

Effect of correlations between growth... 

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Anonymous posted on Thursday, June 24, 2004  12:51 pm



I am specifying a multivariate LGC model with two variables measured at the same 5 time points. When I estimate the growth parameters as two separate models (i.e. model 1 for variable A and model 2 for variable B), I get different parameter estimates than if I estimate them in the same model. This doesn't make sense to me as the sample sizes are exactly the same i models 1 and 2 and I have no regressions between slopes and intercepts, only covariance paths. Any ideas why this is happening? Patrick Sturgis 


If you want the results to be the same, you would need to correlate each observed variable in each process with the observed variables in the other process. For example if the processes are a and b, you would need to correlate a1 with b1, b2, b3, b4, and b5; a2 with b1, b2, b3, b4, and b5, etc. 

bmuthen posted on Thursday, June 24, 2004  3:41 pm



Often when doing joint growth modeling of two concurrent growth processes, the two processes need to correlate not only via their growth factors but also via their concurrent residuals. The betterfitting the joint model is, the closer the results are likely to be to the model for each process. 

Anonymous posted on Thursday, June 24, 2004  5:05 pm



Thank you for prompt replies. Can I take it, then, that the separate model for each process is the best approximation of the true growth function? The reason I ask is that in the models fitted separately, I obtain nonsignificant quadratic term for one of the growth processes and nonsignificant variance for both the slope and the quadratic parameters. When I fit them in the concurrent model, these all become signficant which makes more substantive sense but does not fit so well. On a related matter, I am actually modelling British election panel data and am fitting growth curves for intended vote for each of the 2 main parties (if you are unfamiliar with UK politics, thinks of this as equivalent to Republican and Democrat). I have 2 questions about doing this: 1. is there a problem in that the 2 variables come from the same vote choice question and are, therefore, not independent (i.e. if you vote democrat, you can't also vote republican)? 2. How should I interpret the intercept and slope parameters in this instance? The intercept is zero, due to the model paramerterization for categorical outcomes but can I take the slope to be the growth in probability of voting for each party over the period of the panel? Many thanks, Patrick 

bmuthen posted on Friday, June 25, 2004  3:15 pm



Let me see if I understand this. You have 2 processes  let's call them y and z. Are you saying that when y_t = 1 as opposed to 0, z_t = 0 as opposed to 1? If so, there is really only one variable (one process). But I may misunderstand you. Regarding the question in your first paragraph, if you have a wellfitting model for the joint processes, it can give better estimates for each process if the model is correct  this is due to using more information (crossprocess info). But if the joint model is somewhat misspecified, you might do worse. 

Anonymous posted on Friday, June 25, 2004  5:14 pm



With regard to the first point, you could be 0 on both y and z simultaneously but not 1 on both y and z simultaneously. this is because y = democrat vote, z = republican vote, leaving x = 1 for other parties for which no process is being explicitly modeled. 

bmuthen posted on Sunday, June 27, 2004  10:20 pm



I see. Then it sounds like there is one process which has an unordered categorical (nominal) outcome with 3 categories. Is that right? 

Anonymous posted on Monday, June 28, 2004  9:57 am



Yes, I suppose that would be the best way to conceptualise it. Is there a way of modeling this kind of nominal outcome variable via growth modeling? Patrick 

bmuthen posted on Monday, June 28, 2004  4:13 pm



I am not familiar with literature on nominal growth modeling. But it seems possible to try this out in Mplus Version 3. One way to do this is to consider twolevel modeling with time points nested within individuals (so the id variable is the cluster variable). Because Mplus does not yet allow for type=twolevel with nominal outcomes, you can use type=twolevel mixture where you fix threshold parameters at + and minus 15 to set the latent class variable c to be the same as your nominal (3category) outcome variable. Then you can have 2 (only 2 since the 3rd category has coefficients standardized to zero) random intercepts that vary across individuals, and are correlated (correlating the processes in this way), and you can regress c#1 and c#2 on a time variable (fixed slopes for simplicity). So a bit complicated, but doable it seems. 

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