"CR1" Formula

[wviechtb]

Shouldn't the adjustment factor for "CR1" be m / (m - p), where m is the number of clusters and p the rank of the model matrix (instead of m / (m - 1))? This would be analogous to 'HC1'. See, for example, MacKinnon and White (1985).

[jepusto]

We use the definition from Cameron and Miller (2015, p. 9). There's not a clear right answer even for very simple cases because the degree of bias depends on whether the predictors are identified within each cluster or between clusters:

• If you've got all between-cluster predictors (no within-cluster variation), then m / (m - p) will be a closer approximation.
• If the predictor of interest is identified within each cluster, then the CRVE is roughly the sample variance of the cluster-specific slope estimates, in which case m / (m - 1) will be a closer approximation.

But I think the take-away is clear: CR1 (either version) doesn't account for the fact that the degree of bias adjustment depends on the structure of the predictors. Better to use CR2, which takes these features into account, instead.

[wviechtb]

I agree that CR2 is better. I was just comparing results from clubSandwich with robust() from metafor, where I use m / (m - p) by default. One can set adjust = "Stata2", which then uses m / (m - 1), but this is currently undocumented (and adjust = "Stata1" which is the same as CR1S, but see issue #23). Would you mind adding m / (m - p) as another option (as CR1<?>)?

[jepusto]

I guess I could add "CR1p" that uses the factor m / (m - p). Is the rationale just compatibility/comparability with metafor?

…

Sent from my iPhone

On Aug 17, 2017, at 4:24 PM, Wolfgang Viechtbauer ***@***.***> wrote: I agree that CR2 is better. I was just comparing results from clubSandwich with robust() from metafor, where I use m / (m - p) by default. One can set adjust = "Stata2", which then uses m / (m - 1), but this is currently undocumented (and adjust = "Stata1" which is the same as CR1S, but see issue #23). Would you mind adding m / (m - p) as another option (as CR1<?>)? — You are receiving this because you commented. Reply to this email directly, view it on GitHub, or mute the thread.

[wviechtb]

Is the rationale just compatibility/comparability with metafor?

Indeed. Thanks for considering.