I am studying the effect of plant survival on location and genotype. I fitted a binomial GLM and conducted a post-hoc test after significant interaction using the
emmeans package. When survival was 100%, i.e. no mortality whatsoever, the lower and upper confidence limits extended all the way from 0 to 1 and were not significantly different from the other survival probabilities:
m1 <- glm(cbind(totalalive, totaldead) ~ f1 * f2, family = binomial, df) summary(m1) #Call: #glm(formula = cbind(totalalive, totaldead) ~ f1 * f2, family = binomial, # data = df) # #Deviance Residuals: # Min 1Q Median 3Q Max #-2.94105 0.00011 0.00011 0.78201 1.68444 # #Coefficients: # Estimate Std. Error z value Pr(>|z|) #(Intercept) 2.092e+01 2.371e+03 0.009 0.993 #f1B 2.002e-08 3.353e+03 0.000 1.000 #f1C -1.655e+01 2.371e+03 -0.007 0.994 #f2V2 2.032e-08 3.353e+03 0.000 1.000 #f2V3 -1.858e+01 2.371e+03 -0.008 0.994 #f1B:f2V2 -1.928e+01 4.106e+03 -0.005 0.996 #f1C:f2V2 -2.730e+00 3.353e+03 -0.001 0.999 #f1B:f2V3 3.635e-01 3.353e+03 0.000 1.000 #f1C:f2V3 1.746e+01 2.371e+03 0.007 0.994 # #(Dispersion parameter for binomial family taken to be 1) # # Null deviance: 137.380 on 89 degrees of freedom #Residual deviance: 80.419 on 81 degrees of freedom #AIC: 148.99 # #Number of Fisher Scoring iterations: 18
To conduct a post-hoc test, I used the
emmeans() function of the
cld(emmeans(m1, ~f1 : f2), type="response", Letters = letters, adjust = "none") #f1 f2 prob SE df asymp.LCL asymp.UCL .group #C V2 0.8375 4.124527e-02 Inf 7.399573e-01 0.9032387 a #B V2 0.8375 4.124527e-02 Inf 7.399573e-01 0.9032387 a #A V3 0.9125 3.159188e-02 Inf 8.276478e-01 0.9577123 ab #B V3 0.9375 2.706329e-02 Inf 8.584872e-01 0.9737457 ab #C V3 0.9625 2.124081e-02 Inf 8.901011e-01 0.9878549 b #C V1 0.9875 1.242163e-02 Inf 9.166073e-01 0.9982419 b #A V1 1.0000 1.939592e-06 Inf 2.220446e-16 1.0000000 ab #B V1 1.0000 1.939592e-06 Inf 2.220446e-16 1.0000000 ab #A V2 1.0000 1.939592e-06 Inf 2.220446e-16 1.0000000 ab
And here is a plot of the results:
As can be seen by the lower and upper confidence limits, the instances with 100% survival are not significantly different from the other groups. I am sure the reason for this is that there is no variation in those cases with 100% survival (standard error is effectively zero) and it is not possible to test whether they are significantly different to the others.
Is this correct? If that's the case, would it be:
(a) reasonable to remove the letters from those cases with 100% survival and test for significant differences only on those cases where the probability of survival is $<1$?
Or (b) should I leave the significance letters in the plot and just simply explain it in the figure caption as I did above?
At this point (see figure above) it may look strange to the reader how
SiteC - GenotypeV2 can be different from
SiteC - GenotypeV1 but
SiteB - GenotypeV2 is not different from
SiteB - GenotypeV1.
For clarification, I also added a boxplot of the raw data to illustrate this. The number of replicates is 10 per factor combination: