Odds Ratios
Message/Author
 Kelly Landman posted on Saturday, November 23, 2013 - 12:25 am
I'm running a 4 class model on reading scores across 4 time points with gender(a dummy coded variable) as a categorical variable. I'm trying to determine the odds of a student being male or female in each class. It looks like the output only gives me the odds for the first class:

LOGISTIC REGRESSION ODDS RATIO RESULTS

Categorical Latent Variables

C#1 ON
G 0.794

my original model specifies:
model:
%OVERALL%
i s | R3@0 R4@1 R5@2 R6@3;
i-s@0;
i s on G;
c#1 on G

Do I need to add c#2 on G to get the odds ratios for the second class?
 Bengt O. Muthen posted on Saturday, November 23, 2013 - 12:29 pm
With 4 classes you want to say

c#1-c#3 on G;

or simply

c on G;

That will give you 3 odds ratios in the output, one for each regression slope.

Some teaching can be helpful in shedding more light.

Look at our Topic 2 handout on page 29 (slide 58) and you find equation (94) which gives the log odds equal to a sum of beta_{0c} and beta_{1c}*x, where x is your G and your c=1, 2, 3, 4.

For G=0, the log odds is the intercept beta_{0c}, so the odds is exp(beta_{0c}), where exp is exponentiation. For G=1, the log odds is beta_{0c}+beta_{1c}*1, so you have to exponentiate that. And you do this for each of the first 3 classes (the last class is the reference class for the odds).

The Mplus output gives you the exponentiation only of the slope beta_{1c} which therefore gives you the odds ratio, directly comparing males and females on their odds.
 Soohyun Shin posted on Tuesday, September 15, 2015 - 2:20 pm
Dear Dr. Muthen

I ran LCGA with a predictor of parental overprotection(PBI) on class membership.
I am confused about the interpretation.

According to ALTERNATIVE PARAMETERIZATIONS ....REGRESSION results, higher PBI only predicted higher chance of being in class 2 than class 1.
Now the question is..
1) In LOGISTIC REGRESSION ODDS RATIO RESULTS, how do I know if these odds ratios are significant?
2) These odd ratios seem to show that higher PBI increased the chance of being in class 1 than class 3, and being in the class 3 than class 2. They are inconsistent with the other result that showed higher PBI only increased the chance of being in class 2 than class 1.

I think I'm missing something here. How do I interpret them?

Thank you so much in advance.

LOGISTIC REGRESSION ODDS RATIO RESULTS
Categorical Latent Variables

C#1 ON
PBIF_O 1.016

C#2 ON
PBIF_O 0.956

ALTERNATIVE PARAMETERIZATIONS FOR THE CATEGORICAL LATENT VARIABLE REGRESSION

Parameterization using Reference Class 1

C#2 ON
PBIF_O -0.062 0.026 -2.387 0.017

C#3 ON
PBIF_O -0.016 0.046 -0.350 0.727
 Bengt O. Muthen posted on Tuesday, September 15, 2015 - 7:31 pm
The output you show:

Parameterization using Reference Class 1

C#2 ON
PBIF_O -0.062 0.026 -2.387 0.017

says that relative to class 1, the class 2 probability is lowered by high PBIF_0 value. Isn't that consistent with the odds ratio being lower for C#2 than C#1 below?

C#1 ON
PBIF_O 1.016

C#2 ON
PBIF_O 0.956
 Soohyun Shin posted on Wednesday, September 16, 2015 - 2:02 pm

Should I report OR = 1.016 (C#1 ON PBIF_O) to show that relative to class 1, the class 2 probability is lowered by high PBIF_0 value?
Also how do I know if they are significant (p value)?

Thank you again.
 Bengt O. Muthen posted on Wednesday, September 16, 2015 - 11:26 pm
I would interpret the logit values that are printed and have SEs. If you prefer ORs you can get their SEs and significance as described in the FAQ on our website:

Odds ratio confidence interval from logOR estimate and SE