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Here is my syntax: type is mixture; model: %overall% x1x9; %c#1% [x1x9*1]; %c#2% [x1x9*0]; %c#3% [x1x9*1]; True or False: Observed covariance matrix is class specific. Thanks, 

bmuthen posted on Friday, May 09, 2003  6:44 am



This model implies a classinvariant covariance matrix for the x's. The covariances are fixed to zero as the default. 


That's correct. I estimated classinvariant covariance matrix (diagonal), as I intended. However, the residual covariance matrices (Observed  estimated) vary across classes, which led me think that observed covariance matrices differ across classes. Is that right? 

bmuthen posted on Monday, May 12, 2003  7:28 am



Here "Observed" is a classspecific covariance matrix computed by weighting the raw data with the individuals' posterior probabilities as estimated from the model. This means that the "observed" covariance matrix does change over the classes. This is the closest to observed that one can get with unknown mixture classes. 

Anonymous posted on Friday, May 14, 2004  11:28 am



I am new to Mplus and I need help on my problem below. I have a structural model has two exogenous latent models effecting one endogenous latent variable. One of the exogenous latent variables has four categorical manifest variables and the other exogenous latent variable has three manifest variables. The endogenous latent variable is continuous and has 4 continuous manifest variables. I am considering using latent profile analysis and the Mplus program. Am I right and how do I go about it. Thanks so much for your assistance. 

Anonymous posted on Friday, May 14, 2004  12:35 pm



Sorry I did not preview my first message. Below is the corrected version. I am new to latent variable modeling (not SEM) and Mplus. I need help to solve a modeling problem. I have a model that has two exogenous latent variables effecting one endogenous latent variable. The latter has four continous manifest variables. One of the exogenous latent variables has four categorical manifest variables and the other has three continous manifest variables. I want to use latent profile analysis and Mplus. Am I right in using LPA? Can Mplus perform the analysis? Thanks 


So you want to look for unobserved heterogeneity in your data in the form of latent classes using an SEM model? 

Anonymous posted on Tuesday, May 18, 2004  7:19 am



Yes. 


There are two papers on the homepage at www.statmodel.com that describe such models using Mplus. The first author is Lubke. 

Scott Weaver posted on Wednesday, August 02, 2006  11:30 pm



I am conducting a latent profile analysis. I have specified tech11 to get the LMR test, but am having difficulty figuring out how to specify the start values such that the first class is the smallest class. I tried specifying the start value for the latent class mean (C#1*2 in a 2 class model) but that does not seem to work to make class 1 be the smallest class. Your help is very much appreciated! 


You should be specifying starting values so that the largest class is last. You do this by using the parameter values of the means of the latent class indicators not the means of the categorical latent variable. 


I tried what you suggested, but it does not seem to be working either. In my initial run of a 2 class model, the largest class is first. So I used the estimated means from the largest class as start values for the last class (%c#2%) and ran the model with starts = 0 0. I verified that my specified start values were used with tech1. However, the results still are such where the largest class is first. Any suggestions? Thanks! 


You would need to send your input, data, output, and license number to support@statmodel.com so I can see where you are going wrong. 


any opinions about the difference between Latent Profile Analysis and Latent Class Analysis? From the Lubke and Muthen's paper about factor mixture models, I think for LPA, the latent class indicators are continuous variables, but for LCA, the latent class indicators are categorical or ordinal variables? Am I right? 


That sounds correct. 


This is a question regarding the output file from a mixture model. I am saving the output from a mixture model with the cprobs for segment membership but I would also like to get the id's of the observations  in order to do some additional post hoc analysis using other variables not used in the mplus models. Is there a way that I can do this? In other words, can I get mplus to carry forward an id variable from the input data file into the output data file Thanks in advance! 


If you include the IDVARIABLE option in the VARIABLE command, the id variable will be saved. 


Hi I have pre and post measures on five cognitive domains for a large sample of healthy older adults with a family history of Alzheimer's disease. The five preand post measures were adjusted for age, gender, and IQ using data from a control sample We are interested in identifying 3 possible groups in terms of cognitive performance at both time points: improver, stable, or decliner. I have thought about 3 possible approaches to analyze the data in MPLUS 1. Include all 10 measures (5pre and 5post) as indicators of class membership. Do latent Profile analysis. 2. Compute five change scores: post  pre, in which case a negative score would indicate decline, and then use both the five change scores and also the Time 1 scores as indicators of class membership. (Including performance at time 1 and also change would capture those with low initial performance and also a decline.) 3. Assign a score to each individual on each of the five cognitive dimension according to the following scheme: Assign 2 to those performing 1SD or more above Controls Assign 1 to those performing within +/1SD relative to controls Assign 0 to those performing 1SD or more below Controls. Use these 10 categories in a latent Class Analysis. What would be the best approach to identify decliners, stables, and "improvers"? Thank you very much in advance for your help! MF 


How about Latent Transition Analysis, where you have a latent class model for the 5 outcomes at each of the two time points? With say 2 classes at each time point you would have a chance to get the decliners, stables, and improvers. 


Dr. Muthen, Thanks for your response. Could you point me to an example of the commands set up using MPLUS? Thank you! MF 


See Example 8.13 and 8.14 in the Mplus User's Guide. See also the Nylund dissertation that is on the website. 


Are there any guidelines for the minimum number of continuous indicators for latent profile analysis? Alternatively asked, is there a way to calculate df for latent profile analysis? Thanks! 


Degrees of freedom are not relevant for LPA because there is no unrestricted set of sample statistics to test against. I know of no guidelines for the minimum number of continuous indicators for latent profile analysis. 


