Estimating Individual Random Effects

[Eddie Oczkowski]

I am interested in estimating and testing for the significance of individual random effects (u_i). I understand that u_i can be estimated after a xtreg (with re) and using predict (with the u option). I also understand that the model assumes that u_i is iid with a constant variance (sigma_u_2). I wish to test the individual significance of each u_i. In constructing the t-ratio I assume it will be (u_i/sigma_u) where the u_i comes from predict and sigma_u is generated as part of the xtreg (re) output. I hope this is sensible?

My lack of understanding now starts. If u_i is iid then in large enough samples it will be niid (normal) with a standard error of sigma_u. We know in a normal distribution that only a small fraction of observations fall outside of the 95% range +/- 1.96(sigma_u). Now the fact then we use sigma_u in generating the t-ratio for testing does this mean only 5% of estimated u_i will be significantly different from zero at the 5% level, and this holds in all cases for RE individual predictions in large enough samples?

Any explaining references or applications would be appreciated.

I am not sure that what I wish to do makes any sense at all?

Regards, Eddie

[Jorge Eduardo Perez Perez]

Testing for significance of random effects doesn't make sense. Random effects are realizations of a random variable, they're not parameters.

[Eddie Oczkowski]

Thanks Jorge. How do we know if a realisation is large?

[Eddie Oczkowski]

Hi All,

After a bit more reading I now understand the notion that the individual prediction from random effects are just relaziations of a random variable, but I am still interested to know what constitutes a large (from the mean of zero) individual random effect. I suppose it comes down to its practical importance? I am hard pressed to find many examples which present predictions for individual random effects and discuss their practical meaning.

Any references to examples of the presentation of predictions for individual random effects would be appreciated?

Regards, Eddie

[Jorge Eduardo Perez Perez]

Maybe the literature about standardized and studentized residuals would be useful. I have not seen these used in the context of random effects regressions, but they may help.

[Joshua D Merfeld]

Jorge is right. However, is it at all possible that what you are interested in testing is whether random effects is appropriate (as opposed to OLS)?

[Eddie Oczkowski]

Hi Joshua,

Thanks for your post. My interest is in predicting the actual individual effects from a random effects model. What I am after is some interpretation of what constitutes a large individual predicted individual effect. For example would one standard error from the the mean of zero for the RE prediction be considered large? I am trying to find some literature or previous practice examples for this.

Cheers, Eddie