# regression in Mplus : comparison between all dummy variables using model test

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#### !Stat

##### Guest
Hello there,

I want to do a logistic regression using the Mplus software. One of my independent variable is a nominal variable with 4 categories (thus 3 dummy variables). In my case, there is no particular reason to favor one reference group over another. Thus, I would like to be able to make a comparison between all categories.

In the UCLA website http://www.ats.ucla.edu/stat/mplus/dae/logit.htm, it is stated that we can do so by using the model test option in mplus. So, assuming that I have three dummy variables (var1 var2 and var3 omitting the reference group - var0), the syntax looks like this if I want to compare var1 with var2

VD ON
var1(v1)
var2 (v2)
var3 (v3);

Model test:
v1 = v2;

I could then do the same thing for v1 = v3, and v2 = v3.

My questions are:

1- Do I have to use a more conservative p-value if I do all these comparisons, or I can stay with the traditional 0.05? Is it a good way to make comparison between all dummy variables?

2- Could I do the same thing for other types of regression (linear, ordinal and multinomial)?

#### Lazar

##### Phineas Packard
You can have an omnibus test and univariate tests as follows:
Code:
Model Test:
v1 = v2;
v2 = v3;
v1 = v3; ! produces a single omnibus wald test
Model Constraint:
new(contrast1-contrast3);
contrast1 = v1 - v2; ! the degree to which v1 is different from v2
contrast2 = v2 - v3;! and so on
contrast3 = v1 - v3;
The omnibus test will be called the wald test in the output and will be where the fit indices are. The univariate tests will be at the end of standadized results section.

1. Provided the wald test is significant you can check all univariate tests without adjusting p-values
2. Yes for sure you can use this method to compare regression weights

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#### !Stat

##### Guest

Just one quick follow-up question:

Does that mean that if the wald test is > 0.05, I can't consider any univariate analysis, including the comparison with the reference group (var0) ?

#### Lazar

##### Phineas Packard
That is kind of up to you. Personally I would have just looked at the model constraint output (but see my signature). However another way to check everything is to run the model you have then run a model with the only change being:

Code:
VD ON
var1@0
var2@0
var3@0
and use a chi-square difference test on the fit of the two models. If this is significant go ahead and use the reference group results and the model constraint parameters.

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#### !Stat

##### Guest
Thank you!

I have other questions, if you don’t mind

Now for multinomial logistic regression, it seems a little more complicated to use the constraint command (I’m not even sure that it is possible).

So, since the constraint in the logistic model (if I understand correctly) is equivalent to simply switch the reference category of the independent variable, can I simply do that in multinomial regressions(?); that is, one time I use the var0 as a reference group, do the analysis again with var1 as a reference group, and so on …

Just to be clear, I’m talking about changing the reference category for my independent variable, not the dependant one.

Again, thank you for your time.

#### Lazar

##### Phineas Packard
You could but this will merely give you the same information as you get from model constraint except that you now need to run a bunch of models which seems like a mighty waste of time and still does not solve the ominbus test issue.