repeated-measures linear mixed-effect model

Question

I have two soil treatments: CT and NT.

For each treatment, I have 11 CO2 measurements taken in 7 times, i.e. 11 "replicates" for 7 dates.

I'd like to evaluate if the measurements are different in time for the two treatments.

I have:

• replicates(11)=random factor;
• days=repeated measure factor (fixed factor)
• treatment = between subject factor (fixed factor)
• CO2 = Co2 emission measures (=dependent variable)

Is it correct to consider this as a nested two-level repeated measures ANOVA?

Is it correct to use the following R syntax?

m1 <- lmer(CO2~days*treatment+(days|replicates),mydata) 

Is this a random intercept and slope model with replicates nested in treatment?

Is it correct to say that this model accounts for:

• the main effect of treatment and time and
• the interaction between the two?

What would be the difference between m1 and m2?

m2 <- lmer(CO2~days*treatment+(1|replicates),mydata)

Answer 1

Is it correct to consider this as a nested two-level repeated measures ANOVA?

No, it is a linear mixed effects model.

Is it correct to use the following R syntax?

m1 <- lmer(CO2~days*treatment+(days|replicates),mydata)

It is correct if you wish to account for clustering, ie repeated measures, within each replicate, and allow the slope of days to vary between replicates.

Is this a random intercept and slope model with replicates nested in treatment?

It is a random intercept and slope model, but observations are nested within replicates.

Is it correct to say that this model accounts for:

• the main effect of treatment and time and
• the interaction between the two?

Yes, these are modeled as fixed effects.

What would be the difference between m1 and m2?

m2 <- lmer(CO2~days*treatment+(1|replicates),mydata)

m2 is a random intercept model, it accounts for clustering (repeated measures) but the slopes, are assumed to be constant for east replicate. m1 allows the slope for days to vary between clusters (replicates in your case).