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From |
Andrea Bennett <mac.stata@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Mon, 9 Jun 2008 08:47:20 +0200 |

Many thanks for your additional view on this! So, there are two things to do a) think about a plausible reason why or why not dummies should be used (vice versa for the categorical case) and b) test the assumption validity with tests such as Richard Williams has promoted.

Many thanks, this has helped me a lot in getting a feel for the relevant questions/right approach to these kind of variables!

kind regards,

Andrea

On Jun 9, 2008, at 3:13 AM, Austin Nichols wrote:

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:Ch. 9 of Long & Freese's book (see especially pp. 421-422) shows how to

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

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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**References**:**Re: st: RE: Your opinion on income groups and inflation***From:*Andrea Bennett <mac.stata@gmail.com>

**Re: st: RE: Your opinion on income groups and inflation***From:*bmilanovic@worldbank.org

**Re: st: RE: Your opinion on income groups and inflation***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

**Re: st: RE: Your opinion on income groups and inflation***From:*Andrea Bennett <mac.stata@gmail.com>

**Re: st: RE: Your opinion on income groups and inflation***From:*"Austin Nichols" <austinnichols@gmail.com>

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