Hi. I have a question regarding Latent Profile Analysis. I have several measures of child "executive function" that include behavior (e.g. impulsivity and attention) and language (e.g. expressive and reflective) that I am using in a profile analysis. These measures are popular in the field and are measured on different scales and thus have different variances. I was wondering if there was a general rule about the degree of difference (between smallest/largest) in variances for continuous items in a latent profile analysis (I know in this is an issue in other forms of "profile analyses" e.g. Tabachnick & Fidell and an issue in SEM e.g., Kline or Bentler). Is it a requirement that all items are measured on the same scale and have similar variances?? Thanks in advance.
Hi again. Continued discussion on "child executive function" from the earlier post (3/19). I tested the adequacy of my three class latent profile model by giving each class different start values to make sure the solution I got was the "right" one. The model appeared stable (results and log likelihood). Next, I simply changed the order of class 1 and 2 and kept the same start values (so, in my mind the results shouldn't have changed just the order of the results--what were class "2" results should have become class "1" results).
I ended up with different results both on the means within class and on class sizes (prior I had 27%, 36%, 36% and now have 37%, 37%, and 25%, where the third class [the same class in both analyses] was 36% is now 25%, class one was 27% now 37%) leading to different conclusions, which makes me a little concerned.
Is there something I have overlooked or should be concerned about given the changes in results? My operating assumption was that the start values were important, not the order of the classes (by the way, I am using actual start values, instead of 1 and -1, for convergence, it helps because the items I am using are on different scales). Advice??
I've completed a confirmatory factor analysis with three continuous LVs each represented by a set of indicators (which are items on a paper-and-pencil scale), and the fit appears acceptable. The indicators are each scored from "1" to "4" in a Likert-type response format. I have a preconceived hypothesis that the participants should fall into five separate categories based on their scores on the three continuous factors. For example, those "high" on the first factor and "low" on the other two will form one group, those "high" on the second and third factors will form a second group (regardless of scores on the first factor), etc. In addition, I expect to see certain gender differences in the proportions of participants assigned to each category. Is there a way to conduct a confirmatory latent profile analysis to test this hypothesis? Would this be an appropriate thing to do? If so, could you please route me to a reference and/or example in MPlus2? Thank you and happy Thanksgiving!
Bmuthen posted on Thursday, November 22, 2001 - 8:55 am
You may be interested in a new paper by Lubke, Muthen, Larsen (2001), Global and local identifiability of factor mixture models. This can be requested from firstname.lastname@example.org by mentioning paper 94.
Anonymous posted on Friday, March 08, 2002 - 10:00 am
Hi -- I am doing a latent profile analysis, using six indicators of "social capital", each measured on a 1-10 Likert-type scale. My model converges with all variances constrained (the BIC continues to decrease up to a six-class model, but a 3-class model fits better with theory, gives better class probabilities, and the entropy measure is higher). When I free variances past a 1-class model I have a variety of problems -- including within class means that are outside the scale, and/or at the min or max, and with 0 variance (and a variety of error messages re. the model not converging). Also, the class sizes change and patterns between the variable means within classes change when any variances are freed. My data is negatively skewed (less skewed within the classes than in the full group), but within the limits recommended by Kline. Should I trust my results with the variances constrained? Or, can you recomment how to proceed?
bmuthen posted on Friday, March 08, 2002 - 5:47 pm
Latent profile analysis can have these types of behaviors when the variances are allowed to vary across classes. The literature so far seems to have little guidance to offer in this area. You may want to consider the following approach. Using the model with class-invariant variances, you can classify individuals into the latent classes using their posterior probabilities. You can then go back to the raw data and study the variation of each variable in each class. If a variable is considerably more or less variable in a certain class, you can modify the model to allow that variable to have a class-specific variance for that class.
Anonymous posted on Monday, June 10, 2002 - 3:43 pm
I want to classify respondents from several ethnic groups into classes, three classes for each ethnic group. There are 24 5-point Likert variables (never to always) that measure five latent constructs. The classification will be based on the five latent constructs. The minimum and maximum subsample sizes are 190 and 300, totaling about 1,000. I want to see how the class proportions differ from one another group. Could you give some guidence on how to run this analysis. Thanks!
bmuthen posted on Tuesday, June 11, 2002 - 9:31 am
Let me first ask you if by classes you refer to a latent class(latent profile; LPA) analysis using the 5 latent constructs? If so, have you done preliminary LPA analyses of the factor scores within each ethnic group?
Anonymous posted on Tuesday, June 11, 2002 - 10:04 am
I have tried LPA with the factor scores for one subsample and the result looked ok! I am not quite sure if I should procede with this approach. Should I obtain the factor scores from a Multigroup CFA or from a single group CFA? If multigroup CFA is preferred, what constraints are needed on what parameters?
bmuthen posted on Tuesday, June 11, 2002 - 11:26 am
A multiple-group analysis is very valuable to do first because you want to make sure that you have a sufficient degree of measurement invariance before you compare the latent variables (or classes from them) across groups. You should use the default Mplus setup for a multiple-group meanstructure analysis which holds intercepts and loadings equal across groups. You can then look at modification indices to see if some items are not invariant wrt to either parameter type (intercept or loading).
Anonymous posted on Saturday, February 28, 2004 - 6:51 pm
Hello I am running a Latent Profile Analysis using a set of 15 behavioral characteristics. Some of the characteristics are highly correlated (e.g., .7 to .8), but the majority of characteristics have moderate to low relationships. Only 10 pairs of variables from the entire correlation matrix showed correlations above .7. Also, all variables are on the same metric (T scores).
In one run, the variables were considered independent, where the latent class variable was driving the relationship between the observed variables. In a second run, those variables which were highly related were allowed to correlate (using the WITH statement). In the run which considered the variables to be independent, the results were much more meaningful (e.g., lower BIC, higher entropy, MUCH easier to interpret) than the results in which the selected variables were correlated.
Can the LPA solution which considers the variables to be independent be interpreted? Or, is this solution 'invalid' due to the high correlations between some of the variables? How strong is the assumption of independent variables when running/intepreting LPAs?
