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

 From "Austin Nichols" To statalist@hsphsun2.harvard.edu Subject Re: st: RE: Your opinion on income groups and inflation Date Sun, 8 Jun 2008 21:13:47 -0400

```Andrea--
I strongly disagree with Martin Weiss, SamL, and Branko milanovic who
claim that an ordered categorical explanatory variable can be included
as a sensible regressor without justification.  Creating dummies *is*
justifiable; you are merely computing conditional means.  Including
income (or "trust") as a single explanatory variable when income (or
"trust") is measured as an ordered categorical explanatory variable
requires a strong assumption that the effect is linear in the index of
categories.  The dummy variable approach requires no such assumption.
As Richard Williams quite rightly points out, you can -test- whether
the effect is linear in the index, or whether groups of individual
dummies all have the same effect.  One useful way is to create dummies
that correspond to more interpretable groups, like above the median,
more than twice the median, less than half the median, etc. so you can
see directly from the regression output where deviations from
linearity occur...  graphs are also helpful for this purpose.

On Sun, Jun 8, 2008 at 4:14 AM, Andrea Bennett <mac.stata@gmail.com> wrote:
> Many thanks for this revealing illustration of tests! I will clearly look
> into this...
>
> Kind regards,
>
> Andrea
>
>
> On Jun 7, 2008, at 9:58 PM, Richard Williams wrote:
>
>> At 02:42 PM 6/7/2008, bmilanovic@worldbank.org 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
>>
>> http://www.stata.com/bookstore/regmodcdvs.html
>>
>> 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
>> WWW:    http://www.nd.edu/~rwilliam
>>
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