*In Anthony’s revegetation study (Exercise 10.3), he classified
anything that fell into his pitfall traps to Order, and thus counted the
abundance of each of 24 invertebrate Orders across ten sites. He wants
to know: Is there evidence of a change in invertebrate communities due
to revegetation efforts?*

*What type of response variable(s) does he have? How should
Anthony analyse his data?*

He has a multivariate abundance dataset, with 24 correlated counts of
invertebrates in different Orders. He needs to use some GLM approach
that can handle correlation and many responses, like
`manyglm`

from the `mvabund`

package.

*In Exercise 1.13, David and Alistair looked at invertebrate
epifauna settling on algal beds (seaweed) with different levels of
isolation (0, 2, or 10 metre buffer) from each other, at two sampling
times (5 and 10 weeks). They observed presence/absence patterns of 16
different types of invertebrate (across 10 replicates). They would like
to know if there is any evidence of a difference in invertebrate
presence/absence patterns with Distance of Isolation.*

*How should they analyse the data?*

They have a multivariate abundance dataset, with 16 correlated
presence/absence measurements of invertebrates. They need to use some
GLM approach that can handle correlation and many responses, like
`manyglm`

from the `mvabund`

package.

*As in Exercise 10.2, Lena studied the effects of an offshore wind
farm on fish communities, by collecting paired data before and after
wind farm construction, at 36 stations in each of three zones (wind
farm, North, or South). She counted how many fish were caught at each
station, classified into 16 different taxa. Lena wants to know if there
is any evidence of a change in fish communities at wind farm stations,
as compared to others, following construction of the wind farm.*

*How should she analyse the data?*

She has a multivariate abundance dataset, with 16 correlated counts
of different fish species. She needs to use some GLM approach that can
handle correlation and many responses, like `manyglm`

from
the `mvabund`

package.

```
library(ecostats)
library(mvabund)
data(reveg)
$abundMV=mvabund(reveg$abund)
reveg=manyglm(abundMV~treatment+offset(log(pitfalls)),
ft_revegfamily="negative.binomial", data=reveg) # offset included as in Exercise 10.9
anova(ft_reveg)
#> Time elapsed: 0 hr 0 min 7 sec
#> Analysis of Deviance Table
#>
#> Model: abundMV ~ treatment + offset(log(pitfalls))
#>
#> Multivariate test:
#> Res.Df Df.diff Dev Pr(>Dev)
#> (Intercept) 9
#> treatment 8 1 78.25 0.02 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> Arguments:
#> Test statistics calculated assuming uncorrelated response (for faster computation)
#> P-value calculated using 999 iterations via PIT-trap resampling.
```

*Consider the seaweed dataset from David’s and
Alistair’s study of invertebrate epifauna settling on algal beds with
different levels of isolation (0, 2 or 10 metre buffer) at different
sampling times (5 and 10 weeks), with varying seaweed biomass in each
patch.*

*What sort of model is appropriate for this dataset? Fit this
model and call it ft_epiAlt and run
anova(ft_epiAlt). (This might take a couple of minutes to
run.)*

Previous experience suggests anything beyond second-order
interactions does not seem to matter – you could fit more but it would
take longer. Because of the warning that this will take a long time to
run I will set `nBoot=99`

for a quicker, rough answer:

```
data(seaweed)
$Dist = as.factor(seaweed$Dist)
seaweed# set up presence-absence response:
$PA = mvabund(seaweed[,6:21])
seaweed$PA[seaweed$PA>1] = 1
seaweed
#fit model
= manyglm(PA~(Wmass+Size+Time)*Dist,family="cloglog", data=seaweed)
ft_epiAlt anova(ft_epiAlt,nBoot=99)
#> Time elapsed: 0 hr 0 min 13 sec
#> Analysis of Deviance Table
#>
#> Model: PA ~ (Wmass + Size + Time) * Dist
#>
#> Multivariate test:
#> Res.Df Df.diff Dev Pr(>Dev)
#> (Intercept) 56
#> Wmass 55 1 6.66 0.93
#> Size 54 1 36.98 0.02 *
#> Time 53 1 32.35 0.04 *
#> Dist 51 2 28.26 0.79
#> Wmass:Dist 49 2 33.29 0.25
#> Size:Dist 47 2 26.77 0.10 .
#> Time:Dist 45 2 32.56 0.07 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> Arguments:
#> Test statistics calculated assuming uncorrelated response (for faster computation)
#> P-value calculated using 99 iterations via PIT-trap resampling.
```

