An ANOVA should yield the same results as a generalized linear mixed model.

see e.g.:

https://stats.stackexchange.com/questions/289226/what-are-the-differences-between-anovas-and-glms

or

https://www.isixsigma.com/topic/two-way-anova-vs-glm/

Thank you for your reply Dear Jos Feys

It's been very helpful. I think, mine is a balanced case with two independent variables (time and treatment), far from being a complex design. So, I can use two way repeated measures instead of GLM, and it will be just fine. I understand that now.

Note, you've provided me some useful information about R codes on https://stats.stackexchange.com/questions/289226/what-are-the-differences-between-anovas-and-glms

I cannot understand clearly the example mentioned there. So, I' just tried to run the following chunk in R, but error comes out saying "non-numeric argument to binary operator". As far as I know, R knows how to apply a binary operator for a numeric variable. So, I think I've missed something about this example. I think I've missed the main point but just focused on a detail. Maybe I think the example about color contrasts over there may have been shared as an analogy as to what differs between ANOVAs and GLMs in principle.

m1

Maybe the R script in attachment can help.

Thank you for your time and help Dr. Jos Feys

I've just opened the data and run a series of simulations with different means, standard deviations and sample sizes through rnorm() function. Now, I understand the difference better. As far as I understand, we can say that an ANOVA is a kind of analysis depending on a linear regression. I mean an ANOVA is a special case of GLM. That's all. Thank you for sharing it. It helps a lot.

I note that some replies have cited GLM (general linear model) rather than Linear Mixed Effects (LMM) model. I notice that in very simple situations--for example when there is just on factor (a repeated-measures factor) and no missing observations, repeated-measured ANOVA and and LMM give the same results. However, if I have a design consisting of two repeated-measures factors, I typically get an LMM result that is only an approximation to the repeated-measures ANOVA result. Some tutorials indicate that we shouldn't expect the same results for the two types of analysis. See https://gamlj.github.io/mixed_example2.html

Richard Anderson

Thank you for your reply!

In my experiments,the experimental setup was like that: There was only one dependent variable (drug treatment) needed to be measured and compared across the groups. We measured this variable at 4 different time points which were consecutive. The in vivo animal experiments have already been completed. During the experiments, a few animals from each group died as a virtue of severe diabetic symptoms, so, as you understand, the sample size of any group differed from another. There were 5 groups. After the deaths, some of the groups consisted of 8 animals, some of the others did 10 or 9 animals. In this case, I think I need to perform linear mixed model not a repeated measure ANOVA, because sample sizes are different and data are unbalanced. Could we think this way?

First, it is fine to do repeated-measures ANOVA for the design you just described--that is, one continuous dependent variable and two factors: time (a repeated-measures factor) and group ( a non-repeated-measures factor). It does not matter that the group sizes are different. Second, as I mentioned previously, you could restructure your data a do an LMM instead, but you would not necessarily get the same p value. I only get the same p value in simple situations in which there is is just one factor (the repeated-measures factor), not two ( see https://gamlj.github.io/mixed_example2.html ).

Richard Anderson Cinar Furkan Ilhan

Thank you for your answer Richard Anderson, it was very helpfull.

I and one of my colleagues, Cinar, not only have been reading materials on variation analysis, repeated measures, and mixed models, but been following threads, asking questions and trying to learn new approaches related to statistics for almost three years.

We would like to be keeping in touch with you! Your contribution is greatly appreciated!