Hi, I am in the last year of my PhD and I am thinking to purchase Mplus to test a model for my thesis. My model consists in 3 latent variables (X,Y,Z) each of them related to 3 observed variables. I want to test if the latent variables follow a specific order, say X->Y->Z->X. The problem is that the variables were observed in 3 successive time points, so we actually have 9 latent variables (X1,Y1,Z1,X2,Y2,Z2,X3,Y3,Z3 ), and what we want to test is:
I would like to ask if Mplus can test a hypothesis like that and how can I start doing it. Also, what are the implications when the latent variables are correlated (in my case X1, X2, X3 are the same variable measured at different time points)? Since each latent variable has 3 indicator variables (9x3=27 parameters), and there are 9 relations between the latent variables, we have a total of 27 + 9 =36 parameters to be estimated. Are there any parameters that should be fixed, or can I let them all be free? I would really appreciate your help. Thanks
bmuthen posted on Monday, February 07, 2005 - 11:05 pm
You want to first test your measurement models, letting the factors correlate freely (not imposing the orders you gave). And you want to start that by doing it for each construct at a time, including all 3 time points. Here, you may want to test time-invariance of loadings. So build up the model stepwise from its components.
Dear bmuthen, I think my model is a bit more complicated. Each factor or latent variable represents a pathology. The idea is to test a hypothesis that postulates sequential pathological changes, so it doesn't make sense to test a different model for each time point. The hypothesis says that, for example, someone with pathology X at time t will have pathology Y at time t+1 and then will suffer pathology Z at time t+2, after that going back to pathology X at time t+3. Is there any way of testing if my latent variables follow a specific order or if they are just randomly occurring? Many Thanks
bmuthen posted on Wednesday, February 09, 2005 - 4:45 pm
You still want to test your measurement model first. I am not saying that you should stop there. When that's settled, you go on to your tests of the paths for the latent variables - and the testing of the paths that you want to do appears feasible statistically and reasonable given the time ordering that you have.
Thanks for your responses. I still don't understand how I have to do it.Could you please recomend me a manual or book that could help me start with Mplus?
bmuthen posted on Thursday, February 10, 2005 - 11:49 pm
Sound like a general SEM book would be useful - see the reference to the Bollen book under Continuous outcomes, SEM on our web site. Or, for a more introductory treatment, the Kline book. Then, the set of Mplus examples in the User's Guide will be easily understandable.
Anonymous posted on Friday, February 11, 2005 - 7:48 am
I am using Mplus to fit a LC model. I have 12 binary indicators and have tried to specify 2,3, and 4 classes as alternative possible solutions. From the BIC value, the 3 class solution seems to be the best(smallest BIC). I would also like to assess the difference between the models, I have looked at –twice the difference of the loglikelihood (-2LL, as recommended). This difference was 177 between the 2 class and the 3 class models, with a p-value of 0.0008 suggesting the 3 class model has significantly improved the fit. When I however, looked at –2LL between the models with 4 and 3 classes the difference in –2LL is 54, the p value was 0.36 suggesting no significant improvement in the fit was achieved by specifying 4 classes. My problem is: from what I understand that –2LL difference follow a Chi square distribution, to test its significance one would compare that value with a critical value from the Chi square table under a pre-specified value alpha(0.05 say). When looking at the difference of 54 at 13 DF (difference between the number of parameters in 3 and 4 class models) this value seems to be much greater than the tabulated value of 22.36. If that is correct then one would assume the difference is significant at the 5% level?. I am not sure what I am missing here? I guess I might be missing a crucial point!. I very much appreciate your assistance!. Many thanks .
bmuthen posted on Friday, February 11, 2005 - 2:16 pm
Chi-square of 54 with 13 degrees of freedom does not have p=0.36 but p less than 0.001, so this would be significant. However, -2LL is not chi-square distributed when comparing models with different number of classes because your nested model has a parameter on the border (class prob = 0). This is why Mplus offers Tech11 - the Lo-Mendell-Rubin test. Nevertheless, -2LL can be used in a rough sense, as a descriptive measure. Note also that the sample-size adjusted BIC that Mplus gives has been shown useful.
Anonymous posted on Monday, February 14, 2005 - 7:38 am
Thanks very much for your response to my query on 11/2/05 regarding the change of 54 on 13 DF and different number of classess, that was helpful, further explanation is however requested if you don't mind!. I did use Tech 11 and the Lo-Mendell-Rubin test; the change of 54 I equired about was based on that, would the fact that the 54 is the 2*change in the Loglikelihoo of Tech 11 affect your previous answer to my query?, second, if not I think I am not clear about what you mentined as "nested model has a parameter on the border (class prob = 0)". I appreciates any further explanation here or a suitable reference. Most grateful for your hepful suggestions!.
The difference in degrees of freedom between the 3 and 4 class models does not change depending on the test used. See the following reference for a discussion of parameters on the border:
Lo, Mendel, & Rubin (2001). Testing the number of components in a normal mixture. Biometrika, 88, 767-778.
Anonymous posted on Tuesday, February 15, 2005 - 7:11 am
Indeed it doesn't, I haven't said it does in my query, 54 is: 2*change in the loglikelihood, the Lo-Mendell&Rubin loglikelihood used by Tech 11. I guess this makes my question still unanswered. Nonetheless many thanks for your time and for the reference!.
There is no preference for raw versus standardized coefficients based on the estimator being used. If the signficance of raw and standardized coefficients don't agree, I would be skeptical of claiming significance based on only one of them. Unless you have a reason for using standardized coefficients, I would use raw coefficients.