Thank you for your comments and also for MPLUS.
bmuthen posted on Sunday, February 29, 2004 - 7:49 am
The sample correlations should be signficant for LPA. It is the within class correlations that are zero. Although LPA specifies zero within-class correlations among the variables, it reproduces correlations among the variables because the variables are all influenced by the latent class variable, so the variables become correlated when mixing across the classes. If some variables correlate more than others this can be due to these variables differing more in means across the classes than other variables. This means that you don't have to include WITH statements to make your model fit. Perhaps you need to include more classes, which have particularly high across-class mean differences on the highly correlated variables. It is also the case that IF you allow WITH for some variables, you may be able to use a smaller number of classes and still get the same model fit. WITH represents within-class correlation and should have a well-interpretable substantive meaning such as a measurement methods effect. So, to some extent classes and WITHs have similar effects on model fit, and substantive arguments will have to be brough in to make a choice. Related to this, you may also study chapter 3 of the Hagenaars-McCutcheon latent class book of 2002 published by Cambridge Univ Press, "Applied Latent Class Analysis".
As I've seen LPA used and described as a way to identify homogeneous populations within a larger heterogeneous population, indicator variables are usually either all continuous or all binary/categorical. What are the potential problems of combining binary/categorical indicators and continuous indicators in the use of LPA?
Do you know of a good example of where this mixed model has been applied using LPA to describe subpopulations within a heterogeneous group? I'm currious as to how descriptions of the differences between groups among the indicator variables are made (means for continuous and item endorsement probabilities for binary/categorical)?
Can anyone point me to a resource in which latent profile analysis was used with MPlus, and/or a general introduction to latent profile analysis including a description of the parameters that the analysis generates to determine these profiles? Thanks!
bmuthen posted on Tuesday, November 30, 2004 - 7:49 pm
Although not using Mplus, the Vermunt-Magidson chapter 3 in the Hagenaars-McCutcheon book Applied Latent Class Analysis is useful in this regard. An introduction using Mplus has yet to be written.
We have just run a latent profile analysis using Mplus. We have 18 variables that are continuous in nature and 1 variable that is categorical with 4 levels or groups. With respect to the output, we understand how to interpret the output for the 18 continuous variables. However, the output for the 1 categorical variable is unclear to us. Values for this variable are listed under the heading Means, and give us values only for 3 of the 4 groups that compose this categorical variable. Our questions include (a) why are these categories list under Means? (b) shouldn't we be getting proportions for this variable since it is categorical? and (c) in general, if these means are interpretatively meaningful, what do negative means tell us? Thank you for any help you can provide.
If this is an observed categorical variable, then you should get thresholds. This variable should be on the CATEGORICAL list. If this is a categorical latent variable, you should get means. I think you mean the former but am not totally certain.
I now change the categorical variable to be listed as CATEGORICAL rather than NOMINAL, and received the thresholds. I guess I am still confused why I did not receive probabilities for these as well, like one receives in an LCA. Thanks!
With binary outcomes, CATEGORICAL and NOMINAL should yield the same results. I suggest that you send the two outputs and data to email@example.com to be checked. You may not be using the most recent version of Mplus or there may be another explanation. I would need more information to determine this.
I have a question regarding the determination of the appropriate number of classes in an LPA. For example, if the Vuong-Lo-Mendell-Rubin Likelihood test is not significant for a 3 class solution (compared to a 2 class solution) but the BIC is smaller for the 3 class solution, which should trump? Meaning...how do go about evaluating whether the 2 or 3 class solution is superior?
bmuthen posted on Friday, February 04, 2005 - 6:03 pm
This does not have a simple answer. BIC and LMR can disagree. You may also want to consider sample-size-adjusted BIC which has shown superior results in some studies. When fit indices do not give a clear answer I would go with interpretability - often a k-class solution is merely an elaboration of a (k-1)-class solution, not a contradictory finding.
Also, are you sure you are interpreting the MLR p value correctly? See the User's Guide.
Could you tell me how MPlus sorts results files (.dat).? I have imported a results file into SPSS and want to be able to link subjects to their original case id’s—I should be able to do this if I can figure out how Mplus is sorting the file. Just so you have a little background (if necessary to answer the question), the LPA that I conducted includes only a subset of the total subjects in the original data file. The original file includes 3 sets of subjects, and I used the command syntax to include only those subjects with a code=1 on a categorical variable in the data set. Thus, the LPA was only conducted on these subjects in this specific analysis.
I have now been able to save the ID it is saving it like this 10.000**********, which is not the proper format. The subject ids are supposed to look like this 030100102. Can you suggest how I might change the commands so that the subject id's are accurately saved?
See the Mplus User's Guide where it states that the length of the ID variable can not exceed seven. You will have to shorten this variable. There is usually a unique part that does not exceed seven.
Anonymous posted on Thursday, February 17, 2005 - 4:56 pm
Regarding the interpretation of the MLR, discussed on Feb.4...If the p value of the MLR is less than .05, this means that the solution is superior to the k-1 solution? Conversely, if the p value is greater than .05, the k-1 solution is superior. Is this correct? Thank you.
bmuthen posted on Thursday, February 17, 2005 - 5:08 pm
You mean LMR (Lo-Mendell-Rubin). Yes, your description is correct.
Anonymous posted on Saturday, March 19, 2005 - 1:51 pm
I am running a latent profile analysis (LPA) of four count variables that index health care utilization (e.g. # ER visits). Initially I plunged ahead and did the LPA and found that a two class solution was indicated by the Vuong-Lo-Mendell-Rubin and Lo-Mendell-Rubin Likelihood Tests (i.e the two class colution was superior to the one class solution, and the three class solution did not improve on the two class solution). At the same time the BIC argued for a single class. I became concerned with the inconsistency and (as I should have done originally) I investigated the "Poissoness" of the utilization variables. On convexity plots three of the four variables showed deviations from poissoness. I suppose my initial question is, "In the latent mixture model context of an LPA how robust are findings to violations of dispersion for count (poisson) variables?" I took the additional step of running LPA's with inflation parameters. This showed more consistent results in terms of the likelihood ratio tests and the BIC, and argued for the existence of three groups. The problem with this is that I cannot seem to test 3 vs. 4 groups in order to establish this classification scheme with more certainty. I am receiving several error messages and do not think I am going to get the model to run. So I suppose my next question is this,"Assuming that I do not get the 3 vs. 4 class model to run, would it be reasonable to acknowledge the existence of three classes, establish that the three class solution is a variation on the two class (k-1) model and move on with my analyses using two groups?"
bmuthen posted on Saturday, March 19, 2005 - 4:12 pm
It sounds like you needed the zero-inflated version of the Poisson model. But you say you don't get a solution for 4 classes - or perhaps you don't get a tech11 (LMR) result in the 4-class run; I am not sure from your message. If you have tried to use many random starts (say starts = 100 5) and still fail, it may be due to 4 classes being too ill defined in these data, and staying with 3 is the way to go. So my inclination would be to say yes to your last question.
