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Mplus Discussion > Growth Modeling of Longitudinal Data >
 Sanjoy Bhattacharjee posted on Tuesday, August 15, 2006 - 5:21 pm
Dear Professor Muthen

I have a cross-sectional (represented by i) time-series (represented by t) data, loosely speaking Panel data model to estimate. In particular, I have the following model;
Yit = max{0; Yit-1 + Xit + alpha(i) + epsilon(it)};
where Yit is the dependent variable or the variable of interest, Xit is a vector of explanatory variables, alpha(i) is an individual effect, and epsilon(it) is a random error.

We call it dynamic because Yit is a function of its previous value, and nonlinear since Yit can take only non-negative values.

My question is

Q1. Could we solve this model with MPlus, and could you suggest me the reference?

Thanks and regards
 Bengt O. Muthen posted on Tuesday, August 15, 2006 - 5:45 pm
You may want to take a look at the 2001 Olsen-Schafer article in Journal of the American Statistical Association, where they discuss censored-normal modeling and two-part (semicontinuous) modeling. Both approaches can be handled by Mplus. Examples are in the User's Guide - see Version 4.1 on our web site.
 Sanjoy Bhattacharjee posted on Tuesday, August 15, 2006 - 7:27 pm
Dear Professor Muthen

Thank you a lot. I browsed quickly through the Olsen and Shafer’s article; “A two-part random-effects model for semi-continuous longitudinal data”, JASA: Jun 2001. Vol. 96, Iss. 454; p. 730.

It’s a fantastic article, and especially given the nature of our Y's, semi-continuous modeling would be more appropriate rather than treating them as censored data (defined typically). However I am not very sure about the way we can handle endogeneity using their model. Let me go through it once more.

 Sanjoy Bhattacharjee posted on Thursday, October 05, 2006 - 1:17 pm
Dear Professors

I have a question in regards to Olsen-Schafer 2001 JASA article on two-part Semi-continuous model vs. MPlus example 6.16, which you have suggested to handle Olsen-Schafer model. I believe, we can make the above code more general combining MPlus example 6.10 with 6.16. By doing so, we can incorporate the impact of time-varying and time-invariant covariates on continuous dependent (Y) variables and categorical indicators (U).

I f I got them correct, Olsen-Schafer model is a regular (from Econometric standpoint) “Panel data type” extension of Duan and Manning model, while MPlus code seems to suggest something different, particularly if we combine 6.10 and 6.16. For example, why would we need intercept and slope growth factor regressed separately on covariates rather than doing a set of regular panel-data type regression of Y’s on X’s and another set of U’s on X’s, when the two set of regression assumed to be correlated. Could you please help me to resolve the confusion?

Thanks and regards
 Bengt O. Muthen posted on Friday, October 06, 2006 - 6:59 pm
I agree with your first paragraph.

By "panel-data" type modeling, perhaps you mean auto-regressive modeling such as

y3 on y1 x;
y2 on y1 x;

The growth model - with its random effect growth factors - makes it possible to identify a correlation between the 2 parts/processes (y and u) that is over and above that generated by the 2 parts having common x's. In regular Duan regression that correlation is not identified - and the 2 parts can be done separately.
 Sanjoy Bhattacharjee posted on Monday, October 09, 2006 - 4:30 am
Dear Professor Muthen

Thank you very much for pointing out the differences.

By "panel-data-Econometrics" type modeling we particularly mean

1. Y_it = constant + betas*X_it + error terms (we may have some time-invariant X's) and we estimate the betas and the constant. If we have K number of X-variables in our model, we estimate ONLY K-number of betas (for all Y 's). Unlike MPlus example 6.10, we do NOT separately regress Y on X-vector (let's assume which is K-dimensional) for every time period and get T*K number of betas, where T is the total time period.

2. we do NOT assume mean vector of X is increasing(decreasing) at some rate, which in turn inducing an increase(decrease) in the mean of Y's. However, somebody may have time trend in his her data set.

Thanks and regards
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