For my research I am implementing LPA on my data set. We have determined that the 4 class solution is best. One part of the results I am confused about are the Average Latent Class Probabilities for Most Likely Latent Class Membership (Row) and Latent Class (Column), and Classification Probabilities for the Most Likely Latent Class Membership (Column) by Latent Class (Row) [the results for each can be found below respectively).
I believe these (in particular the diagonal) represent the probability that observations are getting classified into a correct group. My wording may be a bit off, but this is my understanding of it.
My question is, what is the difference between these, and when reporting results in a paper, which should be used? Should one take the average of the diagonals? Should one only report one of them? Why?
Typically, the first table is used. For an explanation of this, see our Short course Topic 5 video and handout on the web.
You also find a discussion of these 2 different tables in the Mplus Web Note 15 on our website. See also explanations in
Nylund-Gibson, K., Grimm, R., Quirk, M., & Furlong, M. (2014): A latent transition mixture model using the three-step specification. Structural Equation Modeling: A Multidisciplinary Journal, 21, 439-454. contact first author
Indeed Web Note 15 explains the difference. For anyone else who stumbles upon this discussion, here is what they represent:
Consider you have 2 variables, the latent class variable C and the most likely latent class variable N. C is the latent class the observation belongs to, N is the latent class you end up classifying it as using LPA/LCA because it's the most likely class (at least to my understanding).
The first table plots the probability P that C=(latent class i) given N=(latent class j) [P(C=i|N=j)]. In other words, for the diagonal, this represents the probability given that you have classified an observation as a latent class that it is actually a part of said class.
The second table plots the probability P that N=(latent class i) given C=(latent class j) [P(N=i|C=j)]. In other words, for the diagonal, this represents the probability given that the an observation is a part of a specific latent class that you will classify it as said class.
They may look the same, but they are distinct. Thank you Dr. Muthen.
I'm using Mplus version 8.4 on PC, performing LCGA. In my output I only have "Classification Probabilities for the Most Likely Latent Class Membership (Column) by Latent Class (Row)", and the logits for these.
Please can someone tell me how to produce the "Average Latent Class Probabilities for Most Likely Latent Class Membership (Row) and Latent Class (Column)" as well?