When ICC was proposed, its assumed that the measurements are independent or it's necessary to be? (to apply correctly the icc)
Do you have any idea how to measure what is loss if you apply the ICC to dependent data?
What is your opinion about this?
I haven't found any reference about that...
Regards,
Paulo
To put it in another way, no independence assumption is required to obtain a point estimate of the ICC. However, if you want to do a hypothesis test (eg. whether the ICC is 0) or want to obtain the standard error of the estimate, independence assumption may be required, depending on what test or standard error formula you are using. If the test/standard error formula requires independence, and the data are not, the inference will be faulty. The amount of error will again depend on what you are trying to do and how the data actually are. If you provide a specific example of what is the dependence structure of the data and what inference you are trying to make, I can probably give an idea about how "wrong" you can be.
Dear Pratyaydipta Rudra
thanks for your interest, could you please take a read at here? https://www.researchgate.net/post/Which_ICC_should_be_used
I am using ICC(3,1)
Will prepare a specific example.
Paulo, for your problem, you should use a modified model rather than directly using ICC(3,1) unless you are just looking at the point estimate. The model will be very similar to equation (2) in the Shrout and Fleiss paper. Just that x and e will have one more subscript t for time. eg. xijt will now mean observation on jth subject at time t as measured by the ith machine. If you don't understand this, I suggest you to look up and read a little bit about mixed effects models.
The point estimate will be same for the modified model. But the confidence interval may not be. I have to spend more time on this to say what it would exactly be. If you just want to look at your point estimate of ICC and interpret it in terms of proportion of variance explained, you don't need to worry about that.
P.S. - I am assuming that this data doesn't have a time effect. However, I am not very familiar with such data. If you believe that there might be a time effect (trend or periodic effect), the best strategy would be to remove it using some time series method prior to computing ICC. If it's just a linear trend, that can be accommodated in the model too, again, without affecting the point estimate of ICC.
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