Intepretation of LCA with nominal i... PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
 Derek posted on Monday, October 12, 2015 - 7:13 pm
Hi all,

Thanks for your help in advance. I am running a Latent Class Analysis Model with 3 dummy variables and 3 nominal variables (1 is ordinal in nature and 2 are truly nominal).

I am wondering how I can best interpret the obtained probabilities from the LCA model with nominal indicators. I believe the graph/plot approach is only available for binary indicators but not applicable to nominal indicators (Please correct me if I am wrong here; I hope I am wrong).

For example, the below are probabilities from a three-class model. Please help me interpret the probabilities associated with "people" (4 categories--nominal), "location" (4 categories--nominal) and "weapon" (3 categories--ordinal)

0.093 0.296 0.086
0.168 0.253 0.649
0.144 0.064 0.013
0.595 0.387 0.252

0.930 0.002 0.310
0.001 0.717 0.594
0.067 0.120 0.089
0.002 0.161 0.007

0.003 0.004 0.021
0.007 0.015 0.028
0.990 0.981 0.951

0.964 0.912 0.144
0.036 0.088 0.856

0.023 0.002 0.213
0.977 0.998 0.787

0.209 0.184 0.174
0.791 0.816 0.826

Thank you very much.
 Derek posted on Monday, October 12, 2015 - 7:22 pm
In other words, how can I use these probabilities to define my classes? Thanks.
 Bengt O. Muthen posted on Wednesday, October 14, 2015 - 2:44 pm
For each column (latent class) the 4 values corresponding to the 4 nominal categories sum to 1. For each column you want to see where the big probabilities are. Take people as an example. So class 1 people tend to have the highest prob for answering category 4, class 2 people tend to have the highest probs for cats 1, 2 and 4, etc
 Derek posted on Wednesday, October 14, 2015 - 3:26 pm
Thanks a lot for your answer, Dr. Muthen. An additional question is: is it also necessary to compare horizontally? (in other words, to compare across latent classes?)

For example, for "weapon", the overall sample has a very low probability of carrying a gun or other weapon. If we only compare within class, we would say people from all three classes are low-risk there. But, as you can see, when we make horizontal comparisons, class 3 exhibits higher probabilities of both carrying a gun or other weapon (for the whole sample: 0.006, 0.013, 0.982). Should this kind of information also be taken into account when we assign meaningful labels to different classes and understand the nature of the classes?

In general, are nominal variables likely to lead to low homogeneity due to multiple categories?

Thanks very much again.
 Bengt O. Muthen posted on Wednesday, October 14, 2015 - 5:18 pm
Yes, vertically characterizes the class and horizontally characterizes the differences among classes. The totality gives the story.

We talk about these interpretational matters a bit for binary variables in our Topic 5 video and handout on our web site.

I don't think nominal variables create any special difficulties in principle.
 Derek posted on Wednesday, October 14, 2015 - 5:53 pm
Thanks again for answering my questions.
 Dinh Son Bui posted on Monday, November 19, 2018 - 9:48 pm
Dear Dr Muthen,
1. Dose it matter if I code one nominal variable with 3 levels as 0/1/2 or 1/2/3 in an LCA model?

2. Is it compulsory for the reference category of a nominal variable to be coded as the lowest value or highest value? Dose it apply to ordinal variables as well?

3. If one nominal variable is included in the model but I only use "categorical are.." but not "Nominal are..." in the syntax. In this case the model will treat the variable as an ordinal variable. Is it correct and what is the consequence?

Thank you
 Bengt O. Muthen posted on Tuesday, November 20, 2018 - 5:27 pm
1. No

2. Highest value gives the reference category. No, there is no counterpart for ordinal variables.

3. Right. An ordinal variable has only 1 slope for each predictor but a nominal variable has several (C-1).
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