Re: st: heteroskedasticity in ordered probit model

[Richard Williams <richardwilliams.ndu@gmail.com>]

At 06:25 AM 12/23/2012, John Stymans wrote:
> Dear Statalist Users,
> I have a problem with heteroskedasticity in an oprobit model.
> I am using Stata 12.
> I am new to econometrics and Stata, however I would like to estimate 
> an equation with following set-up (number of observations are around 200) ;
> Dependent variable (y) is ordered (0-no, 1- sometimes, 2- a lot) 
> over 2 countries, so I use a country dummy as independent variable. 
> Other independent variables are: size, budget, service, R&D.
> Given the dependent I used an ordered probit model.
> Setup in Stata is the following: oprobit y size budget service R&D 
> country dummy
> Yet literature (e.g. Cameron and Trivedi (2009) Microeconometrics 
> Using  Stata, chapter 14 page 455) says the above model has a 
> weakness: heteroskedasticity. So I decided to test this and I 
> compared the model with one including a heteroskedasticity term. 
> This term included budget. A Likelihood ratio test confirmed the 
> presence of heteroskedasticy as did a Wald test.
> Setup in Stata: oglm y size budget service R&D country dummy, 
> link(probit) het(budget)
> When comparing results, I noticed that 2 terms which are not 
> significant in the first equation without heteroskedasticity term 
> are actually significant in the equation with heteroskedasticity 
> term. Is this possible: can heteroskedasticity affect the 
> significance of variables, or is something else going on?

See section 4.4 of 
http://www.stata-journal.com/article.html?article=st0208. The first 
paragraph of that section states

"In many types of analyses, it often makes little difference whether 
z tests or Wald tests or likelihood-ratio chi-squared tests are used 
to test hypotheses about individual coefficients. It is important to 
realize that this is often not the case with heterogeneous
choice models. In particular, seemingly trivial changes in the coding 
of variables used in the variance equation can change the hypotheses 
that z tests or Wald tests of coefficients in the choice equation 
address. In brief, z tests of individual coefficients in the choice
equation are conditional on the coding of the variables in the 
variance equation, while likelihood-ratio tests are not."

If you don't have access to the Stata Journal, an earlier working 
paper version is available at

http://www.nd.edu/~rwilliam/oglm/oglm_Stata.pdf

In short, you should use LR tests, not Wald tests, to test the 
coefficients in the choice equation.

Consider too if there are ways to make the hetero go away. The next 
section of that piece shows how adding a squared term to the model 
made a variance equation unnecessary. In your case, it might make 
sense to add budget^2. Life is much simpler if you don't have to add 
a variance equation to the model.

> In a second step I would like to run a Mont Carlo simulation (I will 
> have to figure this out, any advice on how to run such a thing is 
> greatly appreciated) with a similar setup and check the above. Is 
> this possible, can I use a Monte Carlo simulation to check if 
> heteroskedasticity influences the significance of variables?
> There is a lot of literature on the effect of heteroskedasticity on 
> size of determinants (which often uses Monte Carlo simulations), yet 
> I did not find any using Monte Carlo to check the significance (can 
> however be my fault).
> Many thanks in advance and best regards,
> JOhn
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-------------------------------------------
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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