Multicollinearity in multi level models

[Agustina Malvido]

Dear All,
How can I examine multicollinearity in multilevel models?
all the best,
agustina

[Clyde Schechter]

If you are talking about some kind of test for multicollinearity in a multilevel model, there is no difference between a single-level model and a multi-level model in that regard. Whatever tests you would use following -regress- are equally applicable, conceptually, to a multi-level model. That said, many of those tests as implemented in Stata will not run after any command other than -regress-. But you can just quickly run -regress- on your same variables, and then run your multicollinearity test.

That said, testing for multicollinearity is usually a waste of time anyway. If your model output has acceptably small standard errors for all your variables, then, whether you have multicollinearity in your data or not, you don't have a multicollinearity problem. If only variables whose effect is of no importance to you, but which was included in the model just to reduce confounding, then the fact that the standard error is large is of no importance and you need not spend any time investigating the cause.

If a variable whose effect it is part of your goals to estimate has a large standard error, then you have a problem that might be due to multicollinearity, and that might be worth looking in to. But, unless you are prepared to remove some or all of the variables that are implicated in the multicollinearity from the model, you are just stuck: you have a problem with no solution in the existing data. The only thing you could do in that case is either gather a much larger data set, or start the whole study over with a different sampling design that would break the relationships among the offending variables.

[Agustina Malvido]

Dear Clyde,
thanks for your answer. These are my results, how can I be sure my standard errors are acceptably small?

Linear regression		Number of obs =	5131
	F( 8, 5122) =	329.79
	Prob > F =	0.0000
	R-squared =	0.3433
	Root MSE =	.34127
	Robust
logrealpricehl	Coef.	Std. Err.	t P>t	[95% Conf.	Interval]
realmonthly_av_price_must_hl	-.0001589	.0006371	-0.25 0.803	-.0014079	.00109
red	.4629257	.0096178	48.13 0.000	.4440707	.4817808
ownbrand	.1127598	.0114982	9.81 0.000	.0902184	.1353011
number_wineries_dept	-.0004403	.0001266	-3.48 0.001	-.0006884	-.0001922
sh_vin_under_5ha	-.0043688	.0009148	-4.78 0.000	-.0061622	-.0025755
coop_buyer	-.1262478	.0196122	-6.44 0.000	-.1646961	-.0877995
swyshare_of_wine	-.0003351	.0009619	-0.35 0.728	-.0022208	.0015506
int_coop_sh_wine	.0028522	.0009577	2.98 0.003	.0009747	.0047297
_cons	4.258727	.0371062	114.77 0.000	4.185983	4.331471

thanks again!
agustina

[Clyde Schechter]

Acceptably small means acceptable for the purposes for which you are doing the analysis. So take, for example, coop_buyer,which, among the predictor variables has the highest standard error. That standard error is 0.0196122. Its coefficient has a point estimate of -0.1262478. The 95% CI is from -.1646961 to -0.0877995. So the question is, is that degree of precision in estimating the effect of coop_buyer on your outcome sufficient for your purposes. Do you need to know that effect more precisely than that? Or is that good enough? Does it matter that you can't, for example, have much confidence in asserting that it isn't really, say, -.156 instead of -.126? If that's a problem, then your standard errors are not small enough. But if you don't care about that level of difference, then they are fine.

If that's good enough, then there is no problem. If you need an estimate that's more precise, then you have to think about getting more data, or using a different design to or better measurements to sharpen the estimates. The same considerations apply to each of the variables in the model. The question to ask yourself is: is this estimate of the effect of this variable sufficiently precise to be useful for whatever purpose this analysis is intended to serve. (And remember that if a variable is included solely to control for its possible effects as a confounder, then the precision of its effect estimate is not important in any case.) Is there some important consequence if the actual effects differ from the estimated coefficients by amounts that are comfortably inside my confidence intervals? If so, my standard errors are too wide. If not, they're fine.

[Agustina Malvido]

Thanks Clyde for a very clear explanation...I will think about the questions you pose.