*Now fit a model under the null hypothesis that there is no effect
of Distance of isolation, and call it ft_epiNull. Run
anova(ft_epiNull, ft_epiAlt). This second anova took much
less time to fit – why? Is there evidence of an effect of distance of
isolation on presence/absence patterns in the invertebrate
community?*

To see if there is an effect of `Dist`

I guess we could
remove it from the model entirely and see if that does anything:

```
= manyglm(PA~Wmass+Size+Time,family="cloglog", data=seaweed)
ft_epiNull anova(ft_epiNull, ft_epiAlt, nBoot=99)
#> Time elapsed: 0 hr 0 min 2 sec
#> Analysis of Deviance Table
#>
#> ft_epiNull: PA ~ Wmass + Size + Time
#> ft_epiAlt: PA ~ (Wmass + Size + Time) * Dist
#>
#> Multivariate test:
#> Res.Df Df.diff Dev Pr(>Dev)
#> ft_epiNull 53
#> ft_epiAlt 45 8 115.2 0.41
#> Arguments:
#> Test statistics calculated assuming uncorrelated response (for faster computation)
#> P-value calculated using 99 iterations via PIT-trap resampling.
```

*This second anova took much less time to fit –
why?*

Because it only has to test one hypothesis, not seven, so took about a seventh of the time!

*Is there evidence of an effect of distance of isolation on
presence/absence patterns in the invertebrate community?*

No :(

```
par(mfrow=c(1,3),mar=c(3,3,2,1),mgp=c(1.75,0.75,0))
=manyglm(abundMV~treatment,offset=log(pitfalls),family="negative.binomial", data=reveg)
ft_revegplotenvelope(ft_reveg, which=1:3)
```

*What do you reckon?*

Assumptions seem reasonable here.

```
=manyglm(abundMV~treatment, offset=log(pitfalls), family="poisson", data=reveg)
ft_revegPpar(mfrow=c(1,3),mar=c(3,3,1,1),mgp=c(1.75,0.75,0))
plotenvelope(ft_revegP, which=1:3, sim.method="stand.norm")
```

```
meanvar.plot(reveg$abundMV~reveg$treatment)
#> START SECTION 2
#> Plotting if overlay is TRUE
#> using grouping variable reveg$treatment 7 mean values were 0 and could
#> not be included in the log-plot
#> using grouping variable reveg$treatment 10 variance values were 0 and could not
#> be included in the log-plot
#> FINISHED SECTION 2
abline(a=0,b=1,col="darkgreen")
```

*How’s the Poisson assumption looking?*

It is in all sorts of trouble, there is a very strong fan-shape on the residuals vs fits plot, points drift well outside the simulation envelope on the nromal quantile plot (with many residuals larger than 5 or less than -5) and a strong increasing trend on the residual vs fits plot. These are all symptomatic of overdispersion, confirmed by the sample mean-variance plot, where points tend to fall above the one-to-one line at large means.

*What assumptions were made?*

We assumed:

- observations are conditionally independent
- data are Bernoulli
- the cloglog of the mean is a linear function of predictors
- residuals have constant correlation

*Where possible, check these assumptions.*

```
par(mfrow=c(1,3),mar=c(3,3,1,1),mgp=c(1.75,0.75,0))
= manyglm(PA~(Wmass+Size+Time)*Dist,family=binomial("cloglog"), data=seaweed)
ft_epiAlt plotenvelope(ft_epiAlt, which=1:3)
```

*Do assumptions seem reasonable?*

Yes it all looks good to me. This is not unexpected because presence-absence data are by definition Bernoulli, the only potential issues could be if there were higher order interactions or violations of te independence assumption.

