$Help structure linear mixed effects model random effects structure$

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$Help structure linear mixed effects model random effects structure$

Nesting random effects models hurts my head.

I want to identify if there is an effect of 1) age, 2) task condition in an eye tracking task on a longitudinal sample.

There are 8 trials with half a pixelated and unpixelated version of 4 videos in the eye tracking task

Task Variables: TrialOrder (Dummy: 0 - 8), Content (Dummy: 0 - 4), Social/Nonsocial (Dummy: 0,1)

Infants came in at different ages over 1 - 6 visits spanning 2 - 50 months

We had about 250 infants with 750 recordings (~ 200 with 500 recording after data quality assurance)

Participant Variable: Age(Continuous), SexM (Dummy: 0,1)

Each recording had an associated data quality measure to ensure effects are not spuriously acocunted for by noise or missing data etc

Data Quality: %ValidData (Continuous), Accuracy (Continuous), Precision (Continuous)

Given it is repeated measures I believe this is required, plus it provides indepedent intercepts for individual...

Saccade Amplitude ~ Age + SexM + TrialOrder + Content + Social/Nonsocial + %ValidData + Accuracy + Precision + (1 | ID)

and if I think participants might have different different slopes

Saccade Amplitude ~ Age + SexM + TrialOrder + Content + Social/Nonsocial + %ValidData + Accuracy + Precision + (age | ID)

Now how do I integrate the multiple trials within a recording?

Saccade Amplitude ~ Age + SexM + TrialOrder + Content + Social/Nonsocial + %ValidData + Accuracy + Precision + (age | ID) + (1 | trials)
Saccade Amplitude ~ Age + SexM + TrialOrder + Content + Social/Nonsocial + %ValidData + Accuracy + Precision + (age + trials | ID)

or... nesting...

uhhhhh....

Saccade Amplitude ~ Age + SexM + TrialOrder + Content + Social/Nonsocial + %ValidData + Accuracy + Precision + (trials | age /ID)

Please also include reasoning on why nesting works... the way it should...

(Im using lme4/glmmTMB in R for my analysis)

Statistics Regression

Esharer

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Kav10

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Low bounty!
- Daniel90
  
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  I second that. The offered bounty is low for the level of the question.

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Kav10

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Low bounty!

Daniel90

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I second that. The offered bounty is low for the level of the question.
Daniel90

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I second that. The offered bounty is low for the level of the question.

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Hi Esharer,

I think you have a good understanding of how to model your data and the models you proposed seem reasonable. You are right that constructing random effects models can be challenging. It was (and still is to some extent) for me too, specifically when there can be multiple levels of nesting. The most important thing is to specify the appropriate random effects structure to account for the non-independence of the data.

In your case, since you have multiple recordings within each trial, I think you need to incorporate trial as a random effect. The first model you proposed, including only (1|trials), assumes that the variance in saccade amplitude is the same across trials, which might not be true. The second model, including (age + trials | ID), is a better choice because it allows for the possibility that different trials may have different effects by adding the trial variable as a random slope. It allows for both random intercepts and random slopes for trials.

Regarding the random effects structure for ID, your first model which includes only (1|ID) assumes that each participant has a different intercept but the same slope across all trials. The second model, including (age | ID), allows for individual differences in the effect of age on saccade amplitude, which may be important if there are individual differences in the rate of development. However, this model assumes that the variance in saccade amplitude is the same across trials within each participant, which might not be true.

In general, when there are multiple levels of non-independence in the data, the nested random effects structure is appropriate. It allows for the estimation of random effects at each level of the hierarchy, which helps to account for the dependence within each level and across levels. Here, nesting trials within participants allows for the estimation of random effects at both the participant and trial levels, which can help to identify individual differences in the effect of trials on saccade amplitude and to account for the non-independence of the data within each participant and across participants.

You need to specify the appropriate random effects structure that allows for the non-independence of the data, to be able to integrate multiple recording within a trial. In this case, since you have repeated measures of saccade amplitude within each recording, you need to include a random effect for recordings nested within trials.

Nesting is used when there is a hierarchical structure to the data, such that lower-level units (e.g. recordings) are nested within higher-level units (e.g. trials) and the effects of the lower-level units are assumed to be constant across the higher-level units.

Therefore, using Recording as a random effect is more appropriate than nesting "age/trials" within "ID".

You can specify the random effect for recordings within trials as a random slope:

Saccade Amplitude ~ Age + SexM + TrialOrder + Content + Social/Nonsocial + %ValidData + Accuracy + Precision + (age | ID) + (1 | Recording) + (Recordings | trials)

In this one, the random effect for Recording allows for individual differences in the overall intercept across recordings, while the random slope for Recording within trials allows for individual differences in the effect of recordings on saccade amplitude within each trial. The fixed effects remain the same as in your models.

The reasoning behind nesting recordings within trials is that the saccade amplitudes measured in each recording within a trial are not independent, because they are measured from the same participant in the same trial. In the proposed models above, by specifying a random effect for Recordings nested within Trials, you can account for the non-independence of the data and obtain more accurate estimates of the fixed effects of interest. This is important for avoiding biased and inefficient estimates of the model parameters and for obtaining valid statistical inferences.

By specifying a nested random effect structure, you can also estimate individual differences in the effects of trials on saccade amplitude within each participant and across participants.

You mentioned you are using lme4 and glmmTMB to do this analysis. To implement the ones I suggested, you can simply include the appropriate syntax for the random effects term in the formula argument of the lme or glm function, respectively.

Here are examples of how you can implement those random effects structure I suggested using lme4 and glmm (assuming you already have installed and loaded the required packages like the lme4).

Replace ??? with the name of your actual data frame containing the variables you want to include in the model.