Anonymous posted on Friday, April 22, 2005 - 10:02 am
Hello I have run a k-means cluster analysis and a LPA analysis on the same set of data. I found an 8 cluster solution that made sense. But, I only found 4 classes (5 classes would not converge) I've tried varied start values for the LPA, allowed variables to correlate within class, etc. in attempts to try to get the same number of groups across both methods.
My question is: should I expect the procedures to uncover the same number of classes/clusters or could I find different solutions because one method is uncovering latent groups/subpopulations and one method is working more on the observed level?
bmuthen posted on Friday, April 22, 2005 - 11:07 am
I think k-means clustering uses a more restrictive model that LPA - doesn't it also assume equal variances across variables (in addition to the assumption of equality of variances across clusters)? See for example McLachlan's new Wiley book on Microarray analysis. In Mplus you can add the equal variance restriction.
Anonymous posted on Friday, April 22, 2005 - 11:51 am
Thank you for your reply. You're correcct - in k-means variables should be roughly equal across variables. I was wondering if the differences in solutions was related to "level" of results (latent classes vs. observable clusters). In general, I haven't seen LPA models uncover as many groups as Cluster Analysis (mainly 2-4 classes found). I know that hierarchial cluster methods (e.g. Wards) let you 'see' the different cluster solutions & was wondering if this was similar to differences between k-means and LPA.
In MPLUS, the default is equal variance across cluster, correct? Is this relaxed with the WITH Statment to allow correlations between variables?
bmuthen posted on Friday, April 22, 2005 - 3:20 pm
I don't see the "level" of results as being different between the two approaches. You can "vizualize" the LPA results by using Mplus to plot the observed variable mean profiles for the different classes. You probably get more LPA classes when you hold variances equal across variables (try it). Yes, the Mplus default is equal variances across classes (but not across variables). And adding WITH statements relaxes the conditional independence assumption, allowing correlations. See also the Vermunt-Magidson article in the Hagenaars-McCutcheon Applied LCA book (Mplus web site refs).
Anonymous posted on Monday, April 25, 2005 - 8:03 am
Thank you again for your reply.
How do you hold the variances equal across variables? I'm not sure if this is needed, since I am dealing with T-scores, but the variances should differ by class.
Also, on p.121 of the MPLUS (Ver 3) manual, an example mentions that by mentioning the variances of the latent class indicators, the default equality constraint of equal variances (across classes) is relaxed. Will this allow for estimates of different variances within each class as well as different variances for individual variables?
However, to compare to k-means, which creates groups based on minimum w/in cluster error, shouldn't the MPLUS default be imposed?
To hold variances equal across variables, give the variable names which is how you refer to variances and use parentheses with a number inside to represent equality,
y1 y2 y3 (1);
holds the variances of y1, y2, and y3 equal.
In the example, the equality constraint on a regression slope is relaxed. If you want to relax the equality constraint on another parameter such as a variance, then you would mention that parameter.
If you want to compare to k-means, then you should place the same constraints as k-means does.
bmuthen posted on Monday, April 25, 2005 - 3:01 pm
You mention T scores so it sounds like you are standardizing your observed variables. This may be necessary for k-means clustering. I would, however, recommend not doing that in the LPA - and if the variables have different metrics then also not hold the variances equal across variables (only across classes).
Anonymous posted on Tuesday, April 26, 2005 - 1:36 pm
Regarding yesterday's discussion about comparisons between LPA & k-means - Thank you very much. You both cleared up a lot of questions.
Dr Muthen, you mentioned that I would probably get more LPA classes when variances were held equal across variables (4/22 note)-- and this did produce results very similar to k-means. (up to 8 classes found before nonconvergence)
However, when variances were allowed to vary across classes (but not across variables), there were fewer number of classes found (up to 4 classes found).
Why would relaxing an assumption lead to finding fewer classes? Thanks again for your assistance
bmuthen posted on Tuesday, April 26, 2005 - 2:02 pm
The more flexible the model is for each class, the better it can fit data and therefore the fewer classes you need. Your finding suggests that the "true" classes have different variances (across classes). If class-varying variances is the true state of nature and you force classes to have equal variances in your analysis, you have to have more classes in order to fit the data. Same thing if the true state of nature is within-class covariance - if you force classes to be formed with uncorrelated variables within class, then you need more classes to fit the data (this can be vizualized if you draw a 2-dimensional plot with a single correlated pair of variables - that 1-class data situation need 2 or more uncorrelated classes to be fit).
Anonymous posted on Wednesday, April 27, 2005 - 1:07 pm
Re: yesterday's conversation: Thank you very much. So, if I have this right, with LPA we may want to start with a restrictive model (essentially K-means) and systematically "relax" assumptions (allow different variances across classes, allow covariances w/in class) until we find the model that fits the best in terms of parsimony, interpretablity, and fit indices -- correct?
Is there any reference for this procedure or is it just standard practice? Thanks again -- this conversation has been most helpful.
BMuthen posted on Wednesday, April 27, 2005 - 5:58 pm
See Chapter 3 by Vermunt and Magidson, Latent cluster analysis, in Hagenaars and McCutcheon's book Applied Latent Class Analysis.
Anonymous posted on Saturday, May 21, 2005 - 5:29 pm
I am trying to specify a latent profile analysis with covariates. I want the the latent class variable to be measured by one set of variables, and class membership to be "predicted" using a *different* set of variables. Most of the examples in Chapter 7 of the User's Guide have the covariates ALSO affecting (or covarying with)the indicators of class membership.
