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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