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I used Hausman test in R in order to decide whether I should use fixed effects or random effects model. This is the result I got:

Hausman Test

data: Deviation ~ Concentration chisq = 1.721, df = 1, p-value = 0.1896 alternative hypothesis: one model is inconsistent

I would appreciate some help in interpreting this result (I have not studied Statistics ever, and I am yet facing this challenge), and which model should I use - fe or re?

thank you!!

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When the $p$-value is low, commonly less than $0.05$, the $H_0$ must go!

In short the Hausman test (sometimes also called Durbin--Wu--Hausman test) in R assumes $H_{0}$ is that the preferred model is random effects, i.e. no significant correlation vs. the alternative, $H_{a}$, the fixed effects, i.e. whether the errors ($\mu_i$) are correlated with the regressors, see see Section 4.3 in Baltagi (2005).

Running ?plm::phtest in R would give you further details and refrences.

--

Baltagi (2005), Econometric Analysis Of Panel Data

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  • $\begingroup$ Catchy phrase, but not necessarily exhaustive. But granted, without at least some statistics background it will be hard to give a more refined answer. But maybe the original question is not suited for a non-statistical answer. $\endgroup$
    – cherub
    Commented May 25, 2018 at 17:41
  • $\begingroup$ Good points. The answer linked in the comments does provide an exhaustive answer. I mainly wanted to provide something accessible in line with the answer. $\endgroup$
    – uT5r
    Commented May 26, 2018 at 17:30
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Every statistical test has what we call a "null hypothesis" - this is the "default assumption," our starting point. If the test is significant at a given level of confidence (if the p value is small enough) that tells us that we have enough evidence to reject that null hypothesis in favor of some other alternative.

For the Hausman test, the null hypothesis is that the random effects model is OK. In your case the p value is .1896, which is much higher than it would need to be to reject the null at even a pretty lax level of statistical confidence (less than .05 would mean significance at 95% confidence, less than .1 significant at 90% confidence, etc.). So this result is telling you that it does NOT see strong evidence to shift away from a random effects model.

However, the Hausman test doesn't really tell you whether the fixed or random effects models are better. It tells you if the results are significantly different, which in turn would imply that there is some bias in the random effects model that could be addressed by including fixed effects. But there are lots of other reasons why you might want (or need) to use a random effects model even if the Hausman test is significant, see here for more.

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