I've tried this:
model: %overall% c#1 by Fsamed FsameBm AshrCC blauCCm blauCCv; c#1 on meanphd acadappl psoc pmale quant sameIB samephdB;
But MPLUS output tells me it is no longer allowed, and I should see chapter 9, which is about multilevel modeling and complex data ... I couldn't see the link. Can you tell me how to model this?
The BY option was used in Version 1 for latent profile analysis. It is no longer used. See Example 7.12 for the Version 3 specification. Just delete the CATEGORICAL option because your indicators are continuous and delete the direct effect u4 ON x; from the MODEL command.
Anonymous posted on Sunday, May 22, 2005 - 6:26 pm
Thanks for the quick reply, that worked! I am now wondering about how to get all possible contrasts for the multinomial logistic regression of the latent class variable on the covariates. I am working with 3 classes.
When I type:
c#1 on meanphd acadappl psoc pmale quant sameIB samephdB; c#2 on meanphd acadappl psoc pmale quant sameIB samephdB;
MPLUS appears to give me the effect that each of these covariates has on the probability of being in the stated class (1 or 2) relative to being in class 3. But what about the probability of being in class 2 relative to class 3? MPLUS would not allow me to make any reference to the "last" class (#3) at all.
c#2 on meanphd acadappl psoc pmale quant sameIB samephdB;
gives the probability of being in class 2 relative to class 3. You can't make reference to the last class. It is the reference class with coefficients zero. See Chapter 13 of the Version 3 Mplus User's Guide for a description of multinomial logistic regression.
Anonymous posted on Thursday, May 26, 2005 - 2:52 pm
oops, sorry, I wasn't clear.
c#1 on meanphd acadappl psoc pmale quant sameIB samephdB; gives the probability of being in class 1 relative to class 3.
c#2 on meanphd acadappl psoc pmale quant sameIB samephdB; gives the probability of being in class 2 relative to class 3.
How do I get the probably of being in class 1 relative to class 2? (In STATA, "Mcross" gives you such results).
You would have to make class 2 the last class to do this. You can do this by using the old class 2 ending values as user-specified starting values for class 3 in the run where you want to compare class 1 to class 3.
Hello, I am considering estimating a latent profile analysis using a set of behavior ratings measured on a 5-point Likert scale. An alternative to this would be treating the items as ordinal, and estimating a latent class analysis. Another alternative is to consider the items as nominal. Is there any empirical way to determine which parameterization is most appropriate? The BIC from the 3 models is: 289368.688 from the LPA of the ratings treated as continuous indicators; 290569.173 from the LCA of the ratings treated as ordinal/categorical; and 290953.619 from the LCA of the ratings treated as nomial (2 class solution for each model). Thanks for your advice.
I don't think you can make this determination by comparing BIC's. I would need to know more about these variables to answer this but basically if this is an ordered polytomous variable, it is best to treat it that way. If it does not have strong floor or ceilling effects, you may be able to treat it as continous. I am not sure why you would want to treat it as nominal.
Sandra posted on Thursday, October 20, 2005 - 7:41 am
I’m working on a latent profile analysis using seven scales which measure different life goals. I tried some mixture models where I allowed variables to be correlated within classes and with variances allowed to vary across classes.
My problem is that even in the two-class solution I receive a class in which one scale (a_aibz) has a variance of zero. This scale measures relationship goals and has already in the empirical data set a very small variance. Fixing the variance to zero in one class does not solve the problem, because Mplus tells me that the covariance matrix could not be inverted.
Is there anything I can do to avoid this? Shall I drop the scale from the analysis? If not, what is the reason for this problem?
I attach the output of the two class mixture solution with variances set free across the classes:
Your options are to increase the MITERATIONS as the error message suggests, hold the variance of the problem variable equal across classes, or remove the variable from the analysis.
As a rule, if it is necessary to show output to describe a problem, you should send your input, data, output, and license number to firstname.lastname@example.org. We try to reserve Mplus Discussion for shorter posts.
I would like to run a LPA on personality trait information we have collected. This data includes both probands and siblings. I would like to examine the LPAs but feel the siblings relations should be modeled. How would I best do this?
See the LCA section of my paper under Recent Papers on our web site:
Muthén, B., Asparouhov, T. & Rebollo, I. (2006). Advances in behavioral genetics modeling using Mplus: Applications of factor mixture modeling to twin data. Forthcoming in the special issue "Advances in statistical models and methods", Twin Research and Human Genetics.
I have downloaded this paper and am trying to recreate these models. However, I am new to LPA, and I am not accounting for the presence of two latent class variables (and two groups of individuals) in the model. Is there another resource you might recommend?
I am running a LTA for two time points on 10 likert-scale items at each time point and have arrived at a 4 class model (2 at each wave). I am attempting to run the model by freeing the variance to be estimated for each class separately. I am unsure if I have the correct model commands specified to request this.
%c1#1% [s3ptp1-s3ptp12*] ;
%c1#2% [s3ptp1-s3ptp12*] ;
%c2#1% [s4ptp1-s4ptp12*] ;
%c2#2% [s4ptp1-s4ptp12*] ;
Further, when I run this I receive the following error message:
THE LOGLIKELIHOOD DECREASED IN THE LAST EM ITERATION. CHANGE YOUR MODEL AND/OR STARTING VALUES.
WARNING: WHEN ESTIMATING A MODEL WITH MORE THAN TWO CLASSES, IT MAY BE NECESSARY TO INCREASE THE NUMBER OF RANDOM STARTS USING THE STARTS OPTION TO AVOID LOCAL MAXIMA.
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES.
I have two questions concerning LPA: 1) In the LCA & Cluster Analysis discussion bmuthen posted on Wednesday, February 08, 2006 - 6:29 pm that LRT can be bootstraped in M+4. How do i bootstrap the LRT (I assume it is not possible with the MLR estimator?).
2) In the output we got that IT MAY BE NECESSARY TO INCREASE THE NUMBER OF ANDOM STARTS USING THE STARTS OPTION TO AVOID LOCAL MAXIMA. We have 5 continious indicators with a range from 1 to 5, what is a good way to obtain starting values and are the starting values means in this case? Can you give an example?