*Consider Lena’s offshore wind farm study (Exercise 14.3). Fit an
appropriate model to the data. Make sure you include a Station main
effect (to account for the paired sampling design).*

```
data(windFarms)
=manyglm(mvabund(windFarms$abund)~Station+Year+Year:Zone, family="poisson", data=windFarms$X) ft_wind
```

*What assumptions were made?*

We assumed:

- observations are conditionally independent
- data are Poisson
- the log of the mean is a linear function of predictors
- residuals have constant correlation

*Where possible, check these assumptions.*

Used “stand.norm” because this model takes a while to fit.

```
par(mfrow=c(1,3),mar=c(3,3,1,1),mgp=c(1.75,0.75,0))
plotenvelope(ft_wind, which=1:3, sim.method="stand.norm")
```

*Do assumptions seem reasonable? In particular, think about
whether there is evidence that the counts are overdispersed compared to
the Poisson.*

Things generally look OK, but there is a downward trend on the
scale-location plot, weakly suggestive of under-dispersion. Note the sim
envelope was constructed using `"stand.norm"`

, meaning we
compared the smoother to what would be expected for a bunch of standard
normal residuals. But the kink could be a weird artifact of the model
being fitted (which has loads of parameters) so let’s repeat using
`"refit"`

, but with a smaller value of `n.sim`

so
it doesn’t take too long (it will take a few minutes though):

```
par(mfrow=c(1,3),mar=c(3,3,1,1),mgp=c(1.75,0.75,0))
plotenvelope(ft_wind, which=1:3, n.sim=59)
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error : inner loop 1; cannot correct step size
#> Error : inner loop 1; cannot correct step size
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error : inner loop 1; cannot correct step size
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error : inner loop 1; cannot correct step size
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error : inner loop 1; cannot correct step size
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
#> Error in glm.fit(x = structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, :
#> NA/NaN/Inf in 'x'
```

(You can ignore any error messages - these seem to happen because predicted values were numerically zero.)

Anyway, the downward trend in the scale-location plot happened in
simulated data too, so it is nothing really to worry about. It seems to
be an artifact, probably because of overfitting of the data by including
a `Station`

term in the model – this means that there is a
parameter for every two observations in the data! (If a random effect
were used instead, this effect would have been weaker. But it isn’t
really a problem.)

```
anova(ft_reveg,test="wald",cor.type="shrink")
#> Time elapsed: 0 hr 0 min 6 sec
#> Analysis of Variance Table
#>
#> Model: abundMV ~ treatment
#>
#> Multivariate test:
#> Res.Df Df.diff wald Pr(>wald)
#> (Intercept) 9
#> treatment 8 1 8.698 0.05 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> Arguments:
#> Test statistics calculated assuming correlated response via ridge regularization
#> P-value calculated using 999 iterations via PIT-trap resampling.
```

*Fit models [to Lena’s windfarm data] under the null and
alternative hypotheses of interest. Run an anova to compare these two
models, with just 19 bootstrap resamples, to estimate computation
time.*

The null model in this case has no `Year:Zone`

term… there
could still be year-to-year variation, but it should not affect
different Zones in different ways.

```
= mvabund(windFarms$abund)
windMV =manyglm(windMV~Station+Year+Year:Zone, family="poisson", data=windFarms$X)
ft_wind=manyglm(windMV~Station+Year, family="poisson", data=windFarms$X)
ft_windNullanova(ft_windNull, ft_wind, nBoot=19)
#> Time elapsed: 0 hr 0 min 11 sec
#> Analysis of Deviance Table
#>
#> ft_windNull: windMV ~ Station + Year
#> ft_wind: windMV ~ Station + Year + Year:Zone
#>
#> Multivariate test:
#> Res.Df Df.diff Dev Pr(>Dev)
#> ft_windNull 70
#> ft_wind 68 2 81.83 0.05 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> Arguments:
#> Test statistics calculated assuming uncorrelated response (for faster computation)
#> P-value calculated using 19 iterations via PIT-trap resampling.
```

This took 12 seconds for me.

