Solved – Boxplot with glme

boxplotrrepeated measures

I am examining the difference between a physical feature of different species of animals. Due to the nature of my experiments I'm using a nonlinear mixed model with the following setup:

lme(log10(feature) ~ log10(Body.mass) + factor(Trial.Number), random = ~1 | IndividualID, data=animals, subset=Frfactor=="low", na.action=na.omit )

where subset=Frfactor=="low" refers to a specific speed range that I'm interested in.

I get great results which I'm happy about. But now I want to see how species affects my feature. Since the same conditions apply (tons of repeated effects) I've kept the lme and changed the structure to:

lme(log10(feature) ~ specfactor + factor(Trial.Number), random = ~1 | IndividualID, data=animals, subset=Frfactor=="low", na.action=na.omit )

where specfactor lists the names of the species. Looking at the p values it looks like these species are not significantly different from the intercept (which is specfactorserval). However when I create a boxplot, it certainly looks like there are some big interspecies differences!

I guess because the lme is a test for regressions, it doesn't really make sense to use when comparing the feature against categorical variables. But I still need to account for repeated effects. My question is if there's a better way to test for significance between species using the boxplot? I need the usual- p-values, confidence intervals. The "list" command seems to fall short of such comparisons. I don't know if a t-test would cut it.

Thanks!

PS I originally posted an image of my test results and of the boxplot, but I'm too new of a user to be allowed….

Best Answer

Your model (I think) is using the same slopes for all species, and perhaps this is why the boxplots look different.

If the feature shows an allometric reln with the body mass, then there are various possible models about that relationship varies with species and individuals within a species. Species in different groups (eg Reptiles vs mammals vs birds) might share a relationship (= slope) but they could also be in different size ranges.

I think you should add body mass to the second model and test for interaction terms between species and bodywt.

Related Solutions

R – How to Specify Mixed ANOVA with Multiple Repeated Measures and Covariate in R

First of all, you really need to make sure, that adding a covariate makes any sense. Adding a covariate only makes sense, if the covariate is not correlated with the independent variable (i.e., if there is no a priori reason to assume that being in either of the pretrain or trainign conditions affects study). To make sure to you really understand this I highly recommend reading the following brief paper:

Miller, G. A., & Chapman, J. P. (2001). Misunderstanding analysis of covariance. Journal of Abnormal Psychology, 110(1), 40–48. doi:10.1037/0021-843X.110.1.40

Then to run the ANOVA and compare it with an ANOCVA, you can use aov.car or ez.glm from afex (disclaimer: I am the author of afex), as in the following:

require(afex)
#ANOVA
ez.glm("subjid", "accuracy", D, within=c("section","probtype"), 
       between= c("pretrain","training"))

#ANCOVA
ez.glm("subjid", "accuracy", D, within=c("section","probtype"), 
       between= c("pretrain","training"), covariate= "study",
       factorize = FALSE)

A few more things to note:

Your covariate is not centered on 0, this makes afex throw a warning. As it is not in a between-subjects interaction, you should be able to safely ignore that.
You need to set factorize = FALSE when including a numerical covariate as the default behavior of ez.glm and aov.car is to automatically factorize all variables.
The results from ezANOVA with between_covariate should be very similar, however, the last time I checked, the calculation of the df was wrong (ezANOVA, does incorrectly not use one df per numerical covariate, rather covariates do not change the df).
Probably, ANOVA is NOT the correct tool for your analysis. You should definitely read the following excellent paper on why accuracy shouldn't be analyzed with ANOVA:
Jaeger, T. F. (2008). Categorical data analysis: Away from ANOVAs (transformation or not) and towards logit mixed models. Journal of Memory and Language, 59(4), 434–446. doi:10.1016/j.jml.2007.11.007

Solved – Interpreting a significant 2-way interaction with post-hoc tests

Pooling across the remaining group was correct. You don't need anymore tests. Take choice 1. Your interaction means the effect of difficulty (hard - easy) in controls is different from the effect of difficulty in clinical. Since what it means is exactly what you want to know a post hoc is completely unnecessary.

You might want to see Gelman and Stern (2006) for a lesson in why the path you were thinking of taking with post hocs was faulty logic.

Gelman, A., & Stern, H. (2006). The difference between “significant” and “not significant” is not itself statistically significant. The American Statistician, 60(4), 328-331. doi: 10.1198/000313006X152649

Some general information might help others in the same situation. There seems to be a broadly accepted mistaken belief that there must be a significant simple effect when you have a significant interaction. Not only is this false but there is no guarantee of any significant simple effect in an ANOVA with more than 2 levels (in which case it's just an alternative to a t-test). Interactions are about differences among differences. None of the individual differences needs to be significant, or even close to significant, for a significant interaction. Consider a situation where one effect is +5 and another is -5. The difference between those effects is 10, which is much larger than either simple effect. Therefore, it would be very easy to not have a significant simple effect of 5 but a significant interaction of 10.

With something as simple as a 2x2 designs one should never perform a post hoc on the interaction because the interaction told you all of the necessary information. Even with slightly more complex designs post hoc tests are usually unnecessary, especially when one variable only has 2 levels. People generally do far too many post hoc tests following ANOVAs. In school they tell you to do an ANOVA to avoid multiple comparison problems. Of what benefit is that when, after you perform the ANOVA, you perform a bunch of comparisons? Interpret the ANOVA first.

Best Answer

Related Solutions

R – How to Specify Mixed ANOVA with Multiple Repeated Measures and Covariate in R

Solved – Interpreting a significant 2-way interaction with post-hoc tests

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