Dear Ilgim,

I do not understand why the participants are nested within nback conditions. Do you really have repeated measurements for one participant within the same nback condition?  Or do you have for each participant four measurements each under a different nback condition? In the latter case you could use your model 1. But be aware that you don't have a random slope, since nback is categorical (as far as I understand). With this model you assume that the effect of nback on Optode1 varies over the participants. The model also assumes that there is no time effect (i.e. the different levels of nback have been applied in a randomized way). If this is not the case, then you might add time as a covariate.

If you don't think (this can also be tested using e.g. the RLRsim package) that nback has a subject specific effect you could also use the model

lme(fixed = Optode1 ~ NbackType + gender,

method = "ML",

na.action = "na.omit",

random = ~ 1|participant,

data = oxyHb)

The book Linear Mixed Effects Models Using R (see link) would in my opinion be a good reference.

Best, Stephan

http://www.springer.com/de/book/9781461438991

Dear Stephan,

thank you for your detailed explanation. My experimental design is 2(Gender: male & female) * 4(Nback Condition:0,1,2,3).

Each of the participants completed 3 trials and each trial includes four n-back conditions, 0-,1-,2-,3-back. Therefore, in total, each participant had 12 n-back conditions, in a different order. While they were performing n-back task, I have measured their dorsolateral prefrontal cortex via 16-channeled fNIR and obtained oxygenated hemoglobin measures from each of the 16 channels.

I wonder if the oxygenated hemoglobin has changed from 0-back to 3-back in 16 channels, and also wonder whether oxygenated hemoglobin of males and females differ throughout the n-back conditions.

Dear Ilgim,

so you have really several measurements of one participant under the same nback condition. But nevertheless you have observations for each participant under each nback condition. So I would still say the random effect is due the participant and there are no nested effects. There should than also be no time effect since you randomized the treatment (nback) in the different trials. Thus you could work with your model 1 or the  one with the random intercept (I would analyse this using the RLRsim package). You may want to include an interaction effect gender*NbackType if you think that gender has a different effect on Obtode1 given the different levels of NbackType (that's how I would interpret your last sentence).

Best, Stephan

Thank you Stephan,

I will consider your suggestions.

Best regards

Thank you all for your suggestions.

Now, I've changed my model as below. I've included gender interaction and removed Trial. 

Because NbackType is categorical, I've wondered whether it is okey to test random slopes as in my model 1. 

Last but not least, would you share your opinions about how to interpret this random slopes model?

# Random slopes model

• library(lme4)

library(lmerTest)

model1.nbackOpt1 = lmer (Optode1 ~ NbackType * gender +

(NbackType|participant),

na.action = na.exclude,

data=oxyHbConditionCellbyCell,

REML=FALSE)

summary(model1.nbackOpt1)

# Random intercepts model

• library(lme4)

library(lmerTest)

model2.nbackOpt1 = lmer (Optode1 ~ NbackType * gender +

(1|participant:NbackType),

na.action = na.exclude,

data=oxyHbConditionCellbyCell,

REML=FALSE)

summary(model2.nbackOpt1)