[Gretl-users] Re: split dependent variable: looking for a test
Hi Allin,
Your logic sounds similar to that of the PE Test (MacKinnon, White & Davidson, 1983, J
of Econometrics) for comparing models with y vs log(y). I hadn't heard about it until
a couple weeks ago while I was teaching about LM tests. Here's a link to the R
petest() function:
https://www.rdocumentation.org/packages/lmtest/versions/0.9-38/topics/petest.
Cheers,
Peter
-----Original Message-----
From: Allin Cottrell <cottrell(a)wfu.edu>
Sent: Monday, November 30, 2020 5:35 PM
To: Gretl users <gretl-users(a)gretlml.univpm.it>
Subject: [Gretl-users] split dependent variable: looking for a test
This question is not gretl-specific, but answers might show up gretl features and
hopefully it may be of interest.
My dependent variable is the quantity demanded of a certain good, an hourly time series
extending over two years. It exhibits strong seasonality, both by hour of the day and
season of the year; it has an upward trend; and it's clearly affected by various
measures of weather (temperature, humidity, wind speed). Plain OLS produces quite a decent
fit, but by inspecting the loglikelihood-for-level figure produced by gretl (via the
Jacobian) I can see that taking the log of the dependent variable gives a better fit. All
fine.
However, total demand is the sum of demand from two classes of consumer -- call them A and
B -- and I'm wondering if a better fit can be obtained by summing the fitted values
from separate regressions, with dependent variables the demand from consumers A and B
respectively. (Note: a Chow test in dummy variable mode is not applicable, the unit of
observation is the hour, not the
transaction.)
My thought was: compute two SSRs in levels, using (restricted) the exponentiated fitted
values from the overall model and
(unrestricted) the sum of the exponentiated fitted values from the two consumer-class
models, then calculate an F test based on the difference of SSRs in the usual way.
Questions: Does this sound valid? Is there a better way of doing it?
[I'm aware of debate over how best to produce predictions of levels from log-linear
regression, but I'm not sure quite how it applies in this case.]
Allin Cottrell
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