Hi!
I assessed a phenotype on 8 different plant genotypes in 4 real, independent, biological replicates. A priori, half of the genotypes is "classified" as resistant (R), the other half as susceptible (S).
I am interested in the "resistance level" effect; i.e. is the phenotype of R significantly different than S. I could do a Mann-Whitney-U-test in the style "phenotype depends on resistance level". However, I think this would be wrong, because the multiple R and S genotypes within one replication are not independent, thus represent pseudo-replicates. Is it correct to calcualte averages for R and S within the reps and have these means as input for further analysis? (In this case I could also do an ANOVA or t.test; the distribution of the phenotype actually permits so (normality of data, or residuals).
Or would it be more correct to formulate a mixed linear model? In this case I am absolutely not sure how to correctly do this... Something like: phanotype ~ resistance level (FIX) + genotype (RANDOM) + replicate (RANDOM)?
Any comments are greatly appreciated!
Best, Lukas
I also think a mixed model is more appropriate, but I cannot help you with the model since I don't understand your variables. I am not sure what your dependent (response) variable is. Is it the phenotype (is so: which: R/S or something else; you need to be precise about this)? And "resistance level": how is that measured/determined? I also hope the R/S classification is not done on the genotype.
So you need to give more info to get more qualified help.
Thx Jochen Wilhelm !
The phenotype I measured is shoot dry weight - that is my dependent variable.
The 8 genotypes were selected from a previous experiment assessing shoot dry weight (in the context of disease resistance) in a controlled conditions pot experiment on >300 pea (P. sativum) genotypes. Based on this initial experiment, I selected 4 genotypes that grew well (the R genotypes) and 4 that showed strong growth reduction (the S genotypes). So yes, R/S is based on the genotypes: i.e. there are NOT all combinations reslevel x genoytpe.
Following that, I have the independent variables replication (4 levels), resistance level (2) and/or genotype (8). I explicitly write "and/or" because for me the analysis is either with the factor resistance level or factor genotype. That is also the reason why I choose a "simple(r)" statistical test (t-test or non-parametric equivalent) over a more sophisticated model.
Given the response is "weight", I would use a Gamma-GLMM with log link. Alternatively a Gaussian LMM on the log response will do. And I would use the genotype as random intercept.
In R:
lme4::glmer(dryWeight ~ resLevel + (1|genotype), family = Gamma(log))
lme4::lmer(log(dryWeight) ~ resLevel + (1|genotype))
I was thinking over this: The mixed model answer of Jochen Wilhelm is very clear and makes sense. However, it does not address the actual question of that thread: What does stand against averaging within the treatment of interest (in my case the factor "resistance level"). For instance, in my data I have zeros, thus a log-transformation gets more complicated (e.g. do I make a transformation of the type log(y + 1)? I do not want to do that in my case...). Additionally, I run into "singular fit" problems with the mixed models. That is something I do not understand with my limited statistical knowledge (even when reading Ben Bolkers explanations).
So why not just taking the mean to avoid the pseudo replication? I know, and that is clear, I loose some information. However, in my case I am just interested if my two groups are statistically different, with a p-value and an effect size I am happy. I do not need precise calculation of estaimates.
I did not understand where you would have pseudoreplication. You wrote that the 4 measurements were always taken from 4 independent individuals. So averaging these values would mean to disregard relevant information.
Using log(x+1) is common in ecological sciences, but is ia a flawed concept. I would not do this.
The signular fit problem may be caused by the correlation of the random factor with the fixed genotype. Not sure how to slove this. You could try a fixed model considering "genotype" as a fixed factor, too:
glm(dryWeight ~ resLevel + genotype, family = Gamma(log))
The model will fit a separate intercept for each genotype, which may not pay off (and you will see that this model is also over-specified, as not all coefficients can be determined). So another option is to forget about the correlation within genotypes alltogether and fit a simpler fixed model
glm(dryWeight ~ resLevel, family = Gamma(log))
Hard to say... you should actually have theoretical reasons to choose one of these models. If you "let the data decide" you get overoptimistic estimates. So take one (deliberately or not) and stay with it.
In no case there is the need to average the values. But I agree: if all you want is a p-value, it does not matter much (the averages have 1/4 the variance than the single measurements, but you have only 1/4 of the degrees of freedom for the test).
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