<p>In short, because AIC takes the log of the max value of the likelihood function.  Except under strong conditions there is no <em>a priori</em> reason to assume that these values will be the same after log-transforming your model.  In fact, <em>a priori</em> one should assume they will not be the same, since one of the reasons people log-transform their models is to change the sample distribution to be a little closer to normal.</p>

<p>So, you can't simply look at the two AIC values and conclude that they convey the same information, because in general, they do not.</p>

CC BY-SA 4.0
2020-01-27T16:43:16.727Z
2020-01-27T16:43:16.727Z
heh
<p>I have a time series dataset on UK consumption. I can
(1) estimate an exponential trend 
(2) take the logarithm of UK consumption, estimate a linear trend for this logarithm, and exponentiate the result
Why cannot I compare AIC values from these two methods?</p>

<econometrics>
Why cannot I compare AIC values obtained from nonlinear least squares and the ordinary least squares?
Alex Wang
# Why cannot I compare AIC values obtained from nonlinear least squares and the ordinary least squares?

(Asked by: username_0 on 2020-01-27)

I have a time series dataset on UK consumption. I can
(1) estimate an exponential trend
(2) take the logarithm of UK consumption, estimate a linear trend for this logarithm, and exponentiate the result
Why cannot I compare AIC values from these two methods?

**Tags:** econometrics


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## 1 answers

### Answer by username_1 on 2020-01-27. Score: 4 | Accepted answer

In short, because AIC takes the log of the max value of the likelihood function. Except under strong conditions there is no *a priori* reason to assume that these values will be the same after log-transforming your model. In fact, *a priori* one should assume they will not be the same, since one of the reasons people log-transform their models is to change the sample distribution to be a little closer to normal.

So, you can't simply look at the two AIC values and conclude that they convey the same information, because in general, they do not.


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