2) See the "STARTS" option in the version 4.1 UG on our web site.
Kelly Hand posted on Tuesday, October 03, 2006 - 6:57 pm
I have run both a latent class analysis and a latent profile analysis using 5 ordinally scaled items (5 point scale of agreement with 3 indicating "mixed feelings") about mothers' attitudes to employment and child care to create a typology of mothers employment "preferences". I plan to test this typology with a subsample of qualiative interviews.
I have found that the LPA solution is easier to interpret and is a better solution (although they are both good). But am concerned that it may not be acceptable to use 5 ordinal items in this manner. Is this ok to do in your opinion?
Unfortunately the survey only used a very limited number of items about this topic so I am unable to include any more items or create a scale.
I have also tried to search for a reference to support this but have had no luck. If you think it is an appropriate approach to take do you have any suggestions for a reference I could include in my paper?
This boils down to the usual choice of treating ordinal variables as categorical or continuous. I think treating them as continuous, using linear models, is often reasonable unless you have strong floor or ceiling effects. I would however worry if the two approaches gave different interpretations - if they do, I would be more inclined to rely on the categorical version. I would check that I had used a sufficient number of random starts (STARTS=) to make sure you have obtained the correct maximum likelihood solution. I can't think of relevant literature here.
We would like to test four models (4 variables): 1) Variances are held equal across classes, covariances among latent class indicators are fixed to zero 2) allowed for class-dependent variances but constrained covariance terms to zero 3) allowed for class-dependent variances and held selected covariances equal across classes 4) allowed for class-dependent variances and allowed free estimation of selected covariance estimates within class
Are these the corresponding model-inputs?
Ad 1) %OVERALL% Ad 2) %OVERALL%
%c#1% y2 y3 y4 y5;
%c#2% y2 y3 y4 y5;
We have no idea how to write the syntax for models 3 and 4, respectively. May you help with an example for model 3 and 4?
For model 2 we get the message: All variables are uncorrelated with all other variables within class. Check that this is what is intended. Does the model 2 syntax correspondent to what is intended by hypothesis 2?
thank you for you help, I was successful in reordering the classes and thereby maintainig all other parameters. My last question is how to reorder (last class as the largest) a model with this structure:
What happens with the bootstrapped Lo-Mendell-Rubin Likelihood ratio when the last class is not the largest one (for this model and in general)?
Thanks again, this conversation has been most helpful.
I'd like to obtain an LPA but allow correlations/covariances within class to be nonzero. Is this the way to do it? E.G.: ... CLASSES = c(3); ANALYSIS: TYPE = MIXTURE ; MODEL: %OVERALL% MODEL: %OVERALL% y1 WITH y2 y3 y4 y5 y6 y7 y8 ; y2 WITH y3 y4 y5 y6 y7 y8 ; y3 WITH y4 y5 y6 y7 y8 ; y4 WITH y5 y6 y7 y8 ; y5 WITH y6 y7 y8 ; y6 WITH y7 y8 ; y7 WITH y8 ;
Thuy Nguyen posted on Wednesday, February 21, 2007 - 11:12 am
Yes, this will free the covariances within class while holding them equal across class.
anonymous posted on Thursday, March 29, 2007 - 11:41 am
I'm sorry in advance if my question appear naive, I am new to these methods in an geographic area were few "coaches" exist.
I trying to allow for conditional dependance (within class correlations) in a latent profile analysis of seven different variables. I found at least four different ways of allowing conditional dependance:
(1) Including within class WITH statements between all of my indicators. (2) Running a model with conditional independance and relying on modification indices to allow for partial conditional independance (including within class WITH statements between the variables that "could" be correlated according to the modification indices). (3) Doing a factor mixture model without within class BY statements (fixing the factor loadings to remain equivalent accross classes). (4) Doing a factor mixture model with within class BY statements (allowing for differential factor loadings across classes).
I believe that the main advantages of models 3 and 4 is that they result in less parameters beeing estimated.
However, I believe that the real "essence" of conditional dependance is more clearly captured by models 1 or 2. Am I right ?
Are there any other arguments or advantages and disadvantages of doing it one way or the other ?
1. Leads to an unstable model in line with the Everitt-Hand book that we cite under Mplus Examples - not recommended.
2. MI's don't work very well with mixture models, probably due to non-smooth likelihood surface - not recommended
3. Good idea; works well
4. Ok; not always needed beyond 3. Class-varying factor variances can be introduced instead.
anonymous posted on Friday, March 30, 2007 - 3:20 am
Thank you very much for this answer.
It clarify things a lot.
Could you please expand a bit on your answer to 4 (or suggest a reading on this topic). I'm not sure that I properly understand why the freeing up of within class factor variance would be equivalent to the model with free within class "BY" statements or why the more complexe model will not be needed past 3 classes.
Letting factor variances vary across classes is not the same as letting factor loadings vary across classes. However, I have found that a model with class-invariant loadings and class-varying variances often is suitable. I have tried several variations on the factor mixture modeling theme in my articles listed under "Papers" on our web site - see especially articles under the topics General Mixture Modeling and Factor Mixture Analysis.
If my goal is to do a LPA (with two classes) of 3 variables (XX, XY, XZ). After trying the classical model, I can restrict indicators variance to be equal within class. Then I can try a less retricted model by allowing the variances to vary between class.
Following on the previous discussion, if I want to try for conditional dependance, I should rely on a factor mixture model letting the factor variances (and maybe the loadings) vary across classes.
My question is how I can combine conditional dependance (factor mixture) with the previous modifications of equal wihin class variances (A) and of unequal between class variances (B) ? Can I use commands such as theses or is there any additional "twist" ? A: %OVERALL% f BY XX XY XZ ; [f@0]; %c#1% f; [XX XY XZ]; XX (1); XY (1); XZ (1); %c#2% f; [XX XY XZ]; XX (2); XY (2); XZ (2);
B: %OVERALL% f BY XX XY XZ ; [f@0]; %c#1% f; [XX XY XZ]; XX XY XZ; %c#2% f; [XX XY XZ]; XX XY XZ;
If theses commands are right, it would means that example 7.27 reflects a traditional LCA with conditional dependance, equal between class variances and unequal within class variances ?