*Remove zerotons and singletons from the dataset using:
windMV = mvabund( windFarms$abund[,colSums(windFarms$abund>0)>1] )
Now fit a model to this new response variable, again with just 19
bootstrap resamples.*

```
= mvabund(windFarms$abund[,colSums(windFarms$abund>0)>1])
windMV1 =manyglm(windMV1~Station+Year+Year:Zone, family="poisson", data=windFarms$X)
ft_wind1=manyglm(windMV1~Station+Year, family="poisson", data=windFarms$X)
ft_windNull1anova(ft_windNull1, ft_wind1, nBoot=19)
#> Time elapsed: 0 hr 0 min 11 sec
#> Analysis of Deviance Table
#>
#> ft_windNull1: windMV1 ~ Station + Year
#> ft_wind1: windMV1 ~ Station + Year + Year:Zone
#>
#> Multivariate test:
#> Res.Df Df.diff Dev Pr(>Dev)
#> ft_windNull1 70
#> ft_wind1 68 2 81.83 0.05 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> Arguments:
#> Test statistics calculated assuming uncorrelated response (for faster computation)
#> P-value calculated using 19 iterations via PIT-trap resampling.
```

*Did this run take less time?* Yes, but not much less, it took
10 seconds for me.

*How do results compare?* Results were almost identical, with
the same test statistic (to two decimal places).

*How long do you think it would take to fit a model with 999
bootstrap resamples, for an accurate 𝑃-value?*

As a rough estimate, multiply the time you just got by 50. For me this is about 500 seconds, so I would expect it to take about eight minutes.

It is curious that this didn’t change computation time all that much.
Looking at number of non-zero values in `windMV`

:

```
colSums(windFarms$abund>0)
#> Bergvar Oxsimpa Piggvar Roodspotta Rootsimpa
#> 0 51 1 3 30
#> Sandskaadda Sjurygg Skrubbskaadda Skaaggsimpa Skaarsnultra
#> 5 6 22 6 4
#> Stensnultra Svart.smoorbult Torsk Tanglake Aakta.tunga
#> 37 3 134 136 0
#> AL
#> 61
```

we see that only three of the 16 species had one or less presence. A couple more had three counts, removing these as well:

```
= mvabund(windFarms$abund[,colSums(windFarms$abund>0)>3])
windMV3 =manyglm(windMV3~Station+Year+Year:Zone, family="poisson", data=windFarms$X)
ft_wind3=manyglm(windMV3~Station+Year, family="poisson", data=windFarms$X)
ft_windNull3anova(ft_windNull3, ft_wind3, nBoot=19)
#> Time elapsed: 0 hr 0 min 10 sec
#> Analysis of Deviance Table
#>
#> ft_windNull3: windMV3 ~ Station + Year
#> ft_wind3: windMV3 ~ Station + Year + Year:Zone
#>
#> Multivariate test:
#> Res.Df Df.diff Dev Pr(>Dev)
#> ft_windNull3 70
#> ft_wind3 68 2 74.19 0.05 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> Arguments:
#> Test statistics calculated assuming uncorrelated response (for faster computation)
#> P-value calculated using 19 iterations via PIT-trap resampling.
```

