Multiple thresholds and probabilities
Message/Author
 Darren  posted on Wednesday, September 25, 2013 - 4:50 am
I am using the R package MplusAutomation to help visualize results from a latent class analysis that looks like this:

%overall%

[bdyct24\$1 bdyct49\$1] ;
[bdyct24\$2 bdyct49\$2] ;
[bdyct24\$3 bdyct49\$3] ;

With relevant output:

Thresholds
BDYCT24\$1 -0.999
BDYCT24\$2 2.824
BDYCT24\$3 4.837
BDYCT49\$1 -1.588
BDYCT49\$2 2.405
BDYCT49\$3 4.263

BDYCT24
Category 1 0.269
Category 2 0.675
Category 3 0.048
Category 4 0.008
BDYCT49
Category 1 0.170
Category 2 0.748
Category 3 0.069
Category 4 0.014

MplusAutomation only imports the threshold values, so I need to know how to convert these to probabilities. I can do this for binary variables with 1 threshold, but can't seem to work it out for variables with more than 2 categories (and this more than 1 threshold). I've tried to find out how from chapter 14, but can't make it work. Many thanks.

This link gives an example of the calculation for a binary variable, but seems to suggest you can't do the same thing for >2 categories.

http://www.ats.ucla.edu/stat/mplus/code/lca_example2.htm
 Linda K. Muthen posted on Wednesday, September 25, 2013 - 11:46 am
At the top of page 493 of the user's guide, you will find the formulas for probit regression. You can generalize these to logisitic regression using

F (t) = 1 / 1 + exp (-t)
 Darren  posted on Wednesday, September 25, 2013 - 1:08 pm
Perfect, thank you Linda. It's page 441 from the v6 online version.

a <- 1/(1+exp ( 0.999))
b <- 1/(1+exp (-2.824))
c <- 1/(1+exp (-4.837))
d <- 1/(1+exp ( 4.837))

a
[1] 0.2691381

b-a
[1] 0.674821

c-b
[1] 0.04817255

d
[1] 0.007868408
 Bengt O. Muthen posted on Thursday, September 26, 2013 - 9:08 am
That looks right.