I ran a LPA w/6 continuous indicators (values ranging between -2 to +5). Here's the dilemma:
The LMR indicates a 5 class model, and this makes substantive sense.
However, the AIC/BIC/ABIC values continue to decline (never rising) and i've tested this up to a 8 class model. BUT like a scree-test, the differences in IC values between models do decline greatly after the 5 class model.
In addition, the BLRT remains non-significant at every step/model.
No warnings were found and i did "start 500 20".
I'm in the process of correlating the variables (which I am not a fan off), but thus far, no resolve.
I'm satisfied with the 5 class model. In addition to substantive sense, it was choose it based on 1) LMR being & remaining non-significant after the 5 class model, and 2) the IC values begin to level off after the 5 class model. and what do i make of BLRT being non-significant at all steps? I plan on reporting BLRT, but indicating that it is potential limitation of the study? is this all sufficient?
Your statement that BLRT is non-significant for all classes confuses me. In a k-class run, BLRT gives a p value for a k-1-class model being true versus the k-class model. So, a non-significant result (p >0.05) says that the k-1-class model is acceptable. So your statement implies that the k=1-class model is acceptable as judged by BLRT. Is this what you mean? If so, I would think BLRT is not applied correctly because it would imply that your variables are uncorrelated.
If BLRT is correctly applied (no warning messages), that could be a sign of having a lot of power due to a large sample size, in which case I would rely on the substantive reasons for choosing number of classes.
Thanks for the quick replies. The sample size was large (2000+). However, there was one warning "to increase the number of random starts using the starts option to avoid local maxima". I got this warning after increasing starts (500 20, and 1000 20), but read that this warning is typically issued?
So the take messages are to rely on substantive reasons, report LMR & IC values for statistical support, and also report the the BLRT (being significant at each model) but that it is sensitive to large sample size (thus power)?
We have Y11 ….. Y1T, Y21 ….. Y2T, …………………..,Yn1 …. YnT; Yit is continuous and Yit=f(Xit) where “i” indicates unit and T is the Tth time period.
We want to extract the possible grouping using Y’s as indicators.
I believe our Panel-mixture analysis will be in the line of Latent-profile mixture analysis (with covarites) rather than Latent-cluster mixture analysis since Y’s are continuous. Am I right? …. However there is a serial correlation or at least it is likely to be so and we need to test that.
Q1. Could you kindly suggest any established research on Panel-mixture analysis (rho across the error terms has to be calculated)? Q2. Could we estimate the model using MPlus?
I'm doing a latent profile analysis (7 indicators) with covariates (4). I'm running models with conditional independance and models with conditional dependance (CD). For CD models, I rely on factor mixture models with class varying intercepts (only).
Is there any problems if I run these analyses with standardized variables (indicators and covariates)?
I would work with the raw data. I don't know why you want to standardize. If it is because the variables have large variances, I would rescale them by dividing them by a constant. A constant is not sample dependent as are the mean and standard deviation used for standardizing.
In fact, suppose that we already did the analyses with standardized variables following the suggestion of a colleague (because it made it easier to compare the latent classes). What kind of problems might it cause ?
When you standardize variables, you are analyzing a correlation matrix not a covariance matrix. This is fine if your model is scale free but not if it is not. One example of a model that is not scale free is a model that holds variances equal across classes. If a model is scale free, the same results will be obtained whether a correlation or covariance matrix is analyzed. If I were you, I would rerun the analysis using the raw data.
Thanks once again for this valuable resource and for the workshops you have conducted. I am attempting to estimate an LPA with four continuous indicators which are age variables ranging from (age) 5 to 40. The variables represent how old participants were when they reached each of four developmental milestones. Our analyses are attempts to identify sub-groups of individuals who progress through these milestones at different paces. Not an ideal way to model developmental phenomena, of course, but the best we can do with the cross-sectional data we have. My question is whether or not this seems conceptually and statistically reasonable (assuming the models fit well, etc.) and if you know of any other published data that uses similar (age) indicator variables in LPA? I'm a little concerned with the validity of our approach.
My statistician is helping me with a Latent Class analysis. We are looking at latent classes in a group of workers with low back pain. The variables we are using to distinguish between the classes are pain, functional status, depression, fear and some workplace factors. We used age, duration of complaint and time on the job as predictors of class membership. We know that pain, fs, depression and fear probably correlate so we added these correlations to the model. In the output I see that there is (amongst others) a significant covariance between pain and f.s. within the 1st class (in a 2 class solution). Estimates: 24.463 SE: 5.0079 ESt/SE: 4.816. How should I interpret this? Are assumptions violated?
We also saw in earlier analyses that a 4 class solution turned out to be the best fit.
The covariance suggests that among the members of class 1, there is a relationship between pain and functional status. If the correlation is negative, then its a relationship moving in different directions. If the correlation is not significant in class 2, or if its in a different direction then class 2, then that's a really neat finding and supports the contention that there is heterogeneity in your sample
Regarding your 4 class solution question, are you saying that in an earlier analysis without the covariates you found a 4 class solution fit best, but that after adding the covariates only the 2 class solution fit? Bengt notes that class fit will change when covariates are added, and he has advocated that you should consider using the solution when covariates are added.
The correlations are as expected. Somewhat different between the classes. IN a few cases present in one class and not in the other.
We haven't done the 3, 4, (and 5) class analyses yet. (In previous analyses the 6 class solution didn't converge.) We realised we should do the analyses with adding the covariates after reading Bengts opinion on it and to us his point makes sense. (Starting out with SPSS K-means, it's getting better all the time:-) We expect that again the 4 class solution will be best, since the individual membership doesn't change that much, but it gives great info on how the constructs fit together. I expect to find more heterogeneity in the four class solution. We were a bit worried about our n (approx. 400)when adding all these extras. We might want to look into a subgroup in our next step.
Note that whenever there are at least 2 latent classes, the observed variables will correlate. If in a latent class analysis you choose in addition to correlate variables *within* classes, saying e.g.
%overall% y1 with y2;
then this means that your y1 and y2 variables correlate more than their common influence from the latent class variable can explain - so it is like a residual correlation. Often this comes about due to similar question wording or variables logically tied to each other.
