Calculating Probabilities in growth m... PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 Jodie Ullman posted on Saturday, May 22, 2010 - 4:11 pm
This is my first foray into Mplus and I am confused.
I am estimating a logistic regression growth curve mixture model. I have estimated linear and quad growth parameters.

I want to plot the curves (or lack of). I calculated the probabilities, as I would from estimates in logistic regression,

For the first time point

Y’ = 2.054 + (.02*Linear coefficient)+(-.002*Quad coefficient)
Y’ = 2.054 + (.02*1) + (-.002*1)

Prob = EXP(Y’)/1 + EXP(Y’)


I1 2.054 0.305 6.736
S1 0.020 0.072 0.282
Q1 -0.002 0.004 -0.481

The plots I get from doing this are different from the plots I get from when I plot the data from the section labeled,


Category 1 0.588
Category 2 0.412

Obviously I am confused as I had expected these would be the same.

My questions are,
1. Which is correct!
2. What am I plotting (if anything) when I calculate what I thought were prob using just a logistic regression approach?
3. What am I plotting when I plot the data from the “Results in Probability Scale” section?
4. Finally a basic question - Am I predicting the 1 in data or Category 1 as indicated in Mplus?

 Bengt O. Muthen posted on Saturday, May 22, 2010 - 5:07 pm
If your growth model has growth factors (random effects) with non-zero variances the outcome probabilities have to be computed via numerical integration over the distribution of the random effects. This is what is done in the Probability output and in the graphics of Mplus. It is hard to do by hand.

What you are computing is the outcome probabilities at the means of the growth factors. The two approaches are not the same with a non-linear model such as this.

Mplus creates categorical variable scales labeled 0, 1, ... Therefore category 1 in Mplus is 0 and category 2 is 1. With a binary outcome Mplus models the probability of category 2 as usual in logistic regression.
 Jodie Ullman posted on Saturday, May 22, 2010 - 5:31 pm
Thanks for the speedy response! Perfect - I'm on track
 Jacqueline Homel posted on Thursday, January 15, 2015 - 4:29 pm
I have estimated a latent growth model with binary outcomes, over four time points (0,2,4,6). I am interested in differences between males and females:

Intercept = 0
Slope = 11.472
Threshold = 1.132
Intercept on sex = -1.408
Slope on sex = 0.233

I am wondering if there is some way I can present the results as the average predicted probability that the outcome=1 at each time point, for males and females? I have read the technical appendix 1 and the topic 2 handout about converting logits into predicted probabilities using P = 1/1+(exp(-L)

I tried using this to estimate probabilities but the results look nothing like what is obtained from the mplus plot of estimated probabilities.

Is it possible to include the slope in this formula and find an average predicted probability of the outcome at each time point?
If not, is my only option to present the logits at each time point?

Thank you very much!
 Bengt O. Muthen posted on Thursday, January 15, 2015 - 4:39 pm
You can plot this for each gender using the Adjusted means plot.

I assume that your intercept and slope factors have variances so that they are random effects. Computing the probabilities in this case calls for numerical integration over the random effect distribution, so that would explain why your formula won't work. You are essentially computing the probabilities conditional on random effect values of zero.
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