[R-sig-eco] Mixed models and multivariate methods for temporal-spatial nested data

[Bob OHara]

Hm, this is a big job. The optimal solution is to see if your university 
offers a statistical consulting service. I don't see any big conceptual 
problems, but getting a good analysis will take a bit of time and 
exploration. I think you can probably 'just' use a GLMM, but getting the 
right GLMM and deciding what a good model is will take time and some 
poking of the data.

Anyway, some answers below, which may (or may not) help.

On 02/27/2017 04:27 PM, Tania Bird wrote:
> Hi all,
>
> I am seeking advice on how to analyse my unbalanced, multi-nested
> multivariate data set. I realise there are many questions in this
> email and I would be willing to consult with someone privately on this
> if it is an option.
>
> I am using abundance data for insect species (I have the same
> experimental design for reptiles, and annual plants as well). I use
> Simpson's diversity as a univariate response and species composition
> as a multivariate response.
>
> Experimental Design:
> Plots are divided into three habitat types A, B, C based on vegetation.
> Each habitat has 3 or 4 replicate control plots that are repeat
> sampled (one sample a year always in spring).
> In addition B and C have 3 or 4 treatment (vegetation removal) plots.
>   'S' plots are disturbed( trampling and off-road vehicles) but the
> disturbance is unquantified and I don't know the pre-disturbance
> habitat type.
>
> The total data set is across a 12 year period, but the sampling was
> unbalanced for various reasons. I attach a png of the metadata of the
> plots over time to show the unbalanced sampling.
> https://www.dropbox.com/s/7vxvo3x9lnywdbm/insects_years.gif?dl=0
>
> Each year the sampling across plots was conducted at the same time,
> and so plots are comparable within a year.
> In general, As were sampled every year and are considered the 'target'
> habitat. B's were sampled in the earlier years and C's later on, and
> in the last couple of years all three types were sampled together.
>
> The treatments on B & C were conducted using different methods and in
> different years, so in principle I should probably test each
> separately just against their own control pairs. However the
> hypothesis for both treatments is that treated plots will be more
> similar in composition to A plots than the paired control plots (if
> possible I want to check if they become more or less similar to A over
> time).
>
> So in that regard I thought there might be a way to include all
> habitat types in one analysis? Perhaps using time as "number of years
> since treatment" rather than a date? (Although I have no environmental
> data with which to standardise).  S dunes have no "pre-treatment"  but
> the hypothesis is that S plots will be most similar to A compared to
> all other (treated and control) plot types.  I am not sure how to
> include these plots in a testable model.
>
> Questions regarding the design:
>
>>> Can I use all the habitat types in one model (preferable!) or can I only test B treated against B control etc?
Yes you can. you obviously need a Treatment effect, and you should 
expect to have a Treatment by Habitat interaction.

There may also be some sort of interaction with time (either as Time, or 
Time Since Treatment)

>>> Must I remove data to create blocks of sampled or is 'all data useful'?
> e.g. A's were the only plots sampled in 2010- should I remove that
> year completely?
> e.g. C1 & C5 were sampled in 2005 while the rest were not until 2011,-
> should I only include data from 2011 onwards for all C's?
> e.g. Should I remove A4 completely since its only sampled in the last
> few years or its still useable?
No, you should be able to use all of the data, you just have to be a bit 
careful about how you model Time.
>>> Can I include S in the analyses in order to compare them with B and C treated plots in relation to A plots?
Yes, in principal. It just doesn't have a Habitat:Treatment interaction.

> I have already analysed my first research question
> Q1) To understanding the differences in diversity and composition
> across control habitats, irrelevant of time.
>
> The analysis approach I used for this is:
> i) Mixed effect model:  GLMM PQL (Penalised Quasi-Likelihood) using
> MASS R package.
>      Diversity ~   fixed effect = habitat type + random effect = year ,
> Family = poisson
There are better tools than glmmPQL nowadays. Have a look at the lme4 
package, for example.
> ii) Pairwise permutational multivariate analysis of variance (MANOVA)
> with R code based on the adonis2 function, to determine if the
> composition among habitats (visualised in NMDS) were significantly
> different from each other.
>
> iii) RDA with habitat as explanatory and year as covariate to test
> explained variance.
>
> Now I am trying to expand this analysis to include a temporal element
> to answer Q2 & Q3
> Q2) to understand the trends in diversity and composition over time in
> control habitats
> Q3) to understand the impact of treatment on diversity and composition
> (over time if possible?)
>
> The addition of time into the analyses is a bit difficult for me to
> work out, due to the multi-nested and unbalanced design of the data; I
> am not sure what methods to use to include time as a variable for
> looking at a) diversity and b) composition
Take a look at repeated measures models. There are a few ways this could 
be set up, depending a bit on the data.

> Questions regarding analyses:
>> 1> Is there an appropriate mixed effect model I can use to look at differences in diversity on different control plots and include time as a factor (rather than as a random effect)?
There are probably several. :-) For example you could include Time as a 
continuous covariate, alongside the random effect. You could also just 
include it as a fixed effect, but that could get messy.
>> 2> How can I appropriately test if different habitats exhibit different trends in composition over time (ie. a multivariate approach). For example, I might expect that A's will remain relatively stable over time, while C's will exhibit high turnover (fluctuation) across years, or that B's will slowly shift composition to be more similar to C. How can I test these directional hypotheses?
> I thought to create a Principle Response Curve to see relative
> differences over time, but as far as I understand, I cannot use a
> permutation test here due to the unbalance design. I also thought to
> take the scores on the first RDA axis as a univariate measure, and
> then plot this over time.. but I'm not sure if its an appropriate
> approach or how to then test this statistically.
>
> I also thought to try and create some measure of "compositional
> temporal stability" for each plot and test this using ANOVA (like some
> sort of "multivariate Coefficient of Variation"). One such measure
> could be distance of each plot-year from the habitat centroid in
> ordination space but again, I'm not sure if this is an appropriate
> approach. Any suggestions for other measures would be welcome.
That's essentially a question about the variance in responses. There are 
doubly hierarchical models that you could try, but you might not want to 
go there.
>> 3> Finally can I extend these temporal analysis (of diversity and of composition) to look at response trends to treatments, given the structure of my data?
> I would like to see if I can detect some form of resistance to, or
> recovery from, the treatment over time ... But if not, can I test the
> overall treatment affect and use time as a random effect like i did
> for my first question?
>
> Thank you for any suggestions of analyses and/or ways to subset the
> data that would allow me to answer these questions.
Essentially you need some structure on the time covariate. You could 
start by using time since treatment as a factor, and plot those 
estimates. Again, there should be a bit of playing around with the 
model, to see what makes sense.

Bob

-- 
Bob O'Hara
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Institutt for matematiske fag
NTNU
7491 Trondheim
Norway

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