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I am trying to fit a 3 level random and crossed effects model to a continuous outcome to estimate the respective variance components of each level of the 3 (for doctors)

  • Level 3: Physicians ID
  • Level 2: Patient's ID
  • Level 1: stage ( 1 and 2)

For this study, each doctors have predicted the mortality rate for all the patients in two times. Thus clinician and patient is crossed effect and patient and stage is nested ( I think).

I presumed that Physicians id is crossed with patient and patient is nested with stage.

I tried the crossed random effects model for this data

Model1:

xtmixed  mortality_est || doctorsid:R. patient|| doctorsid:R.stage

Model2:

xtmixed  mortality_est || doctorsid:R. patient|| doctorsid:R. stage|| patient:

xtmixed  mortality_est ||stage:||doctorsid:R.patient||z:, variance

but did not converge

Any suggestion will be very appreciated.

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    $\begingroup$ What is the size and structure of your data? $\endgroup$
    – Michael R. Chernick
    Commented Sep 12, 2012 at 10:56
  • $\begingroup$ There are nine doctors and 9 patients. Each doctor see each patient and predicted the mortality rate.This is repeated measures at 2 times (stage 1 and stage2). Thus crossed effect for doctors and patient and nested effect for patients and stage(not sure). Any advice would be much appreciated. $\endgroup$
    – mohana
    Commented Sep 13, 2012 at 5:25

1 Answer 1

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It is difficult to expect that you can fit a nice normal distribution to 9 points, and that's what you are trying to achieve with the doctors and patients. Now, fitting a normal distribution with 2 points for stage is just impossible. I think Stata may not even be able to identify the variance parameter for stage here. You have to model that as a fixed effect. I would go as far as to say that you would want to treat everything as fixed effects, and just run

anova mortality_est doctorsid patient stage

To me, is an example where the complicated model is unnecessary (the perfect is the enemy of the good), and whoever is forcing you to fit the multilevel model to this data must be pretty evil (reviewer, adviser, instructor...).

If your ultimate goal is some sort of doctors' ICC or interrater agreement something, then I could see the point of the exercise, but again with just 9 observations, your variance component estimate will be woefully unstable, and effectively your CI for the ICC would look like (-0.1,0.8) or something like that. In the best case scenario of homoskedastic normal data, it is a (scaled) chi-square with 7 degrees of freedom (I think), so it has a mean of 7, a variance of 14, a standard deviation of 3.74, skewness of 1.07, and an excess kurtosis of 1.71; few statisticians would be happy to bet their publications on a $\chi^2_7$. In the worst case with doctor-patient interactions and heteroskedasticity, you may end up with something closer to chi-square with 1 or 2 d.f., and that isn't something you can really work with as a variance estimate.

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  • $\begingroup$ Thank you very much StasK. Finally I ended up the anova cammand and completed the analysis. $\endgroup$
    – mohana
    Commented Sep 20, 2012 at 4:33

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