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Re: st: RE: Your opinion on income groups and inflation

From   Richard Williams <>
Subject   Re: st: RE: Your opinion on income groups and inflation
Date   Sat, 07 Jun 2008 15:58:47 -0400

At 02:42 PM 6/7/2008, wrote:
On income groups (intervals), I would not use dummies because you have
information about income _levels_  which would be otherwise lost. An income
interval of 300 to 400, is not the same thing as an income interval of 1200 to
3600. Since you do not have information about distribution of income within
Ch. 9 of Long & Freese's book (see especially pp. 421-422) shows how to test whether treating an ordinal variable as interval loses information. Basically, you run an unconstrained model where the ordinal variable is broken up into dummies, and then run a constrained model where you treat the ordinal variable as continuous. If the difference is not significant, then treating the var as continuous is ok. I imagine you can tweak this a bit, e.g. assigning midpoints or whatever to the categories of the variable.

For info on the book, see

Here is an example:

sysuse auto
reg price rep78
est store constrained
xi: reg price i.rep78
est store unconstrained
lrtest constrained unconstrained

The output from the last part is

. lrtest constrained unconstrained

Likelihood-ratio test LR chi2(3) = 1.00
(Assumption: constrained nested in unconstrained) Prob > chi2 = 0.8002

This is kind of a crummy example because the N is so small and the relationship so weak; but in any event the test says it is ok to treat rep78 as continuous.

You can also set it up as a Wald test, which may be handy in situations where a LR test is inappropriate. If the X variable has k categories, then include X and k-2 of the dummies computed from X, and then test the dummies. e.g.

tab1 rep78, gen(rep)
reg price rep78 rep3 rep4 rep5
test rep3 rep4 rep5

The last command gives

. test rep3 rep4 rep5

( 1) rep3 = 0
( 2) rep4 = 0
( 3) rep5 = 0

F( 3, 64) = 0.31
Prob > F = 0.8160

This sort of thing is also useful if, say, your X variable is continuous (e.g. education) but you suspect its effects are not strictly linear (a year of college has a different effect than a year of grade school).

Now, if the N is large, you may well find that the dummy variable approach always comes out ahead. At that point, you may wish to consider substantive significance (just how much do the effects differ from straight linearity?) or consider some other criteria for assessing significance that are less affected by sample size, e.g. a BIC test. There is a lot to be said for parsimony.

Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME: (574)289-5227
EMAIL: Richard.A.Williams.5@ND.Edu

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