I was wondering if you could help me figure out how to do an ANOVA that has a random effect. I have a dataset that comes from a split-brood experiment. The study is looking at whether different diets impact the development time within a species of caterpillar. Development time is considered the number of days between hatching and pupation. The egg masses of 10 females were collected, and each egg mass was split into thirds. The three sections of each egg mass were dispersed into one of three treatment groups: Diet A, Diet B, and Diet C. The diets remained the same for each treatment group from hatching until pupation. The development time was recorded for each individual caterpillar.
So, the way I understand this is a simple one-way anova won't account for possible genetic variation between egg masses that could impact development time (like a block design study). So it seems like egg mass is a random factor, while diet type is a fixed factor, and development time is the dependent variable. I'm not sure how to account for the random factor when carrying out an ANOVA in r. It is also worth noting that not all individuals survived until pupation; therefore the data is not equally divided among or within egg masses. Do you have any suggestions?
Hi Sarah,
Firstly, could you clarify whether your response variable is measured in whole days (whole/integer numbers) or fractions/decimals of days (real values, e.g., 2.5 days, 3.75 days...)?
This will help you choose the most appropriate error distribution family for your test (e.g., Poisson for whole days, Normal for fractions), but I'd recommend looking up Generalized Linear Mixed Models (rather than ANOVA - although ANOVA is a special case of GLM) in this case. The 'mixed' part lets you know you can mix fixed and random effects in the same model.
Ben Bolker has a very nice introductory paper (Bolker et al 2009, TREE) that's well worth reading.
There is a 'glmm' function (and various others) available for R http://ugrad.stat.ubc.ca/R/library/repeated/html/glmm.html, but it's not in the base package. A little web searching will send you in the right direction.
Good luck!
Hi Sarah,
Firstly, could you clarify whether your response variable is measured in whole days (whole/integer numbers) or fractions/decimals of days (real values, e.g., 2.5 days, 3.75 days...)?
This will help you choose the most appropriate error distribution family for your test (e.g., Poisson for whole days, Normal for fractions), but I'd recommend looking up Generalized Linear Mixed Models (rather than ANOVA - although ANOVA is a special case of GLM) in this case. The 'mixed' part lets you know you can mix fixed and random effects in the same model.
Ben Bolker has a very nice introductory paper (Bolker et al 2009, TREE) that's well worth reading.
There is a 'glmm' function (and various others) available for R http://ugrad.stat.ubc.ca/R/library/repeated/html/glmm.html, but it's not in the base package. A little web searching will send you in the right direction.
Good luck!
IIn the case of normality to test hypotheses about fixed parameters or variances in mixed model (regular or balansed) see my and cooperators papers the exact tests are given. Using R program you can simply use standard algebraic procedures to calculate estimators or construct tests
I agree with the above that the mixed (i.e., multilevel, hierarchical, ...) approach is preferred, but sometimes that can seem daunting for those used to the ANOVA world. The linked website is good for this.
http://personality-project.org/r/r.anova.html
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