Dr. Muthen, I'm using Latent Profile Analysis on the data collected from three different sample sources. I could try to use sample sources are a covariate, but am wondering if there are any other ways to take different sample sources into account in the analysis. Thank you. 


You can treat sample source as "KNOWNCLASS" which makes it possible to test equality across samples of any of the parameters in your model. 


Hello Dr.'s Muthen, I have run an LPA on three continuous indcators and have found a good 4 class model. I would now like to use that Latent class variable as 'predictor,' if you will, in another LV model that has dependent variable that is defined by 3 binary indicators and ther observed covariates. Is there any syntax or examples about how to do this? Thank you, ***Melissa 


Look at how UG ex8.6 handles the influence of c on u. You don't say u ON c, but the u thresholds/means vary over the c classes by default. 

Erika Wolf posted on Wednesday, April 11, 2012  1:34 pm



How do I request output with the observedexpected residual covariance matrix for a latent profile analysis when type = complex mixture? 


Use the RESIDUAL option of the OUTPUT command. 


Dear Dr.'s MuthenI am running a LPA with decision making variables. However, theoretically I should include indicator variables that "overlap" for instance, benefits of taking a risk, costs of taking a risk, and "depth of processing" (the sum of all benefits and costs), and benefitto rewardratio (benefits/costs). This would be an issue in regression, I believe, according to Cohen, Cohen, West, & Aiken. From your view, is there a similar issue in LPA? The solution converges in Mplus but my concern is that variables with "overlap" may be less likely to "drive" the differences across profiles. Thank you very much for your time. 


In regression you worry about collinearity (too high correlation) among the predictors (covariates; x's; IVs), but in LPA your variables are outcomes (y's; DVs) so that issue isn't involved. Still, overlapping indicators may create residual covariances in LPA which may cause BIC to point to too many latent classes. If this is a concern, you can also do mixture modeling with all covariances in the model in line with UG ex 7.22. 


Hello, I am hoping for a bit of clarification/guidance in terms of picking analytic strategy. I am using data that involves ratings of emotions that are, obviously, correlated. Thus, I initially was examining using the syntax noted above (UG ex 7.22). However, in other places, I saw a suggestion that when variables may correlate within class, factor mixture modeling (similar to ex 7.17) is the way to go. Is there any guidance you can provide as to how to decide which strategy is best? 


Hello Dr. Muthen, In my study, I used LPA to investigate highability students' personality profiles. I submitted the paper to a journal in our field (gifted education). They asked for a major revision and reviewers' asked some important questions. One of the comments was about the way of how I conducted analysis: The instrument that I used is the FiveFactor Model (FFM) personality inventory, which has five factors (Extraversion, Openness, and etc.). I submitted the five subtest scores from the FFM for the sample of 410 students. The analysis yielded three profiles. The reviewer indicated that the the analysis that used data created with factor analysis to then do an LPA to group people together is problematic. The problem with this is that the variables used to created the classes have been designed to be distinct and difficult to group together. The reviewer indicated that this somewhat lows entropy values and makes it difficult to have distinct classes. I am wondering if I can use LPA with those factor scores (latent variables). If I have to use only observable variables, wouldn't it be difficult to interpret profiles? I do not know how the result will look like if I include all 45 items from the dataset into LPA analysis. What is the correct way of using LPA in this study? Is the reviewer right with his/her concern? I appreciate your time and explanation about this issue. Thanks, 


Note that you don't have to have correlations among indicators within class for the indicators to correlate  they correlate because they are all influenced by the latent class variable. For an application, you may want to take a look at the papers on our website: Muthén, B. (2006). Should substance use disorders be considered as categorical or dimensional? Addiction, 101 (Suppl. 1), 616. Muthén, B. & Asparouhov, T. (2006). Item response mixture modeling: Application to tobacco dependence criteria. Addictive Behaviors, 31, 10501066. 


Thank you for the quick response. Given that, when is it necessary/beneficial to specify covariances (ex 7.22) versus not? In reviewing papers which have published in my area which use LPA this is not very common, but it is not clear how this decision is to be made. I have a followup question as well. If I want to include a covariate (gender), it is my understanding that the model presented in Figure 3b in that 2006 paper is the best way to go due to the model parsimony it provides over traditional LPA. Is that correct? 


It depends on substantive theory to a large extent. LPA (no correlations within class) is a simple parsimonious model. You can add more classes so that the zero withinclass correlation specification is more realistic. But sometimes you get a better BIC by adding some WITH statements rather than adding classes. UG ex 7.22 is an extreme case of that where you add all possible WITH statements. Such a model is more often used in the classification literature where there is little or no theory of a set of items designed to measure a latent class variable (and therefore more likely have zero withinclass correlations). Instead of adding all WITH, the factor of factor mixture captures withinclass correlations more parsimoniously (fewer parameters) than using all WITH statements. Such a factor would be relevant if substantive theory suggests a "severity dimension" within class. Gender can predict the latent class variable or also a severity factor within class. For a further modeling overview, see also the paper on our website under General Mixture Modeling: Muthén, B. (2008). Latent variable hybrids: Overview of old and new models. In Hancock, G. R., & Samuelsen, K. M. (Eds.), Advances in latent variable mixture models, pp. 124. Charlotte, NC: Information Age Publishing, Inc. Click here for information about the book. 


Answer to Mammadov post: I don't see a problem with doing LPA on factor scores if correlation among the factors is substantively motivated (a latent class variable influencing the factors make the factors correlate). It would be different if the factors were obtained with orthogonal rotation using say Varimax. You can also do LPA based on the 45 items but that might well lead to a different picture. 

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