R help - Apr 2007 - 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

	[[alternative HTML version deleted]]

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
> 
> 	[[alternative HTML version deleted]]
> 
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