The plots I get from doing this are different from the plots I get from when I plot the data from the section labeled,
RESULTS IN PROBABILITY SCALE
SAL1 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?
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.
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?
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.