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I have recently read an article by Kruger, Markon, Patrick, & Iacono (2005). Externalizing Psychopathology in Adulthood: A DimensionalSpectrum Conceptualization and it Implications for DSMV [journal of abnormal psychology, 114, 537550] and wondered if I could execute the analyses described in the paper with Mplus. In the article, Kruger et al. (2005) described comparing a LCA model with a "Latent Trait Model," which they described as an IRT model with severity and discrimination parameters to determine which model better accounts for commorbidity. I would like to test this with my own data, but would also like to incorporate covariates into the analyses. Would this be feasible with Mplus? I also wondered if it were possible with the Mplus plot commands to display Item Characteristic Curves. Thanks in advance. 


You will be interested in reading about related topics in three new papers that I am a coauthor on  they are posted on our web site under Recent Papers, Factor Mixture Analysis. These discuss a new set of models that can be used in these situations. See also the Version 4 User'r Guide, ex7.27. ICCs can not be plotted yet in Mplus, but this is very high on our list to add (together with information functions). 


Bengt, Thank you for the references. They were all very helpful and applicable to my data. Do you have any examples of input you would be willing to share? I haven't yet ordered the Version 4 User's Guide. 


Yes, I can send input. When you get to it, let me know which specific ones are of interest. 


I would be interested in seeing how you set up a FMA for diagnostic criteria as you did in Muthen & Asparouhov (2006) with the tobacco dependence criteria. I'm also interested in investigating the effect of several covariates on both the categorical and continuous latent variables. Any thoughts on how to set this up would be much appreciated. Thanks for all your help. Tom 


See Example 7.27 in the Version 4 user's guide. Use the ON statement to regress the continuous and categorical latent variables on the covariates, for example, f ON x1 x2; c#1 ON x1 x2; 


Bengt, I've been trying to apply the FMA model to a couple of data sets that I have (one with steroid users; the other with Alcoholics). The example that you described (7.27) and papers available on the website use binary indicators. Would there be any issue with an FMA that had both binary and continuous indicators? My second question is related to sample size. Are there any recomendations for this type of model or would standard SEM based recomendations be adequate? best wishes, Tom 


It is fine to have both categorical and continuous indicators in FMA. One factor related to sample size is how well separated the classes are. You need a larger sample size when the classes are not well separated. The best way to determine sample size is to do a Monte Carlo simulation. 


Bengt, I believe that I have found the best fitting model for one of my data sets (steroid data set; 14 dichotomous LCA indicators, 5 continuous covariates) and it appears as though the FMA model is the best. I have labeled the 4 class (c) variable as "Steroid Group" and the f continous latent variable as "Steroid Use Severity". I have a question about interpreting the parameters. The size of the logistic regression parameters for LCA indicator on the continuous f variable varry quite a bit between classes. Would this be appropriate or even desirable? Secondly, is it fair for me to interpret the differences in these paramaters as differences in which LCA indicators relate to the "Steroid Use Severity". For instance, Class 1 LCA indicators x13 x14 have large Logistic regression parameters whereas x9x11 are largest for Class 2. Thus, I could say that endorsing x13 for class 1 members indicates that individual will score highly on "Steroid Use Severity"? Thanks, Tom 


Yes, classvarying loadings is ok. And your interpretation is on target. You can actually test for classinvariance of the loadings by a regular 2* loglikelihood difference chisquare test. Remember to use many random starts with the FMA. And also check your final model's loglikelihood by using an OPTSEED run based on the best solution's seed, where the default integration=15 is increased to say 30 or 50. 


Bengt, Thank you for the advice, it is very helpful. How would I go about setting setting up a test for class invariance in an FMA? I will double check the loglikelihood based on your suggestions. I was able to get the model to terminate with 50 random starts. Is that enough? Thanks again, Tom 


Factor loadings are invariant across class as the default. Just don't mention them in the classspecific parts of the model. It is enough if you have replicated the best loglikelihood. 


Linda, Thanks so much. I was able to replicate the loglikelihood. Best wishes, Tom 


I have been playing with the hybrid models with a data set containing the 17 variables used to define type A/B typology for alcohol users. I've tried using FMA and have not found it to fit the data better than LCA. I was wondering if you had an example of LCFA input that you would be willing to share. I was also wondering if there was a way to calculate Psuedo R for these hybrid models. Any advice or thoughts would be very much appreciated. Thanks in advance 


Please send me an email and I will send you the inputs I used for my DSMV paper forthcoming in Addiction. In my experience, FMA fits better than LCA and FA (IRT) in a majority of cases I have looked at. I don't know about pseudo Rsquare (I don't use it), but I would assume the ideas carry over. 


I have another quick question about interpreting the output from an FMA. I want to know how much the f variable contributes to variability within each latent class. Basically, I want to know how much each class differs in its f variance. A related question, how would I interpret differences in f residual variance between classes? Thanks in advance! 


You can estimate classvarying factor variances, which would make sense if you have classinvariant loadings. Together with size of factor loadings, factor variance tells you how much the items correlate within class in an FMA due to unobserved causes. You say "differences in f residual variance", which says that you have predictors of f. This leads to classvarying factor variances, which with classinvariant loadings says that your items correlate differently in different classes. 


Bengt, Thank you very much for your response. What would be the case if I did not have classinvariant loadings? Could I still estimate classvarying factor variances? If so, how would I do this in Mplus? I have the same question for f residual variances. Would the interpretation be different if the loadings were different within each class? 


You can estimate classvarying factor variances if you fix one loading per factor to a constant. With classvarying factor loadings, the factor (residual) variances are not comparable across classes. What you can compare are (lambda_j * psi * lambda_k)/SD_j*SD_k which are the item correlations within class (SDs are the standard deviations of the items). 


I'm writing on how to allow for correlations between items within class, for a LCM with binary items. I'd like to compare such a model to factor mixture model. I saw an earlier post that referred the inquirer to UG 7.16, but that was in 2006. I have User's Guide 7.1 and looked at examples in this chapter but can't quite see that any of these model item correlation in a LCM. Are there papers that discuss situations where correlation between variables within classes is examined and tested? Many thanks, Kathy 


UG ex 7.16 handles this by adding a factor behind the two items that need withinclass correlation. There is a paper by Berzofsky et al (2014) in the latest issue of the SM & R journal. I will also send you a paper of ours which is in the pipe line. 

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