treatments. However I would assume I need to do something to account for potential pseudoreplication (e.g. nested design or average by transect, then by site, etc.)

    Thanks so much

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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    Hi Vogtro,

    The best approach is to nest your transects within sites and sits within locations (reserve/non reserve).

    From a modelling point of view I would encourage you to look into generalized linear mixed models. As you have count data it is likley best modelled with a poisson link function. These models for ecologists were recently (well 2010) reviewed in the journal Trends in Ecology and Evolution.

    You should also look at Miller and Anderson "Remedies for pseudoreplcation" 2004 - forget the jouranl, but if you google the title it should come up as a free PDF.
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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    Quote Originally Posted by bugman View Post
    Hi Vogtro,

    The best approach is to nest your transects within sites and sits within locations (reserve/non reserve).

    From a modelling point of view I would encourage you to look into generalized linear mixed models. As you have count data it is likley best modelled with a poisson link function. These models for ecologists were recently (well 2010) reviewed in the journal Trends in Ecology and Evolution.

    You should also look at Miller and Anderson "Remedies for pseudoreplcation" 2004 - forget the jouranl, but if you google the title it should come up as a free PDF.
    Thanks so much! I will look into this paper...

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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    Alright, I spoke too soon and unfortunately I'm still having some issues...

    I placed the data in the following nested hierarchical structure:

    Protection
    Site[Protection]
    Transect[Protection,Site]

    where:
    Response variable = Fish Biomass in kg

    Model effects:

    Protection= "Reserve" or "Non-reserve"
    Site = "Site 1", "Site 2", "Site 3", or "Site 4"
    Transect = # 1-6

    If I run it as-is, I get an incomplete output, all of the std. error columns are empty and clearly something is wrong.

    Am I supposed to specify transects as a random effect? If I do this, it seems to work and the output looks ok, but I still don't know if the model is setup right.

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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    I think I may have found the answer here: http://facecouncil.org/puf/wp-conten...-2009-TREE.pdf

    Seems like I should be specifying the pseudo-replicated term (in this case, transects) as a random effect. In that case my choices seem to be either an ANOVA with data transformation or a GLMM like you suggested which accepts random effects. Unfortunately JMP doesn't support GLMM, and while R does support it I haven't been able to find any good tutorials out there that help with the interpretation of the results.

    I'm feeling a case of analysis paralysis coming on, and I'm tempted to stick with standard least-squares ANOVA.

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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    I think you may find this book (LINK) extremely helpful. In the meantime I'm sure some of us would be happy to help you with the syntax for the analysis in R if you go that route.
    “In God we trust. All others must bring data.”
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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    Here's another good link for GLMMs (LINK). I'm with everyone else in suggesting that a GLMM with Poisson link is the way to go. Transforming count data can get very ugly. As Jake said, there are numerous people here who are familiar with specifying GLMMs in R.

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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    Quote Originally Posted by vogtro View Post
    I think I may have found the answer here: http://facecouncil.org/puf/wp-conten...-2009-TREE.pdf

    Seems like I should be specifying the pseudo-replicated term (in this case, transects) as a random effect.
    Yep, thats the review I was refering too. Your factor "Sites" should be random also.
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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    I'm feeling a case of analysis paralysis coming on, and I'm tempted to stick with standard least-squares ANOVA.
    Don't give in to the temptation!

    Seems like I should be specifying the pseudo-replicated term (in this case, transects) as a random effect.
    Bugman is right that Sites is important to include. So, the random effects are nested: Transect within Site within ReserveType (like Bugman stated).

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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    So, before diving into GLMM, I tried to do this with a mixed-model ANOVA in JMP as I was successful in square root transforming the data (and luckily there are no zeros). I used the following "model effects":

    Protection
    Site[Protection] & Random
    Transect[Site,Protection] & Random


    I get a non significant result with the above.

    However, if I specify the model effects as follows:

    Protection
    Transect[Site,Protection]& Random


    I get a significant result.

    Which one of these is the correct specification of the model (if either)? I'm guessing it has something to do with how it computes the variance around the mean but I'm lost.

    Sorry for being a complete ignoramus. I would like to learn to do GLMM but I'm on a very tight time frame.
    Last edited by vogtro; 02-13-2012 at 09:32 PM.

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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    Look, sorry I cant be much help with the previous post - I am not familiar with JMP syntax. Check your degrees of freedom your fixed effect (location: i.e. reserve/no reserve) should be tested on 1 and 6 dof (correct me if Im wrong someone).

    Site needs to be nested in Location because each site is not represented in each of your fixed factor "treatments" likewise for transect which need to be nested in Site within Location...
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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help

    I just want to add another point and I am sorry if I am stating the obvious or sounding like a party pooper, but i want you to get this right because I think this type of study is very valuable. If you end up find a difference, becareful with the wording of your interpretation. Because you dont have replciated reserve and non reserve sites, it could well be that protected locations differ fromnon-pretectedjust becasue of intrinsic factors other than theirstatus of being a reserve or not. I understand that replication at that highest level can be ridiculously difficult, but I just wanted to add my 2 cents worth.
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    Re: Nested ANOVA - Replication vs. Pseudoreplication - pulling hair out, please help


    I appreciate that you want me to get this right (believe me, so do I) Thanks for your help, and I appreciate your concern.

    To be honest, my data set consists of 19 sites with different protection statuses. I scaled back my explanation of the data so that it would be easier to interperet, so at least the higher level sample size is larger.

    Im going to try to run this in R, then hopefully I can compare the output.

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