[R] Fitting multinomial response in structural equation

[John Fox]

Dear adschai,

I'm not sure that I entirely follow what you want to do, but if the response
really is qualitative I don't see the sense in transforming it into a single
quantitative variable. Nor does the strategy of generating 24 dichotomous,
separately modelled responses make sense, since these are correlated. In
some circumstances, however, one can resolve a polytomous response into a
set of *nested* dichotomies, which are then independent of one another.
Finally, I wouldn't as a general matter recommend fitting any statistical
model to a 24-category response.

I suspect that you'd do well to find someone with whom you can about your
research problem.

Regards,
 John

--------------------------------
John Fox, Professor
Department of Sociology
McMaster University
Hamilton, Ontario
Canada L8S 4M4
905-525-9140x23604
http://socserv.mcmaster.ca/jfox 
-------------------------------- 

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of 
> adschai at optonline.net
> Sent: Saturday, April 21, 2007 4:32 PM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Fitting multinomial response in structural equation
> 
> Hi - I am confronting a situation where I have a set of 
> structural equation and one or two of my responses are 
> multinomial. I understand that sem would not deal with the 
> unordered response. So I am thinking of the following two ways:
> 
> 1. Expanding my response to a new set of binary variables 
> corresponding to each label of my multinomial response. Then 
> use each of these as a separate response in my model. 
> However, since I have about 24 labels in this single 
> variable, it will be very expensive to do this way.
> 2. I am thinking of transforming this variable into a 
> continous-valued variable. I am thinking of using the 
> observed count to transform this variable using the probit 
> function. Then my new variable is just a step-wise function. 
> The trouble that I am struggling with is that this response 
> variable will also serve as a predictor in another equation 
> in my structural model. The interpretation of this equation 
> is not so straightforward for me. The coefficient of this 
> variable is no longer reading 'a unit change in this variable 
> holding everything else fixed corresponds to the x unit 
> change of the response'. All I can read from this method is 
> that when I change from one label to another, it means p 
> amount change in my step-wise-function predictor variable and 
> it corresponds to x unit change of the response holding 
> everything fixed.
> 
> The main purpose here for myself to post my question here is 
> to obtain your insight especially with respect to using sem 
> with the two approaches above. I would like to ensure that my 
> approaches make sense within the context of sem. Any 
> comments/opinions would be really appreciated. Thank you so 
> much in advance.
> 
> - adschai
> 
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