This is only slightly quicker, which is a tad surprising. The test statistic is only slightly smaller, so we can see clearly that the action is happening for the more abundant species – this is not surprising, there is not enough information in any of the rare species to detect an interaction!

```
= counts = as.matrix( round(seaweed[,6:21]*seaweed$Wmass))
habOrd >0 & counts<10] = 1
habOrd[counts>=10] = 2
habOrd[countslibrary(ordinal)
#>
#> Attaching package: 'ordinal'
#> The following objects are masked from 'package:VGAM':
#>
#> dgumbel, dlgamma, pgumbel, plgamma, qgumbel, rgumbel, wine
#> The following objects are masked from 'package:glmmTMB':
#>
#> ranef, VarCorr
#> The following objects are masked from 'package:nlme':
#>
#> ranef, VarCorr
#> The following objects are masked from 'package:lme4':
#>
#> ranef, VarCorr
#> The following object is masked from 'package:dplyr':
#>
#> slice
summary(habOrd) # Amphipods are all "2" which would return an error in clm
#> Amph Cope Poly Anem Iso Bival
#> Min. :2 Min. :0.000 Min. :0.000 Min. :0.0000 Min. :0.000 Min. :0.000
#> 1st Qu.:2 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:0.0000 1st Qu.:2.000 1st Qu.:0.000
#> Median :2 Median :2.000 Median :2.000 Median :0.0000 Median :2.000 Median :2.000
#> Mean :2 Mean :1.895 Mean :1.772 Mean :0.2456 Mean :1.877 Mean :1.351
#> 3rd Qu.:2 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:0.0000 3rd Qu.:2.000 3rd Qu.:2.000
#> Max. :2 Max. :2.000 Max. :2.000 Max. :2.0000 Max. :2.000 Max. :2.000
#> Gast Turb Prawn Urchin Fish
#> Min. :1.000 Min. :0.00000 Min. :0.0000 Min. :0.00000 Min. :0.0000
#> 1st Qu.:2.000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000
#> Median :2.000 Median :0.00000 Median :0.0000 Median :0.00000 Median :0.0000
#> Mean :1.947 Mean :0.08772 Mean :0.5263 Mean :0.07018 Mean :0.1754
#> 3rd Qu.:2.000 3rd Qu.:0.00000 3rd Qu.:2.0000 3rd Qu.:0.00000 3rd Qu.:0.0000
#> Max. :2.000 Max. :2.00000 Max. :2.0000 Max. :2.00000 Max. :2.0000
#> Crab Caddis Opi Ost Bstar
#> Min. :0.0000 Min. :0.00000 Min. :0.0000 Min. :0.000 Min. :0.0000
#> 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:0.0000
#> Median :0.0000 Median :0.00000 Median :0.0000 Median :2.000 Median :0.0000
#> Mean :0.5965 Mean :0.03509 Mean :0.1404 Mean :1.404 Mean :0.2105
#> 3rd Qu.:2.0000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:2.000 3rd Qu.:0.0000
#> Max. :2.0000 Max. :2.00000 Max. :2.0000 Max. :2.000 Max. :2.0000
=habOrd[,-1] #remove Amphipods
habOrd=manyany(habOrd~Dist*Time*Size,"clm",data=seaweed)
manyOrd=manyany(habOrd~Time*Size,"clm",data=seaweed)
manyOrdNullanova(manyOrdNull, manyOrd)
#>
#> LR Pr(>LR)
#> sum-of-LR 101.1 0.17
```

*What hypothesis has been tested here? Is there any evidence
against it?*

We tested for an effect of distance on abundance, when classified
into a three-level ordinal factor. There is no evidence of a
`Dist`

effect.

The `ordinal`

package has a bug in it (in version 2019.12)
so it conflicts with `lme4`

(specifically it overwrites the
`ranef`

function), [issue posted on Github] (https://github.com/runehaubo/ordinal/issues/48). So if
you are running analyses using both packages, you need to *detach the
ordinal package* before continuing…

```
detach("package:ordinal", unload=TRUE)
#> Warning: 'ordinal' namespace cannot be unloaded:
#> namespace 'ordinal' is imported by 'ecoCopula' so cannot be unloaded
```

data

```
=manyglm(abundMV~treatment+offset(log(pitfalls)), data=reveg, composition=TRUE)
ft_companova(ft_comp,nBoot=99)
#> Time elapsed: 0 hr 0 min 21 sec
#> Analysis of Deviance Table
#>
#> Model: abundMV ~ cols + treatment + offset(log(pitfalls)) + rows + cols:(treatment + offset(log(pitfalls)))
#>
#> Multivariate test:
#> Res.Df Df.diff Dev Pr(>Dev)
#> (Intercept) 239
#> cols 216 23 361.2 0.01 **
#> treatment 215 1 14.1 0.01 **
#> rows 206 9 25.5 0.02 *
#> cols:treatment 184 23 56.7 0.01 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> Arguments: P-value calculated using 99 iterations via PIT-trap resampling.
```