Note that this is not a model violation. Although the standard LCA assumption of "conditional independence" no longer holds, you are using a perfectly legitimate generalized latent class model.
OK thanks very much. This helps a lot. The variables seems to be logically tied together. The LCA shows that some do in certain classes and some don't, which is good information.
A different question. We are now looking into latent classes within a subgroup (from n=441 to n=183). Only those people that haven't returned to work at baseline interview are now included in the LCA. Same variables, same observed independent variables, but without the (residual?)correlations in the model. The 4 class solution now doesn't converge (minimum number in 1 class is 33). I expected the 3 class solution to be optimal because the " low risk class" seemed to overlap with those who had returned to work. And that's an easier variable compared to the 5 we've used to determine classes. Unfortunately we now don't get information on model fit. Is there a way to get around this? Or does it just tell us that the results should be interpreted with caution?
I would not expect a four-class solution to be optimal if you have basically removed one of the classes. I would expect the three-class solution to be better. You will not get any fit statistics if the model does not converge. Is this what you mean?
I also expected the 3 class solution to be the best fit.
Yes, that is what I mean. In the previous analysis (n=441) we also could get fit statistics for a model with 5 (optimal fit +1 class) classes. I was hoping to get it (for the 4 class model) in this analysis (n=183)as well. We changed the setting to 500 iterations, but that doesn't help. Well, it's a sensitivity analysis anyway.
OK that worked, thanks for that. When submitting a paper a reviewer might ask: Why 8000 iterations, any suggestions? By the way: it seems that the SE decreases.
Another question: One of the people in the team asked me what the main drivers for the class solution where, so we now have a description of what the classes look like and we know that the total model has a better fit in the 3 (and the 4) class solution, but which factors predict or drive the class membership. "Predict" might be a bit confusing since we also are using some counfounding variables as "predictors" . We where think of using a multinomial logistic regression to get the estimates. Do you have any other sugggestions, perhaps how we should model this using M-Plus?
It is not 8000 iterations. It is 8000 sets of initial random starts and 800 solutions carried out completely. Read in the user's guide under STARTS. You may not need that many. You should not compare standard errors from a local solution to a replicated solution.
The model is estimated with the objective of conditional independence of the latent class indicators within each class. If you want to use covariates to predict latent class membership, you can regress the categorical latent variable on a covariate or set of covariates.
OK thanks, it's now quite obvious tha tit would be useful to do the course next year :-). You have been great help.
Vilma posted on Tuesday, November 27, 2007 - 6:35 am
I was running LPA with 3 continuous indicators. My sample is 210. According to fit criteria, it seems that could be 5 profiles, but the one of the profiles has only few people. My choice was 4 profiles (it makes more sense from theoretical point of view). These profiles differ from each other. The reviewers give me a hard time about LPA with a small sample and only 3 indicators. Basically, they said that I cannot do with 3 indicators 4 profiles (it is stretching data too far). Might be it is the truth. But could I check somehow that. Or should be better to have more indicators?
I think what you are trying to do is possible, although the solutation may not be very stable. The classic Fisher's Iris data had n=150 with 4 continuous indicators and 3 latent classes - see the Everitt & Hand (1981) book. That model did not use the LPA assumption of zero correlation within classes and so is harder to fit. Perhaps the reviewers are thinking LCA with binary indicators in which case only 2 classes can be obtained with 3 indicators.
To convince the reviewers (and yourself) you can do two things. You can use the Mplus Tech14 facility to test for the number of latent classes. You can also use the Mplus Monte Carlo facility to simulate data with exactly your parameter values and see how well or poorly the model is recovered.
Having more indicators, however, certainly helps.
Vilma posted on Wednesday, November 28, 2007 - 12:49 am
I have a question related to variable types (continuous, categorical, count) within LCA/LPA. I'm working with 11 variables that are neuropsychological test subscales. These subscale scores are really sums of successes on a number of binary items (eg remember name y/n). The subscale variables range in levels from 2 to 37 and some are very skewed. I fit an initial LCA model with binary variables, dichotomising the subscale scores at the median values in this sample. A 4-class model seemed to fit the data well (with interesting results) but the modelling approach was criticised for not using all the information available in the data. I then tried modeling all the variables as count variables but ran into problems with the variables with fewer than 3 levels. A mixed categorical and count variable model ran without errors but the results are difficult to interpret (variables are on pretty different scales)and not terribly interesting, plus I have concerns with model fit (one class with very low probability and Lo-Mendell Rubin and BIC fit results conflict).
In short, I’m more comfortable with the initial binary model. My question, then, is whether I really should be concerned over potential loss of information in the binary classification model – how much value does using the full scales really add? Could my binary model findings be invalid? Apologies if this is obvious; I’m new to latent variable modelling and Mplus.
No obvious decision here. Seems to me that the reduced-information binary approach is fine as long as the 11 subscales are a good summary. You could finesse it by using ordered polytomous representations of the number of successes (e.g. low, medium, high). Or you could stay with binary items, but go fancy by working with the original, total set of binary items used to create all of the 11 subscales. That large original set can be used for (1) LCA, or (2) factor analysis to see if 11 dimensions - or fewer - turn out, and then perhaps do LCA on the factors (either in 2 steps, or better still, by having a mixture for the factor means).
Unfortunately I don't have access to the original item-level questionnaire responses, only the 11 aggregated subscale scores. Am sure there would be an interesting underlying factor structure as many of the questions could measure multiple domains of cognition. May aim to look at this in a replication analysis!
Are these results interpretable, that is, do they suggest going with 2 profiles, 3 profiles, or continuing until Tech14 is no longer significant? More to the point, do these divergent results suggest that there is something fundamentally wrong with our data or input specifications?
I have found the proportions of membership in each class under the output for the LPA, but I was wondering how I could find out where each case was placed among the classes. Is there specific syntax for output I could request? Thanks!
Hi, I am performing a lca with items measured on a 6 point likert scale. my number of observations is for one sample 70, for another sample 170. How can I check via monte carlo if the model is appropriate (you stated in an answer above:You can also use the Mplus Monte Carlo facility to simulate data with exactly your parameter values and see how well or poorly the model is recovered.)
