Reference category
Message/Author
 David James posted on Thursday, December 17, 2015 - 10:21 pm
Hi Mplus team,

I have a question in regards to multiple regression modelling:

When completing the multiple regression model, Mplus considers the last option as the reference alternative. Parameters are then expressed relative to that alternative.

However, I am not sure how you define the model if you want to also know the parameters of the last option

For example, if you have the utility functions:

U1 = Alt1 + B1 x Z1 + B2 x Z2
U2 = Alt2 + B3 x Z3 + B4 x Z4
U3 = B5 x Z5 + B6 x Z6

U3 will be the reference model and B1,B2,B3,B4 will be defined in reference to U3.

How do you therefore determine B5 and B6?

Thank you for your assistance.

David
 Bengt O. Muthen posted on Friday, December 18, 2015 - 5:44 pm
Are you thinking about multinomial logistic regression?
 David James posted on Saturday, December 19, 2015 - 2:17 am
Hi Mr Muthen,

Yes, i am trying to complete a multinomial logistic regression model.

Is there a way to determine the parameters of the reference alternatives?

Any help would be much appreciated.

Thank you

David
 Bengt O. Muthen posted on Sunday, December 20, 2015 - 5:22 pm
All the coefficients for the last category are zero, not only the intercept but also the slopes. See multinomial logistic regression at the end of Chapter 14 in our UG.
 David James posted on Sunday, December 20, 2015 - 6:46 pm
Thank you for your quick response. I really appreciate the assistance.

I have read chapter 14 and am aware that the last category will be set to zero.

However, if this is the case, how do you determine the slopes of coefficients in the last category??

Thanks again for all your assistance.

David
 Bengt O. Muthen posted on Monday, December 21, 2015 - 6:32 pm
The slopes in the last category are zero. This is all because the multinomial model models log odds, that is, the log of the ratio of a prob for one category versus the last. As the plot on page 497 shows that doesn't mean that the probability of the last category doesn't change with x; it does.

You can change which category comes last.
 David James posted on Wednesday, December 23, 2015 - 12:36 am
Thank you for the help and guidance. I really appreciate it!!

Another way I have seen this tackled is by expressing the utilities of the other choice options as differences with respect to the last alternative’s utility. This involves making the parameters of the last choice option enters all other utility functions with the opposite sign by specifying the required linear constraint.

For example:
!Multinomial logit model
U#1 ON Z1;
U#1 ON Z2;
U#1 ON (-Z5) (1);
U#1 ON (-Z6) (2);

U#2 ON Z3;
U#2 ON Z4;
U#2 ON (-Z5) (1);
U#2 ON (-Z6) (2);

[U#1 U#2]; !alternative-specific constants

What do you think about this approach? Do you foresee any issues.

Thanks again.

David
 Bengt O. Muthen posted on Thursday, December 24, 2015 - 6:13 pm
I'm afraid I am not familiar with working with utility functions and such differences. I wonder if someone on SEMNET would be. Or an econometrics list.