*Which term measures the effect of treatment on relative
abundance? Is there evidence of an effect on relative
abundance?*

`cols:treatment`

. There is evidence of an effect of
relative abundance.

```
= manyglm(abundMV~cols+rows+offset(log(pitfalls)),
ft_null data=ft_comp$data)
= manyglm(abundMV~cols+rows+treatment:cols
ft_alt +offset(log(pitfalls)), data=ft_comp$data)
anova(ft_null,ft_alt,nBoot=99,block=ft_comp$rows)
#> Time elapsed: 0 hr 0 min 5 sec
#> Analysis of Deviance Table
#>
#> ft_null: abundMV ~ cols + rows + offset(log(pitfalls))
#> ft_alt: abundMV ~ cols + rows + treatment:cols + offset(log(pitfalls))
#>
#> Multivariate test:
#> Res.Df Df.diff Dev Pr(>Dev)
#> ft_null 207
#> ft_alt 184 23 56.74 0.01 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> Arguments: P-value calculated using 99 iterations via PIT-trap resampling.
```

```
= manyglm(abundMV~1+offset(log(pitfalls)), data=reveg)
ft_reveg0 = log(rowSums(reveg$abundMV)) - log( rowSums(fitted(ft_reveg0)) )
QDrows0 =manyglm(abundMV~1+offset(log(pitfalls))+offset(QDrows0), data=reveg)
ft_row0= manyglm(abundMV~treatment+offset(log(pitfalls)), data=reveg)
ft_reveg = log(rowSums(reveg$abundMV)) - log( rowSums(fitted(ft_reveg)) )
QDrows =manyglm(abundMV~treatment+offset(log(pitfalls))+offset(QDrows), data=reveg)
ft_rowanova(ft_row0,ft_row)
#> Time elapsed: 0 hr 0 min 7 sec
#> Analysis of Deviance Table
#>
#> ft_row0: abundMV ~ 1 + offset(log(pitfalls)) + offset(QDrows0)
#> ft_row: abundMV ~ treatment + offset(log(pitfalls)) + offset(QDrows)
#>
#> Multivariate test:
#> Res.Df Df.diff Dev Pr(>Dev)
#> ft_row0 9
#> ft_row 8 1 50.26 0.073 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> Arguments:
#> Test statistics calculated assuming uncorrelated response (for faster computation)
#> P-value calculated using 999 iterations via PIT-trap resampling.
```

*This was over ten times quicker than Code Box 14.7 (note that it
used ten times as many resamples), but results are slightly different –
the test statistic is slightly smaller, and the \(P\)-value larger. Why do you think this
might be the case?*

