The boxplot attached shows the proportion of presence-absences counts of species "GP" in different dune treatments (habitat types) with 3 replicates in each treatment, and between 2-4 years repeated measures (unfortunately I have an unbalanced design of AC = 4 years, CC = 3 years, DC = 2 years repeated measures).
One count is a dune-year, aggregated to dune treat across years and dunes.
From the boxplot it seems quite clear to me that the presence of GP should be significantly different for AC:CC and AC:DC if not for CC:DC as well, given they are 100%, 7% and 0% present in AC, CC, DC samples respectively.... .
I conducted binomial GLM on the presence absence (p/a) data using the formula in R:
glm(formula = p/a ~ dune.treat,
family = "binomial",
data = dat[dat$species == "GP",])
THE OUTPUT WAS:
Deviance Residuals:
Min 1Q Median 3Q Max
-0.78 -0.788 0.00005 0.00005 1.626
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 20.57 3964.63 0.005 0.996
dune.typeC -21.58 3964.63 -0.005 0.996
dune.typeD -41.13 8253.04 -0.005 0.996
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 55.637 on 40 degrees of freedom
Residual deviance: 17.397 on 38 degrees of freedom
AIC: 23.397
This output seems very strange to me. I also tried to run a mixed effect model to include year as a random effect to take into account the unbalanced repeated measures.
glmmPQL(
p/a ~ dune.treat,
random = ~ 1 | year,
family= "binomial",
data = dat[dat$variable == "GP", ]
)
Output:
Linear mixed-effects model fit by maximum likelihood
AIC BIC logLik
NA NA NA
Random effects:
Formula: ~1 | year
(Intercept) Residual
StdDev: 1.460122 0.5028493
Variance function:
Structure: fixed weights
Formula: ~invwt
Fixed effects: value ~ dune.type
Value Std.Error DF t-value p-value
(Intercept) 30.87 274897.7 34 0.00011 0.9999
dune.typeC -32.23 274897.7 34 -0.00012 0.9999
dune.typeD -61.94 505281.0 34 -0.00012 0.9999
Correlation:
(Intr) dn.tyC
dune.typeC -1.000
dune.typeD -0.544 0.544
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.42e+00 -4.89e-01 -7.890e-13 6.215e-12 2.96e+00
Number of Observations: 41
Number of Groups: 5
I realise there is a huge standard error, and large DF, which is probable leading to p-value close to 1. But is this the 'true' result?- I don't really understand why this is happening or what I can do about it?
Is there an error in the models I am running?
What would be a more appropriate model for this data to test for differences between dune.treats?
Thanks
Tania
You have two conditions with perfect separation (100% or 0%); those make it hard for the model to fit (it's impossible to estimate the variance within that condition when there is no variance in it). I'm not sure if there is another way to get around that (there may well be, I'm just not aware of it). My feeling would be, if you can already see that the values in those cells are 0% and 100%, what's the point of statistically testing them? You can't get any more information out of a p-value than you have from already observing that these samples are 100%. It would be possible instead to just test "CC" (if you want to see, e.g., whether it is significantly above or below 50%).
This discussion might be helpful
http://stats.stackexchange.com/questions/183320/logistic-glm-with-good-predictors-is-giving-p-values-1
1. I have the suspicion that the p/a expression in your formula isn't doing what you think it is. See the attached file on logistic regression for an example using counts of Present and Absent.
2. The attached file on logistic regression mimics the simplified data in your plot. Note that the using anova shows a significant result for the effect of dune type.
3. If you want to stick with your simplified data, you could use Fisher exact test. The attached file on Fisher has the code for Fisher test and a post-hoc test. I think because you have fixed the number of samples for each dune type, you meet the fixed marginals assumption of the Fisher test.
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