

Dynamic Nonlinear Panel data 

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Dear Professor Muthen I have a crosssectional (represented by i) timeseries (represented by t) data, loosely speaking Panel data model to estimate. In particular, I have the following model; Yit = max{0; Yit1 + 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 nonnegative values. My question is Q1. Could we solve this model with MPlus, and could you suggest me the reference? Thanks and regards Sanjoy 


You may want to take a look at the 2001 OlsenSchafer article in Journal of the American Statistical Association, where they discuss censorednormal modeling and twopart (semicontinuous) modeling. Both approaches can be handled by Mplus. Examples are in the User's Guide  see Version 4.1 on our web site. 


Dear Professor Muthen Thank you a lot. I browsed quickly through the Olsen and Shafer’s article; “A twopart randomeffects model for semicontinuous 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, semicontinuous 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. Regards Sanjoy 


Dear Professors I have a question in regards to OlsenSchafer 2001 JASA article on twopart Semicontinuous model vs. MPlus example 6.16, which you have suggested to handle OlsenSchafer 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 timevarying and timeinvariant covariates on continuous dependent (Y) variables and categorical indicators (U). I f I got them correct, OlsenSchafer 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 paneldata 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 Sanjoy 


I agree with your first paragraph. By "paneldata" type modeling, perhaps you mean autoregressive 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. 


Dear Professor Muthen Thank you very much for pointing out the differences. By "paneldataEconometrics" type modeling we particularly mean 1. Y_it = constant + betas*X_it + error terms (we may have some timeinvariant X's) and we estimate the betas and the constant. If we have K number of Xvariables in our model, we estimate ONLY Knumber of betas (for all Y 's). Unlike MPlus example 6.10, we do NOT separately regress Y on Xvector (let's assume which is Kdimensional) 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 Sanjoy 

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