The quick-and-dirty offset approach only roughly approximates the row effect, so it would be expected to lose some efficiency (leading to a smaller test statistic and a larger \(P\)-value).

```
= anova(ft_reveg,p.uni="adjusted")
an_reveg #> Time elapsed: 0 hr 0 min 6 sec
an_reveg#> Analysis of Deviance Table
#>
#> Model: abundMV ~ treatment + offset(log(pitfalls))
#>
#> Multivariate test:
#> Res.Df Df.diff Dev Pr(>Dev)
#> (Intercept) 9
#> treatment 8 1 78.25 0.022 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Univariate Tests:
#> Acarina Amphipoda Araneae Blattodea
#> Dev Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev)
#> (Intercept)
#> treatment 8.538 0.183 9.363 0.155 0.493 0.976 10.679 0.118
#> Coleoptera Collembola Dermaptera Diotocardia
#> Dev Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev)
#> (Intercept)
#> treatment 9.741 0.143 6.786 0.297 0.196 0.976 0 0.983
#> Diplura Diptera Formicidae Haplotaxida
#> Dev Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev)
#> (Intercept)
#> treatment 2.24 0.840 5.93 0.348 0.831 0.973 2.889 0.766
#> Hemiptera Hymenoptera Isopoda Larvae
#> Dev Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev)
#> (Intercept)
#> treatment 1.302 0.967 4.254 0.528 1.096 0.973 0.463 0.976
#> Lepidoptera Polydesmida Pseudoscorpionida
#> Dev Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev)
#> (Intercept)
#> treatment 0.913 0.973 1.451 0.957 1.056 0.973
#> Scolopendrida Seolifera Soleolifera Thysanoptera
#> Dev Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev) Dev
#> (Intercept)
#> treatment 0.913 0.973 1.03 0.973 4.223 0.528 1.056
#> Tricladida
#> Pr(>Dev) Dev Pr(>Dev)
#> (Intercept)
#> treatment 0.973 2.804 0.766
#> Arguments:
#> Test statistics calculated assuming uncorrelated response (for faster computation)
#> P-value calculated using 999 iterations via PIT-trap resampling.
```

```
= sort(an_reveg$uni.test[2,],decreasing=T,
sortedRevegStats index.return=T)
$x[1:5]
sortedRevegStats#> Blattodea Coleoptera Amphipoda Acarina Collembola
#> 10.679374 9.741038 9.362519 8.537903 6.785946
sum(sortedRevegStats$x[1:5])/an_reveg$table[2,3]
#> [1] 0.5764636
coef(ft_reveg)[,sortedRevegStats$ix[1:5]]
#> Blattodea Coleoptera Amphipoda Acarina Collembola
#> (Intercept) -0.3566749 -1.609438 -16.42495 1.064711 5.056246
#> treatmentImpact -3.3068867 5.009950 19.42990 2.518570 2.045361
$stderr[,sortedRevegStats$ix[1:5]]
ft_reveg#> Blattodea Coleoptera Amphipoda Acarina Collembola
#> (Intercept) 0.3779645 1.004969 707.1068 0.5171539 0.4879159
#> treatmentImpact 1.0690450 1.066918 707.1069 0.5713194 0.5453801
```

*Which fish species are most strongly associated with offshore
wind farms, in Lena’s study? Reanalyse the data to obtain univariate
test statistics and univariate \(P\)-values that have been adjusted for
multiple testing.*

```
data(windFarms)
= mvabund(windFarms$abund[,colSums(windFarms$abund>0)>1])
windMV1 =manyglm(windMV1~Station+Year+Year:Zone, family="poisson", data=windFarms$X)
ft_wind1= anova(ft_wind1,p.uni="adjusted",nBoot=99)
an_wind1 #> Time elapsed: 0 hr 2 min 48 sec
= sort(an_wind1$uni.test[4,], decreasing=T, index.return=T)
sortedWindStats $x[1:5]
sortedWindStats#> Tanglake Torsk Oxsimpa Rootsimpa AL
#> 29.019951 22.296044 6.899955 6.801339 4.819447
$uni.p[4,sortedWindStats$ix[1:5]]
an_wind1#> Tanglake Torsk Oxsimpa Rootsimpa AL
#> 0.01 0.01 0.15 0.15 0.23
```

*Is there evidence that any species clearly have a Zone:Year
interaction, after adjusting for multiple testing?*

Yes it looks like we have evidence of an effect in
`Tanglake`

(Viviparous Eelpout) and `Torsk`

(cod).

*What proportion of the total Zone:Year effect is
attributable to these potential indicator species?*

*(These code chunk has not been run as it is reliant on the
previous code chunk.)*

`sum(sortedWindStats$x[1:2])/an_wind1$table[4,3]`

So 63% of the `Zone:Year`

effect is just these two
species.

*Plot the abundance of each potential indicator species against
Zone and Year.*

`plot(windMV1~interaction(windFarms$X$Zone,windFarms$X$Year),var.subset=sortedWindStats$ix[1:4])`

*What is the nature of the wind farm effect for each species? Do
you think these species are good indicators of an effect of wind
farms?*

It is hard to say. I guess there has been a big increase in Ellpout in 2010, perhaps more so in wind farms than in North Zone. Cod numbers seemed to increase in 2010 for South Zone and not wind farms. Interaction plots might be a better way to see this…