Timeline for What is the lme4::lmer equivalent of a three-way repeated measures ANOVA?
Current License: CC BY-SA 3.0
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| Jun 19, 2017 at 12:16 | comment | added | amoeba | Given @JakeWestfall's last comment, this answer seems to be wrong, hence -1. I don't have access to Kirk's book and cannot double-check myself, but Masato's answer clearly contradicts the standard advice, see e.g. here dwoll.de/rexrepos/posts/anovaMixed.html. | |
| Nov 4, 2014 at 3:31 | comment | added | Jake Westfall | I have the 2nd edition of Kirk, where I believe the relevant discussion is on pp. 443-449, which discusses a two-way (not three-way) example. Expected mean squares, either assuming additivity of A and B or not, are given on p. 447. Assuming A and B are fixed and subjects/blocks are random, we can see from the expected mean squares listed by Kirk under "non-additive model" that tests of A, B, and AB each involve different error terms, namely, the relevant interactions with block/subject. The same principle extends to the present three-way example. | |
| Oct 2, 2014 at 20:50 | comment | added | Henrik |
Unfortunately I just moved cities and my Kirk is still in one of the moving boxes which I haven't yet opened (and are supposed to go to the uni) so it will take some time. However, the dfs are probably not the way to go. If you test those using my afex::mixed (which I obviously prefer) you will see that for the last lmer example they match the ANOVA. However, the F values are still different.
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| Oct 2, 2014 at 20:39 | comment | added | Masato Nakazawa |
I'm curious to know what you think of Kirk's chapter. I think the chapter number in the 2nd ed. is different. Meanwhile I'll try to fit different lmer models. The best way to check the model fit is to check their dfs using lmerTest because the K-R approximation is supposed to give you exact dfs and hence p-values.
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| Oct 2, 2014 at 20:27 | comment | added | Henrik |
Let's sidestep this question for the moment and assume that the model I fitted would be the correct model. How would you fit this using lmer? I will nevertheless get my copy of Kirk (2nd edition only) and see what it says.
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| Oct 2, 2014 at 20:12 | comment | added | Masato Nakazawa |
Actually how they do it is incorrect. If you have a fully crossed factorial repeated measures design (or randomized block factorial design), you should get only 1 error term, aside from subject, for all effects (i.e., Within). See Experimental Design: Procedures for Behavioral Sciences (2013) by Kirk, chapter 10 (p.458) or my post here
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| Oct 2, 2014 at 20:02 | comment | added | Henrik | They are fixed effects. However, the ANOVA model you fit is not the model that seems to be the classical repeated measures ANOVA model, see e.g., here. See the Error strata in your and my case. | |
| Oct 2, 2014 at 19:58 | history | answered | Masato Nakazawa | CC BY-SA 3.0 |