I am having difficulty deciding the best way to control for covariates in my analysis in my within-subject experiment. I want to identify the effects of Time on brain activity and control for some covariates. I have four conditions of interest (Time1, Time2, Time3, and Time4) and three nuisance covariates (Confidence, Response Time, and Accuracy). The covariates change as a function of Time. That is why they are nuisances.

I have determined that 3dLME would be ideal for this analysis. In this case, the covariates (which vary across my conditions of interest) will be included in order to look for changes in brain activity as a function of Time (4 conditions) independent of the effects of the covariates. This analysis would control for the covariates at the level of the conditions and not at the trial level.

I am also wondering if an amplitude modulated 3dDeconvolve analysis offers a possibility of controlling for the nuisance covariates at the trial level. In this case, I would create 4 stim files, one for each condition of interest. Then I would marry the three covariates to each trial for each condition. In this case, each condition would produce 4 outputs: the unmodulated effect, the effect modulated by Confidence, the effect modulated by Response Time, and the effect modulated by Accuracy.

In this case, does the unmodulated effect I would obtain for each condition of interest represent the effect while controlling for the nuisance covariates? If so, maybe I don’t need to turn to LME to analyze these data. Or does the unmodulated effect represent the effect for each condition while ignoring the nuisance covariates (i.e. pretending they had not been included in the model).

If the former is true, I am wondering whether you would recommend 3dLME or an amplitude modulated analysis for these data.

If you simply model the modulation effect at the trial level, the first effect (you call it the “unmodulated effect”) is the estimated brain response of that subject associated with the average value of the modulation variable. However, that average value of each variable (e.g., Confidence) still varies across subjects; so, when you go to the group level, you would still have to handle those “covariates”.

To bypass the thorny issue, do this:

Obtain the overall mean for each condition across all subjects for each of the four variables (Confidence, Response Time, and Accuracy);

Subtract the original values by the overall mean for each of the four variables from 1);

Create the four modulation regressors for each condition yourself by using the values from 2) (the reason for this step is that 3dDeconvolve automatically removes the within-subject mean when generating the modulation regressor);

Stick the regressors from 3) in 3dDeconvolve;

Perform group analysis with a one-way within-subject ANOVA with the “unmodulated effects”.

One more point for one of the covariates. The covariate called Accuracy is actually a binary number when considering the trial data: 1 = correct and 0 = incorrect. In that case, would you proceed the same way to subtract the group mean for each condition of interest (i.e. Time1, Time2, Time3, and Time4)? For example, if the average accuracy for Time 1 across all participants is 88.7% correct, then would I subtract 88.7 from a 1 or a 0, depending whether the trial was correct or incorrect, respectively. Something seems weird about this approach with a binary variable.

The covariate called Accuracy is actually a binary number when considering the trial data: 1 = correct and 0 = incorrect.
In that case, would you proceed the same way to subtract the group mean for each condition of interest (i.e. Time1, Time2,
Time3, and Time4)? For example, if the average accuracy for Time 1 across all participants is 88.7% correct, then would
I subtract 88.7 from a 1 or a 0, depending whether the trial was correct or incorrect, respectively. Something seems weird
about this approach with a binary variable.

How would you like to interpret your group analysis results with regard to Accuracy: associated with 1) the correct trials, 2) incorrect trials, or 3) some sort of average between correct and incorrect trials?

For 1) (and 2)), it’s better to just separate those trials into two separate regressors, one for correct and the other for incorrect ones. For 3), one possibility (not as weird as your example) is to code them with 1 and -1, respectively, and set the mean to 0.

Because accuracy is one of these nuisance covariates, I would like to interpret the brain activity associated with the 4 time periods without the confound of accuracy. That is, accuracy decreases across the four conditions of interest (Time1, Time2, Time3, and Time4). However, I want to detect brain activity that changes with TIme, where the changes do not simply reflect the concomitant changes in accuracy (or confidence or response time).

I also wanted to mention that two of my participants do not have accuracy data, so I am reluctant to analyze correct and incorrect trials separately because I will not be able to include them in the analysis.

So, would it be best to handle the continuous nuisance variables (confidence and response time) at the trial level using amplitude modulated regressors and then handle the binary nuisance variable (accuracy) at the group level using 3dLME? Note that accuracy becomes a continuous measure when it is calculated for each condition of interest (e.g., Time1= 90% correct, Time2= 80% correct, Time3 = 70% correct and Time4=60% correct).

Or should I simply use 3dLME to handle all of the nuisance variables and forget the amplitude-modulated approach?

The situation for Accuracy is indeed a little tricky: each trial is either correct or incorrect, so, if you want to handle the situation at the trial level, you would essentially have to model with two types of trials (correct and incorrect) separately. If you make the assumption that the average response across the trials for each subject is proportional to their accuracy, then handle the accuracy variability at the group level by using the accuracy percentage as a covariate in 3dLME (centering accuracy within each condition).