#Fit the model with recordings nested within trials

model <- glmmTMB(Saccade Amplitude ~ Age + SexM + TrialOrder + Content + Social/Nonsocial + %ValidData + Accuracy + Precision + (age | ID) + (1 | Recording) + (Recording | Trials), data = ???)

To integrate the multiple trials within a recording, you can add a random intercept for trials nested within ID, like this:

Saccade Amplitude ~ Age + SexM + TrialOrder + Content + Social/Nonsocial + %ValidData + Accuracy + Precision + (age | ID) + (1 | ID:trials)

This model allows for the possibility that the effect of trials may vary between infants, which is a way of accounting for the fact that some infants may be more consistent in their performance across trials than others.

Assuming the effect of trials is the same across all infants and that any differences between infants are accounted for by the random intercepts for ID, you could include a random effect of trials, without nesting within ID, like this:

Saccade Amplitude ~ Age + SexM + TrialOrder + Content + Social/Nonsocial + %ValidData + Accuracy + Precision + (age | ID) + (1 | trials)

The choice between nesting and not nesting the random effect of trials depends on the structure of your data and the research question you are trying to answer. If you think that the effect of trials may vary between infants, then nesting is appropriate.

On the other hand, if you believe that the effect of trials is the same for all infants, then it may be more appropriate to not nest the random effect of trials.

Nesting the random effect of trials within ID can also help to account for the correlation between trials within the same infant. This is because trials within the same infant are likely to be more similar to each other than trials from different infants. By nesting the random effect of trials within ID, you are accounting for this correlation and allowing for the possibility that the effect of trials may vary between infants.

Hope this helps.

Kav10

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Esharer

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Hi Kav10, I think you are considering trial/ recording/visit differently than I do. Bob has a visit at 3, 10, 12 month,s with an eye tracking recording at each, consisting of 8 trials Sally has a visit at 12, 18, 24, 32 months... etc Given the variability in age at each visit and number of visits, age is taken to be the analog for visit. Thus wouldnt trial be within age. How would that update your formulae. Thank you.
Esharer

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To clarify, I have "Recording" variable in question originally outlined question. I use the term "trial" to for the 8 elements of a the stimuli presented. "Visits" (not previously mentioned) range from 1 to 6 but occur at vastly different ages such that I believe they are meaningless. "Age" is the quasi visit measure. So am I looking at (trial|age/ID)?
- Esharer
  
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  I *donot* have "Recording" variable in question originally outlined question.
- Esharer
  
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  That is trials nested in age when measures occured within ID.
- Kav10
  
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  My understanding was that trial is different from recording. Meaning that infants are brought to participate in this study, there were multiple trials, within each, there were multiple recordings. I got it from where you mentioned there were 200 infants with 750 recordings.
- Kav10
  
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  Isn’t that correct?
Kav10

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So, trial is different that recording, correct?
- Esharer
  
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  Yes... data would look like Age 3mo Bob, median saccade latency for each ... trial 1,2,3,4,5,6,7,8 Age 5mo Bob, median saccade latency trial for each... 1,2,3,4,5,6,7,8 ... Age 12mo Bob, median saccade latency for each.... trial 1,2,3,4,5,6,7,8 Age 15 mo Sally, median saccade latency for each... trial 1 2 3 4 5 6 7 8 .. .
Kav10

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Where is the recording? How do you show the 750 recordings? Did you mean 750 records instead of recording?
- Esharer
  
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  Yes... records... observations.... 200 babies + 6 visits + lots of missing data = 700 ... observations
- Kav10
  
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  OK, so that was the confusing piece. Observations. I see. For recording, I thought you meant something like video recordings.
Kav10

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If age is serving as the analog for visit and you want to include trials within each age/visit, you can include a random effect for trials nested within age/visit. Here are the two possible model formulations: Saccade Amplitude ~ Age + SexM + TrialOrder + Content + Social/Nonsocial + %ValidData + Accuracy + Precision + (age | ID) + (1 | trials:age:ID)
- Esharer
  
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  I think this is getting closer! You said two possible models and I see one.
- Esharer
  
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  I ask because I still wonder about my proposed (trial| age/ID) which I dont understand exactly how it is different than (1|trial:age:ID). After all we are doing (age|ID)is understood and we are not using (1|age:ID).
- Kav10
  
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  The model (trial|age/ID) would indicate that trials are nested within age and that age is nested within each ID. This is different from the model specification (1|trials:age:ID), which indicates that trials are nested within age, which is nested within ID. Again, the difference between the two model specifications would depend on the structure of your data and the research question you are trying to answer.
- Kav10
  
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  If you believe that trial effects are specific to each age/visit, then (trial|age/ID) would be more appropriate. If you believe that trial effects are constant across age/visit, then (1|trials:age:ID) may be more appropriate. It may be helpful to try out different model specifications and compare their fit and interpretability.
- Esharer
  
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  Thats a helpful breakdown between the two!
- Kav10
  
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  Glad it was helpfulz
Kav10

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Here is the second one: Saccade Amplitude ~ Age + SexM + TrialOrder + Content + Social/Nonsocial + %ValidData + Accuracy + Precision + (age + 1 | ID) + (1 | trials:age)
- Kav10
  
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  Both models include a random intercept for ID and a fixed effect for age, sex, trial order, content, social/nonsocial, and data quality measures. The first model includes a random intercept for trials nested within age/visit and a random slope for age within each individual. The second model includes a random intercept for trials nested within age/visit and a random slope for age and a random intercept for each individual. The R syntax should be very similar to what I provided before.
Esharer

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Thank you for sticking in there with me!
- Kav10
  
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  Of course! I am glad I was able to help.

$Help structure linear mixed effects model random effects structure$

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