

Absense of local independence 

Message/Author 

Sanjoy posted on Saturday, June 25, 2005  12:24 am



Dear Professor ...this is my model I have two binary(0/1) outcome variables, Y1 and Y2. I am planning to fit LCA along with direct effects of covaraites(X) on Y's ... the two Y's are in effect severely correlated, since both indicates some sort of economic choice decision (rho is almost =0.8)... I have some questions ...I'm sorry, actually they are many 1. Is there any way to check and deal with local DEPENDENCE in Mplus when the outcome variables are categorical (I suppose with continuous variable "WITH" command can handle this)... mine is version 3.12 2. in case we fail to deal with localdependence in Mplus, how severely it will affect my results (I mean in terms of peer reviewed standard Journal acceptance) apart from the possible problem of overfitting number of classes 3. in Mplus, can we do parametric bootstrapping (McLachlan 1999) and MCMC (Bensmail 1997) for determing number of classes and their forms I was going through "LatentGOLD"'s technical appendix ... 4a. there they start with EM and when they come close enough to final solution they switch to NRaphson. Thus they "combine the the advantages of both algorithm, that is, stability of EM even when far away from the optimum and speed of Nraphson when close to optimum" ... 4b.besides ML they also use MAP (maximum posterior) for model parameter estimation ...the advantages of MAP over ML is that "it prevents the occurence of boundary or terminal solution: probabilities and variances cannot become zero" ...I'm just curious about the above two claims ... can you cast some light on these I'm sure in MPlus we calculate posterior class memebership probabilites ... however, I could NOT find (I could have overlooked it though) any corresponding equation in our Mplus Technical appendix (chapter 8) ... is there any reason behind such thanks and regard 


This will be answered after July 1. 

Sanjoy posted on Tuesday, June 28, 2005  1:40 pm



Ok Professor, that would be equally good to get the answer around July 1st,... in between I have read MPlus Example 7.16, "LCA with partial conditional independence" and the article written by Qu, Tan & Kunter, Biometrics, 1996, 797 810 ...it looks like there are some ways to handle the issues of nonindependence even when the manifest/outcome/dependent variable are categorical ...I have couple of questions 1. can MPlus fit Qu, Tan and Kunter model for single categorical latent varaible but with more than two latent classes and when the categorical variables are ordinal (rather than binary)...I have tried but did NOT work …what about the testing of nonindependence 2. I was reading your "Beyond SEM", Behaviormetrika article(equation 28 and 29), same thing is also there in MPlus technical appendix (eq. 150 and 151, chapter 8) ...where you are introducing CONTINUOUS latent variable(eta) and other covariates (X) as explanatory variables for Categorical variable (U)) ... a) I could NOT find any error term in the equation for eta...why is it so? b) you say the model is good for "growth modeling" ... I have a hunch that they could also be used in my situation , where U1 and U2 are two binary indicator, U1 comes first in the survey question, U1 and U2 does share similarity in the sense both deals with economic choices ...can you give us some suggestion Thanks and regards 

bmuthen posted on Sunday, July 03, 2005  4:40 pm



1. Yes. If you have a problem, send to support. 2. a) The dependent variable u* is the logit, and in line with regular logistic regression the RHS does not have a residual. Maybe the notation makes you think that u* is a continuous latent response variable. 2b) Perhaps. 

Andy Ross posted on Thursday, December 01, 2005  7:49 am



Dear Prof. Muthan, I am attempting to run a 3 class LCA with four manifest variables but I also want to allow for local dependence among three pairs of variables. Could you please tell me how to set this up in the modelling command? Using example 7.16 (p.143 of the users guide) I created the following input file: VARIABLE: NAMES ARE u1 u2 u3 u4; CLASSES = c (3); CATEGORICAL = u1 u2 u3 u4; ANALYSIS: TYPE = MIXTURE; STARTS = 100 30; STITERATIONS = 50; MITERATIONS = 5000; MODEL: %OVERALL% f by u1 u2; g by u1 u4; h by u3 u4; (u1u4 are ordinal variables with 3 to 4 levels each) However the results seem to suggest this is incorrect, i.e. the model fit is much worse than the local independent model. Many thanks Andy 


Three classes cannot be identified with only four latent class indicators. 

Andy Ross posted on Tuesday, December 06, 2005  3:40 am



Dear Prof. Muthen Many thanks for your reply. I fear i may not have been very clear in my original message. The manifest variables are not dichotomous. Instead u1u2 have three levels, and u3u4 four levels. My understanding for calculating degrees of freedom in this instance (and without modelling local independence) is: DF = (IJKL1)[(I+J+K3)T1] DF = 14332 DF = 111 However I must admit i am unsure about calculating degrees of freedom when modelling some local dependence. I was assuming that an initial 111 would be enough for this. Could you confirm whether this is correct, and also how i would model local dependence among three pairs of these variables in mplus. Many thanks for your support. Andy 


Actually you were clear. I just did not see the last sentence. You have computed your degrees of freedom correctly. It is a necessary but not sufficient condition that the degrees of freedom be greater than zero. Check the following paper to see if the identification of four classes with three polytomous indicators is discussed: Goodman, L.A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215231. You may have hit a local solution in your analysis. How many of the 30 completed runs have the same loglikelihood? Also, you may want to try adding only one residual covariance at a time. Note that in Example 7.16, this was done in a classspecific model part not in the overall model. If you need further help, please send your input, data, output, and license number to support@statmodel.com. 


Hi Drs. Muthen, When mixture modeling in Mplus, how can you request Mplus to do the Bayesian maximum posterior (MAP) estimation and not maximum likelihood estimation? I have read that this procedure helps when you get very high or very low (0 or 1) estimated probabilities in latent class analysis (ie. when you have boundary issues). Thanks, Brent 


Do you mean estimating values for continuous latent variables in mixtures? Only EAP is available currently, not MAP. If you have a reference for what you refer to, please let us know. 

Li Lin posted on Tuesday, March 19, 2013  1:06 pm



Hi Drs. Muthen, I hesitate to ask following question, but I read one of your papers on difference between Mplus and IRTPRO, so I hope the question is not too inappropriate. I have run a same CFA model in both Mplus and IRTPRO, which is a continuous latent variable is measured by a set of ordinal categorical variables with 35 points scores. The LD statistics were so different in terms of determine what are the worst LD pairs. For one pair, Standardized LD X2 Statistics was 70 (compared to 10 as cutpoint) in IRTPRO, but Residual Correlation was 0.09 (compared to .2 as cutpoint) in Mplus. Why is the huge disagreement? Thanks, Li 


Please send the two outputs and your license number to support@statmodel.com. 

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