Or should I simply use 3dLME to handle all of the nuisance variables and forget the amplitude-modulated approach?

That should be fine since you would have to deal with accuracy at the group level anyway.

I am working with Christine on these data and we have a question about how to interpret AM2 regressors that were put into a LME. I modified what you suggested above to modulate rt and confidence at the trial level, and accuracy at the group level in a LME.

Obtain the overall mean for each condition (Hour, Day, Week, Month) across all subjects for each of the two variables (Confidence, Response Time);

Subtract the overall mean for each condition (Hour, Day, Week, Month) from the original number for each variable within condition (Confidence, Response Time)

Create the four modulation (Hour, Day, Week, Month) regressors for each condition yourself by using the values from 2) (the reason for this step is that 3dDeconvolve automatically removes the within-subject mean when generating the modulation regressor) [i]

Stick the regressors from 3) in 3dDeconvolve

Q1: Are three regressors made separately? 1) modulated activity 2) activity tracking rt 3) activity tracking confidence Q2 Is it possible to run an F test on regressor 2 (i.e. activity that ONLY tracks rt) and 3 separately (i.e. activity that ONLY tracks confidence)

Q3: Does LME only use the 1) modulated activity regressors for F-tests? And is there a way to run an F test with regressors type 2 and 3 separately?

Q4: We are looking at subbrick #2, which is the Cond F-test with AM2 regressors. The significant clusters represent regions that do not track or change with behavior. Is this a correct interpretation?

Q1: Are three regressors made separately? 1) modulated activity 2) activity tracking rt 3) activity tracking confidence

Yes, the three separate regressors represent the modulation effects of three covariates.

Q2 Is it possible to run an F test on regressor 2 (i.e. activity that ONLY tracks rt) and 3 separately (i.e. activity that ONLY tracks confidence)

I assume you’re referring to the subject level analysis. For each condition, you have 4 regressors: one for the condition effect with the three covariates controlled at their center values. By “regressor 2”, do you mean the modulation effect of “RT”? If so, 3dDeconvolve/3dREMLfit should automatically output the statistic value in the output with option -tout or -fout.

Q3: Does LME only use the 1) modulated activity regressors for F-tests? And is there a way to run an F test with regressors type 2 and 3 separately?

Not sure what you mean by “modulated activity regressors”. Which beta coefficients are you feeding into 3dLME?

Q4: We are looking at subbrick #2, which is the Cond F-test with AM2 regressors. The significant clusters represent
regions that do not track or change with behavior. Is this a correct interpretation?

I’m lost since I don’t see a variable ‘Cond’ in your 3dLME script above. And which beta coefficients did you provide to 3dLME?

Q3: Does LME only use the 1) modulated activity regressors for F-tests? And is there a way to run an F test with regressors type 2 and 3 separately? >>Not sure what you mean by “modulated activity regressors”. Which beta coefficients are you feeding into 3dLME?

Previously you had mentioned that three regressors are made when using AM2 1) activation without the effects of rt and confidence 2) RT 3) confidence)

Would it be possible to run an F test on either regressor 2 (representing activation only associated with RT) or regressor 3 (representing activation only associate with confidence)

Q4: We are looking at subbrick #2, which is the Cond F-test with AM2 regressors. The significant clusters represent
regions that do not track or change with behavior. Is this a correct interpretation?

I’m lost since I don’t see a variable ‘Cond’ in your 3dLME script above. And which beta coefficients did you provide to 3dLME?

Sorry I fixed the model. I provided the amplitude modulated regressors to 3dLME.

Would it be possible to run an F test on either regressor 2 (representing activation only associated with RT)
or regressor 3 (representing activation only associate with confidence)

Are you referring to the individual- or population-level analysis? You also have 4 conditions, so F-test about the modulation effect under one particular condition or across the 4 conditions?

Q4: We are looking at subbrick #2, which is the Cond F-test with AM2 regressors. The significant clusters represent
regions that do not track or change with behavior. Is this a correct interpretation?

Which AM2 regressors? If it’s the RT (or confidence) effect, then the F-test shows the statistical evidence for the differences of the RT (or confidence) effect across the 4 conditions. You may add -gltCode to further parse the specifics of the statistical evidence through post hoc tests.

Would it be possible to run an F test on either regressor 2 (representing activation only associated with RT)
or regressor 3 (representing activation only associate with confidence)

Are you referring to the individual- or population-level analysis? You also have 4 conditions, so F-test about the modulation effect under one particular condition or across the 4 conditions?

I am referring to a population-level analysis across the 4 conditions.

Thank you so much for answering all of my questions.

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