I'm dealing with compositional data (data that sum to 1). They are inherently multivariate. One way to analyse compositional data is with a ilr (isometric log-ratio) transformation. I'm following the procedure described here and here.
After an ilr transformation, it is suggested that we can uses traditional ANOVA or MANOVA analysis. I'm more interested in linear mixed models since I'm doing this for other variables. However, there is no clear explanation on how to perform a multivariate model with lme4 (lmer).
Reading online, I came across the following help : From StackExchange, on Rpubs and on github.
However, the explanations are unclear for people who are new to complex statistical analysis. Normally, I would create my model using lme4 and analyze it more traditionally with lmeTest and emmeans. With the help that I've found online, however, I cannot go through the classic MANOVA/ANOVA/PostHoc process. In other words ... I don't understand ''what's next''.
Here is some information about my design. 25 participants 5 trials/condition 2x2x3 design Realized(oui, non) - between subjects FB(GoodFB, ErroneousFB, NoFB) - Within subjects Feet(FT, FA) - Within subjects Compositional variable with 4 level that sum to 1 (these are frequency band contributions) Med, Low, VL, UL
I did some tests following the github procedure and I arrived at a point where I just ... don't know what to do anymore. Note, these are with the raw data, not the ilr transform. One thing at the time ! --> Yes I know, there is a warning. Model probably too complex.
Linear mixed model fit by REML ['lmerModLmerTest']
Formula: Value ~ Bande:(FB * Feet * Realized) + (Bande - 1 | Trial) +
(Bande - 1 | Participant)
Data: Wavelet2
REML criterion at convergence: 23617.9
Random effects:
Groups Name Std.Dev. Corr
Participant BandeLow 4.03193
BandeMed 2.92682 0.58
BandeUL 6.67916 -0.85 -0.66
BandeVL 3.45339 -0.05 -0.27 -0.36
Trial BandeLow 0.56382
BandeMed 0.38568 1.00
BandeUL 1.01499 -1.00 -1.00
BandeVL 0.04408 1.00 1.00 -1.00
Residual 12.76134
Number of obs: 2988, groups: Participant, 25; Trial, 5
Fixed Effects:
(Intercept) BandeLow:FBErroneousFB
18.4113 10.8568
BandeMed:FBErroneousFB BandeUL:FBErroneousFB
-6.7167 20.0527
BandeVL:FBErroneousFB BandeLow:FBGoodFB
1.4899 12.0116
BandeMed:FBGoodFB BandeUL:FBGoodFB
-7.4437 18.4319
BandeVL:FBGoodFB BandeLow:FBNoFB
2.7916 11.8681
BandeMed:FBNoFB BandeUL:FBNoFB
-5.4416 19.2281
BandeLow:FeetFT BandeMed:FeetFT
-0.7688 -5.1311
BandeUL:FeetFT BandeVL:FeetFT
-5.2262 11.6565
BandeLow:Realizedoui BandeMed:Realizedoui
-2.6386 -2.2251
BandeUL:Realizedoui BandeVL:Realizedoui
6.1435 -0.9827
BandeLow:FBGoodFB:FeetFT BandeMed:FBGoodFB:FeetFT
0.5580 1.4025
BandeUL:FBGoodFB:FeetFT BandeVL:FBGoodFB:FeetFT
0.6047 -2.6751
BandeLow:FBNoFB:FeetFT BandeMed:FBNoFB:FeetFT
-4.9176 -1.0432
BandeUL:FBNoFB:FeetFT BandeVL:FBNoFB:FeetFT
7.2515 -1.2547
BandeLow:FBGoodFB:Realizedoui BandeMed:FBGoodFB:Realizedoui
7.3775 12.4733
BandeUL:FBGoodFB:Realizedoui BandeVL:FBGoodFB:Realizedoui
-14.5717 -5.6681
BandeLow:FBNoFB:Realizedoui BandeMed:FBNoFB:Realizedoui
3.5385 5.1612
BandeUL:FBNoFB:Realizedoui BandeVL:FBNoFB:Realizedoui
-7.4511 -1.5036
BandeLow:FeetFT:Realizedoui BandeMed:FeetFT:Realizedoui
1.0658 3.3089
BandeUL:FeetFT:Realizedoui BandeVL:FeetFT:Realizedoui
1.6401 -6.3232
BandeLow:FBGoodFB:FeetFT:Realizedoui BandeMed:FBGoodFB:FeetFT:Realizedoui
1.4889 -10.8614
BandeUL:FBGoodFB:FeetFT:Realizedoui BandeVL:FBGoodFB:FeetFT:Realizedoui
4.0406 5.6913
BandeLow:FBNoFB:FeetFT:Realizedoui BandeMed:FBNoFB:FeetFT:Realizedoui
-1.5140 -6.8196
BandeUL:FBNoFB:FeetFT:Realizedoui BandeVL:FBNoFB:FeetFT:Realizedoui
2.0001 6.5935
fit warnings:
fixed-effect model matrix is rank deficient so dropping 1 column /
coefficient
optimizer (nloptwrap) convergence code: 0 (OK) ; 0 optimizer
warnings; 1 lme4 warnings
Now that I've done that, and I see coorelation ... what's the next step ? Is there a way to write/correct the model to perform further post-hoc analysis like I would do in a traditional MANOVA ? Should I just let it go and perform multiples lmer models for each of the composition (which will be ilr transformed in the future).
Any insight will be much appreciated !
