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In an experiment with 5 technicians from different companies, we investigated effects of new equipments. The interested response variable is categorical.

One thing I am considering is that the technician effect is a random effect. But it's hard to include a random effect in the multinomial logistic model. If there is not much difference, I would enter the effect as a fixed effect. So my question:

How bad is considering a random effect as a fixed effect?

From my old statistics class, I can see variability of response variable will be underestimated because of the true random effect and thus might affect statistical tests in the model. But I am not sure how bad it will be.

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  • $\begingroup$ you can quantify the 'how much' by experimenting on simulated data $\endgroup$ – user603 Mar 12 '13 at 17:12
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Doug Bates (author of R package lme4) writes in his unpublished book (available online) that 6 levels are the minimum number required for obtaining reasonable estimates of variance components. By treating the technician effect as fixed, one loses the interpretation of the regression generalizing to a population of technicians. The strict interpretation is that the regression applies only to those samples. So you have a trade-off between these ideas. Also note that PROC GLIMMIX in SAS will fit multinomial models with random effects.

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    $\begingroup$ Thanks for your answer. So in my case, even if I I enter the random effect in my model, generalizing the model to a population of technicians will not be "reasonable" anyway. I guess I will have to stick to the fixed effect model. $\endgroup$ – Tae-Sung Shin Mar 13 '13 at 2:54

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