Multilevel Linear Modelling Help

[freofan]

Hi,

I'm hoping someone with expertise with MLM/HLM etc might be able to help me. I recently conducted a transmission chain study looking at the impact of mood on production. The study involved participants reading a story and reproducing this story for another person. The second person read the first person's story and reproduced it for a third person and so on until 4 person transmission chains were formed (much like a game of chinese whispers). Half my chains were exposed to a positive mood induction prior to completing the task and half were exposed to a negative mood induction. What I am primarily interested in is the number of positive and negative statements produced by people in the chains. So my model has three levels - person, which is nested within chain, which is nested within mood induction condition. I know I can run this model using MLM. My first question is: Is mood a fixed effect here, as each person within a chain experienced the same mood induction?

The second question I have is more complex. I also took a measure of trait anxiety for each participant. So, within any given chain the trait anxiety of each participant will be different to that of the other members of that chain. I'm interested in the effect of trait anxiety on production and also if this interacts with mood. The hypothesis being that individuals with higher trait anxiety will produce fewer positive/more negative statements under the negative mood induction condition. The question is: is it possible to enter trait anxiety into the model? If so, would this be considered a random effect?

I would greatly appreciate any help with this problem.

Regards,
Keely

 

[CB]

So my model has three levels - person, which is nested within chain, which is nested within mood induction condition.

It sounds like you are thinking of including a random effect for chain (or more specifically, an intercept that randomly varies across chains). That makes intuitive sense, but may not fully deal with the dependence structure in the data. What's affecting a given person's score on the DV isn't so much the chain they're in so much as simply the story told by the person before them in the chain. So you may be looking for something like an AR(1) model within chain, which can be fit using MLM/mixed models.

Is mood a fixed effect here, as each person within a chain experienced the same mood induction?

Yes. I would hate to try and describe what the difference is between a random effect and a fixed effect, because I'd fail miserably, but generally an experimental manipulation is treated as a fixed effect.

is it possible to enter trait anxiety into the model? If so, would this be considered a random effect?

I'm not quite sure how this model would be specified, but hopefully someone else will have an idea!

 

[freofan]

Thanks CowboyBear. What exactly is an AR(1) model? Sorry, I'm new to MLM/mixed models having come from a predominantly ANOVA background.

 

[freofan]

I found what AR(1) is in a stats book. Thanks for the tip. I think you are right. If anyone knows how I could treat trait anxiety in my model I would very much appreciate the help.

 

[Jake]

freofan, you seem to be confused about the fixed vs. random distinction. In the classical ANOVA framework we would look at each factor and say "is this factor fixed or random?" But that's not really how things work in multilevel models, or rather, it's not how we think about things in this newer framework. In multilevel models, we have predictor variables (mood, anxiety) and grouping variables (subjects, chains). The predictor variables all have a fixed component--always, all the time, without question--and in addition they may or may not have a random component that varies across one or more of the grouping factors. So to your first question, "is mood a fixed effect," I would rephrase this as: should my model allow the effect of mood to vary randomly across subjects or chains (in addition to of course being in the fixed part of the model), OR should it not vary randomly across either of the grouping factors, in which case it is only in the fixed part of the model? And the answer is the latter, chains are nested in mood so we cannot estimate a random effect of mood across chains.

The question is: is it possible to enter trait anxiety into the model? If so, would this be considered a random effect?

Yes, it is possible. In addition to being in the fixed part of the model, anxiety can vary randomly across chains but not across participants.

 

[freofan]

Thanks Jake, that's very helpful.

Yes, it is possible. In addition to being in the fixed part of the model, anxiety can vary randomly across chains but not across participants.

From what you've said it sounds like I can't have a trait anxiety score for each participant and include this in the model. I could only include trait anxiety in the model if I had a single trait score for the whole chain? The analogy that keeps presenting itself is that my participants could be considered time points in a repeated measures design. From what you've said it's not possible to have a predictor that is measured at each time point (or each participant). Is that correct?

Would I therefore have to run separate models for each time point to see if trait anxiety predicts participants scores at each point in the chain?

 

[Jake]

... Is that correct?

No. I said:

Yes, it is possible.

You CAN include trait anxiety in the model. Furthermore, you can estimate random slopes for the anxiety predictor across chains. (But not across participants, because you would need to have multiple anxiety scores from each participant to do that.) You do NOT have to run separate models for each time point like you suggested.