[R] Systems of equations in glm?

[John Fox]

Dear Paul and David,

As far as I'm aware, the closest that you'll come to this model currently 
in R is the sem or tsls function in the sem package, both of which assume 
quantitative endogenous variables, however.

Several specialized structural-equations programs (e.g., LISREL) will fit 
models of this form, with an approach very close to David's suggestion, 
based on polychoric and point-polyserial correlations. The calis procedure 
in SAS won't do this; I'm not sure about Stata.

I've been thinking about adding this kind of capability to the sem package, 
but don't know if I'll do it.

I hope that this helps,
  John

At 06:02 PM 5/30/2002 +0100, David Firth wrote:
>On Thursday, May 30, 2002, Paul Johnson wrote:
>
>>
>>I have a student that I'm encouraging to use R rather than SAS or Stata 
>>and within just 2 weeks he has come up with a question that stumps me.
>>
>>What does a person do about endogeneity in generalized linear models?
>>
>>Suppose Y1 and Y2 are 5 category ordinal dependent variables.  I see that 
>>MASS has polr for estimation of models like that, as long as they are 
>>independent. But what if the models were to be written:
>>
>>   Y1.plr <- polr(Y1 ~ Y2 + X1 + X2)
>>
>>   Y2.plr <- polr(Y2 ~ Y1 + X3 + X4)
>>
>>Are estimates of the coefficients for Y1 and Y2 biased, as they would be 
>>in a linear model?  I think yes. Do I need some equivalent of 2SLS or FIML?
>
>yes and yes, I believe.  I presume that you *really* have in mind that Y1 
>and Y2 are imperfect (ie, categorized) observations of underlying 
>continuous variables (Z1 and Z2, say)?  And that the equations whose 
>coefficients you'd really like to estimate are (in your R style)
>
>  lm(Z1 ~ Z2 + X1 + X2)
>  lm(Z2 ~ Z1 + X1 + X2)
>
>-- in which case the likelihood, assuming bivariate normality of (Z1,Z2) 
>given (X1,X2), involves bivariate normal integrals evaluated over 
>rectangles with boundaries determined by category threshold parameters.
>
>I don't think this (ie, maximization of that likelihood) is programmed at 
>present in R.  From what you say, I infer that it's not in Stata or SAS either?
>
>A sensible first analysis might be simply to forget that Y1 and Y2 are 
>multinomial, and fit the linear system using some suitable set(s) of 
>numeric scores for the categories.  Depending on the results, that might 
>also be a sensible last analysis...
>
>Regards,
>David
>
>>It is not entirely clear to me if, in this example, the input Y1 or Y2 is 
>>conceptualized as the 5 point scale or rather if it is thought of as a 
>>continuous variable which is observed with error.
>>
>>Is there an email list besides r-help where I should be asking questions 
>>like this? I understand it is not strictly R related and would gladly go 
>>bother other people than you if you tell me where.

-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox
-----------------------------------------------------

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