I conducted a full 3x2x2 (W1,W2,W3) within design with every participant experiencing the same 12 conditions. Within each condition, there were several measurements of my outcome variable(outcome). Additionally, I want to include a covariate (covariate) in my model that was measured as on the same level as my outcome, i.e. several times within each condition.
I set up the model using nlme(following Field, Miles, & Field, 2012; chapter 13):
Model_lme <-lme(outcome ~ W1 + W2 + W3 + W1:W2 + W1:W3 + W2:W3 + W1:W2:W3 + covariate ,
random = ~covariate|Subject/W1/W2/W3, data = data,control = list(opt = "optim"), method = "ML")
And using lme4
Model_lme4 <- lmer(outcome ~ W1*W2*W3 + covariate + (1 + covariate|Subject/W1:W2:W3),
data=data, REML=FALSE)
I would be very grateful if someone could answer the following questions:
1) Are these model really equivalent? I'm not sure about the Lme4 approach right now.
2) When comparing the models without the covariate, I find a significant effect of W2. After introducing the covariate, this main effect is no longer present. Is it then fine to state that the main effect of W2 was explained by the significant covariate?
3) Finally, I am also not sure how to report my model. As I understand, the models describe my data as follows: W1, W2, and W3 are nested within participants. These factors have random intercepts (meaning that there is an intercept for each condition within each participant), but no random slopes. The covariate is a factor with random intercept and slope.
Is that the way how to describe in a paper? It rather seems like papers only state whether something was handled a fixed or random effect (e.g. Jainta, Blythe, Nikolova, Jones,& Liversedge, 2015, p. 121)
I know these are many questions, but currently I am still really puzzled about mixed models, even though I read and try to understand every literature I can get regarding this topic.
Thanks in advance for your answers!
(W1*W2*W3 + covariate | Subject)random term. You can try but this is a lot of random effects to fit, and you might not have enough data to fit this reliably. So you can simplify, e.g.(W1 + W2 + W3 + covariate | Subject), or with||. What you have is an even further simplification(1 + covariate | Subject) + (1 + covariate | Subject:W1:W2:W3). $\endgroup$(1|subject) + (1|a:subject) + (1|b:subject) + (1|c:subject) + (1|a:b:subject) + (1|a:c:subject) + (1|b:c:subject) + (1|a:b:c:subject)... It's tricky to reproduce this kind of anova with lmer exactly, it might be easier to adopt the mixed model style of thinking ant put w1/w2/w3 to the left of the vertical bar. $\endgroup$