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i have ultrasound data measuring strain of myocardium as the dependant variable. Now i want to compare reliability and agreement of the measurement system between the 2 methods, the test retest and the difference between observers. i am using a LMM to calculate repeatability coeff (2.77 * within patient SD) and ICC (within pat SD / (within pat SD + between pat SD).

I have several factors : patient (1-40), observors (1,2), Method (1,2), scanner (1,2). I am not completely sure how to model this, i know from what i read that the patient should be the random clustering variable, but if seems if i am to calculate ICC and RC's above i have to have observer as a random factor to proportion the variance. does anyone have experience with this type of model? enter image description here

K S
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    It sounds like you might want crossed random effects, for patient and observer. Does this [this](https://stats.stackexchange.com/questions/228800/crossed-vs-nested-random-effects-how-do-they-differ-and-how-are-they-specified) help ? – Robert Long Oct 06 '20 at 08:57
  • thanks for the answer btw! Yeah that is what i was thinking as well, but i started trialling a few things and the best model i come up with is all random factors , and just a fixed intercept. is this even possible? – K S Oct 06 '20 at 10:36
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    No problem. It wasn't an answer, just a comment, as there isn't enough information about your data yet. When fitting random intercepts you need to ensure there are enough levels of each factor (6 as a minimum, is a good rule of thumb). Perhaps you can include more info about your study and data (e.g. by including the output of `str(data)`).What do you mean "all random factors" and what do you mean by "best model" ? – Robert Long Oct 06 '20 at 10:42
  • I am using jamovi btw which is lme4 based. So i mean the largest r2 and the lowest AIC/BIC to indicate model fit, but im not sure if this is appropriate either. so i have the patient as a random factor/ grouping variable, plus the observer and scanner also as random effects. this is based on 2 separate models for each method. so my longitudinal data headers are : Patient,Scanner, Obs, GLS AFI,GLS 2DS. – K S Oct 06 '20 at 11:21
  • OK but how many levels of observer and scanner do you have ? – Robert Long Oct 06 '20 at 11:23
  • 2 scanners, 2 different observors, and there is about 40 patients. – K S Oct 06 '20 at 11:33
  • And you are fitting random intercepts for scanner and observer ? – Robert Long Oct 06 '20 at 11:33
  • this is what the r call looks like for one method: gls 2ds ~ 1 + scanner.+( 1 + Observer. | Patient. ). i think the patient is the intercept, – K S Oct 06 '20 at 11:38
  • So what did you mean by *"the best model i come up with is **all random factors**"* – Robert Long Oct 06 '20 at 11:40
  • sorry that was the wrong model : this one , Gls afi ~ 1 +( 1 + Observer. + scanner. | Patient. ) – K S Oct 06 '20 at 11:45

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