You can use the parameter values from an LCA as population values in a Monte Carlo study with sample size 70 for the parameter values from the analysis of the sample with 70 observations and sample size 170 for the parameter values from the analysis of the sample with 170 observations. Use mcex7.6.inp as a starting point.
to check for power I ran a monte carlo with nobservations=400 and nreps=500. here are the results for % Sig coeff
V25 ON LOY_ACC 0.054 REPURCH 0.106 AUSDEHN 0.251
the interpretation gives me some headache: for loy account and ausdehn: is a non sign path, and shows a low power; so increase of sample size might help - this is clear for me - is this right? for repurch: is a sign path, but also low power: this is puzzling me.
Shouldn't be a sign. path also have a high power or is the positive path only 10.6 % of the replications and so nearly a artefact? And if there is the case that there is a non sign path in the sem but a power of more than 0.8? Would that then also be one case in the 20% of not rejecting H0 although it is wrong?
I would be really glad if you could shed some light on that.
The method we proposed is used to assess the power of a single parameter not a set of parameters.
It sounds like you are making a mistake in your setup. Please send your output and license number to email@example.com.
Anne Chan posted on Monday, September 21, 2009 - 4:23 am
Hello! I am doing a study which compares boys and girls in relation to their motivation, parental support and their learning outcomes. I have two questions:
1) I applied LPA analysis to classify students into different motivational groups. I included Gender and Parent Support as the covariates, the 6-class solution is perfect, both in terms of model fits and theoretical meanings. However, if I run the LPA without covariates, no theoretical meaning solutions can be generated. How should I interpret these results?
2) I am planning to save the LPA class membership (with Gender and Parent Support) of individuals and conduct further analysis to study the differences between boys and girls, both within and between classes. However, I am still a bit confused of how to understand having gender as a covariate in LPA analysis. Is it appropriate for me to use Gender as a covariate in LPA, particularly the goal of my study is to compare the two genders? I mean, if gender is included in the LPA, then gender will affect the classification result, and is it methodologically inappropriate to use this “biased” classification to conduct subsequent gender comparison? Or, instead of thinking the classification is “biased”, it is actually more robust in using Gender as a covariate, as it can more accurately reflect the data?
1) Differences in latent classes when using and not using covariates usually is a sign that there are direct effects of the covariates onto the outcomes, not only indirect effects via the latent class variable. Try exploring direct effects (you cannot indentify all of them). Although that may move you away from your favorite solution, your 2 runs (without and with covariates) may agree more.
2) My opinion is that if Gender influences class membership you are fine including it in the model - the estimates will be better. The same is true for factor scores in MIMIC models.
However, doing analyses in several steps is not always desirable, particularly not with low entropy. Why not do your "further analysis" as part of this model?
For related topics, see also
Clark, S. & Muthén, B. (2009). Relating latent class analysis results to variables not included in the analysis. Submitted for publication.
under Papers, Latent Class Analysis on our web site.
Anne Chan posted on Thursday, September 24, 2009 - 4:20 am
Thanks a lot for your kind suggestion. As a follow-up of question (1), I will explore the direct effects. May I ask how can I do it? Can you please kindly point me to some examples or references? Thank you very much!
I figured I could justify a 3-class solution given close to sig. LMR but the means for the 3-class solution are providing almost no differentiation among the indicators for one relationship. I am not expecting much variation in terms of shape but I think at least two levels is more accurate. LPA for the six indicators for that relationship alone provides fairly clear (again LMR only) 2-class solution.
The means for the 4-class solution provide some differentiation among the indicators for that relationship and a more interpretable set though there is a small group (n = 10). I recognize the small N overall and in one class and the possibility the LMR tends to overestimate (Nylund etal 2007), but I am considering using the 4-class solution based on substantive meaning. Could I please have any insights you may have? Thank you
The non-significance (p=0.0577) for LMR in the 3-class run says that 2 classes cannot be rejected in favor of 3 classes.
Personally, I tend to often simply listen to what BIC says, in a first step. In your case it suggests to me that because you don't have a minimum BIC you may not be in the right model ball park. Perhaps you need to add a factor to your LPA ("factor mixture analysis") and then you might find a BIC minimum.
What do you mean by "add a factor"? I am basically familiar with how FMA integrates factors and classes but did you mean something specfic other than "try FMA"?
I do question whether a latent variable approach is appropriate here. The dimensions are rather skewed in the positive direction for one relation and mostly bipolar for the other. With a relatively small sample for LCA this is probably why a 2-class solution emerges.
Also Ive run separate LPA for each relationship to look at different class combinations as across relationship patterns. With this I get a clear 2-class solution for one relation and clear 3-class for the other but again with these there is no lowest BIC, BLRT is not useful (just .000), and LMR is my only solid indicator with more definitive p-values this time.
So if I continue to not find any lowest BIC is that evidence that latent variable approach may not be appropriate even if the LMRs are suggesting reasonable classes?
I did find that k-means cluster analyses provided an almost identical set group as the 4-class run (means and proportions) but not the 3-class run.
Yes, I meant try FMA. Such as a 2-class, 1-factor FMA where the item intercepts vary across the classes (factor means fixed for identification). So you could try 1-4 classes and see if you find a BIC minumum (where 1 class is a regular 1-factor model).
Thanks Linda, What would be the reference so I can find it. By the way, I just realized that Matt Thullen did ask another question in his last post. I just wanted to make sure that my posting did not "erase" this question. Thanks again
I'd like to build my doctoral thesis on Latent profile Analysis, but I don't know whether I have enough statistical power to identify all relevant classes. So I'm looking for any recommendations about sample size in Latent Profile Analysis. Are there any articles discussing that issue? Thank you very much in advance and best greetings from Germany...
Lubke, G. & Muthén, B. (2007). Performance of factor mixture models as a function of model size, covariate effects, and class-specific parameters. Structural Equation Modeling, 14(1), 26–47.
Lubke, G.H. & Muthén, B. (2005). Investigating population heterogeneity with factor mixture models. Psychological Methods, 10, 21-39.
Nylund, K.L., Asparouhov, T., & Muthen, B. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling. A Monte Carlo simulation study. Structural Equation Modeling, 14, 535-569.