Latent Categorical and Latent Continuous
Message/Author
 Robert Stephens posted on Sunday, March 17, 2013 - 4:09 pm
I am trying to work out a model

X - M - U

Where X is a latent categorical variable with three categorical indicators; M, the mediating variable, is a latent continuous variable with 5 observed continuous indicators, and U is a binary outcome.

I am interested both in the classificatiion of the latent categorical variable, and in how both latent variables effect the outcome variable.

I am struggling to determine how to run this model in Mplus, and feel that I may be overlooking something simple.

Is this a doable model in Mplus?

If so, is there a particular example in the User's guide that might be helpful?
 Linda K. Muthen posted on Sunday, March 17, 2013 - 5:22 pm
A factor with categorical indicators is continuous just as a factor with continuous indicators is continuous. You would put the categorical factor indicators on the CATEGORICAL list and use the following MODEL command:

MODEL:

f1 BY u1 u2 u3;
f2 BY y1 y2 y3 y4 y5;
u ON f2;
f2 ON f1;
 Robert Stephens posted on Sunday, March 17, 2013 - 5:48 pm
Linda, Thanks.

As part of the model, though, I am interested in the categorical classification of f1 (LCA). Considering f1 as a continuous factor bypasses this part (from what I can tell).
 Linda K. Muthen posted on Sunday, March 17, 2013 - 6:17 pm
You can do this as a latent class analysis where the three categorical variables are latent class indicators. The effect you are looking for would be the varying of the means and thresholds of m and u across classes and the varying of u ON m across classes, for example,

MODEL:
%OVERALL%
u ON m;
m BY y1=y5;
%c#1%
u ON m;
[m u\$1];
m;
%c#2%
u ON m;
[m u\$1];
m;
 Robert Stephens posted on Sunday, March 17, 2013 - 6:19 pm
Thanks!
 Yaoyue Hu posted on Sunday, March 24, 2013 - 2:59 am
Hello,
I am also trying to do a model:
c ---> f
c is determined by 6 ordinal variables with 5 groups (w1gf_10 - w1gf_0), and f is measured by 10 ordinal variables with 3 groups (w1pfa - w1pfj).

Model:
%overall%
f by w1pfa w1pfb w1pfc w1pfd w1pfe w1pff w1pfg w1pfh w1pfi w1pfj;

%c#1%
[w1gf_10\$1 - w1gf_0\$1];
[w1gf_10\$2 - w1gf_0\$2];
[w1gf_10\$3 - w1gf_0\$3];
[w1gf_10\$4 - w1gf_0\$4];
[f];
f;
%c#2%
[w1gf_10\$1 - w1gf_0\$1];
[w1gf_10\$2 - w1gf_0\$2];
[w1gf_10\$3 - w1gf_0\$3];
[w1gf_10\$4 - w1gf_0\$4];
[f];
f;
Plot:
Type=plot3;

However, I have come across some questions:
1. Is this model right? Because the class memberships changed in this model compared with LCA model containing w1gf_10 - w1gf_0, when I used 3 classes.
2. In the model results, there is no result in probability scale. Is there a way to have a look at it?
 Linda K. Muthen posted on Sunday, March 24, 2013 - 1:19 pm
1. It looks correct. See Web Note 15 for information regarding changing classes.

2. If results in probability scale are not given automatically, we don't provide them for that model.
 Yaoyue Hu posted on Friday, April 05, 2013 - 1:43 am
Thanks!
 Yaoyue Hu posted on Friday, April 05, 2013 - 2:04 am
Dear Linda

One of my major concern about my model is that, since the class membership changed and I could not obtain the results in probability scale, how do I know the 3-class model is better than the 4-class or 5-class model?

In addition, how do I interpret the classes without any results in probability scale?

Thank you very much for your help.
 Linda K. Muthen posted on Friday, April 05, 2013 - 9:26 am
You can determine the number of classes by using BIC and other measures. See the Topic 5 course handout and video on the website for further information. You can interpret the threshold or mean profiles to interpret the classes. You can also compute the probabilities by hand if you want them.
 Yaoyue Hu posted on Saturday, April 06, 2013 - 8:07 am
Dear Linda

Thank you for answering to my silly questions.

As you suggested me to have a look at the Web Note 15, I am thinking that whether it is possible to do my model (c-->f) by 3-step estimation mannually?

Based on the Appendix E & F in Web Note 15:
1. The auxiliary variable should be observed variable, I revised the first sept as:
Model:
%overall%
f by w1pfa w1pfb w1pfc w1pfd w1pfe w1pff w1pfg w1pfh w1pfi w1pfj;

%c#1%
[w1gf_10\$1 - w1gf_0\$1];
[w1gf_10\$2 - w1gf_0\$2];
[w1gf_10\$3 - w1gf_0\$3];
[w1gf_10\$4 - w1gf_0\$4];

%c#2%
[w1gf_10\$1 - w1gf_0\$1];
[w1gf_10\$2 - w1gf_0\$2];
[w1gf_10\$3 - w1gf_0\$3];
[w1gf_10\$4 - w1gf_0\$4];

%c#3%
[w1gf_10\$1 - w1gf_0\$1];
[w1gf_10\$2 - w1gf_0\$2];
[w1gf_10\$3 - w1gf_0\$3];
[w1gf_10\$4 - w1gf_0\$4];
Savedata:
File=Mmodel.dat;
Save=CPROB;
 Yaoyue Hu posted on Saturday, April 06, 2013 - 8:15 am
Continued:
Baseline on the results of the first step,I did the third step as below:

Analysis:
Type=mixture;
Starts=0;
Model:
%overall%
f by w1pfa w1pfb w1pfc w1pfd w1pfe w1pff w1pfg w1pfh w1pfi w1pfj;

%c#1%
[N#1@5.685];
[N#2@3.638];
[f];
f;

%c#2%
[N#1@1.245];
[N#2@3.874];
[f];
f;

%c#3%
[N#1@-5.766];
[N#2@-3.201];
[f];
f;
However, I got an error message as: Invalid symbol in data file:
"*" at record #: 30, field #: 21

I am not sure whether my 3-step models are wrong or not; and if they are right, how should I do with the error?

Thank you very much for your help!
 Bengt O. Muthen posted on Saturday, April 06, 2013 - 1:28 pm
Looks like you are reading your data wrong in the 3rd step. Is * a missing data symbol and have you declared it as such?
 Yaoyue Hu posted on Sunday, April 07, 2013 - 1:49 am
Dear Bengt

In the 1st step, I decleared that all missing are 9999 in my data file (in the section of variable), and then based on the results of 1st step, I saved another data file for the 3rd step.In the 3rd step, I also decleared missing are 9999.
Is the missing coded as * automatically when I saved the data file in the 1st step?

Moreover, I am not sure whether I can use this 3-step estimation in my case that use the latent class to predict a latent factor. If yes, are my steps right?

Thank you very much for your help.
 Linda K. Muthen posted on Monday, April 08, 2013 - 12:00 pm
Missing is coded as * when data are saved using Mplus.

You can use 3-step for a latent distal outcomes. Your steps look okay.