We have a time-series cross sectional data set, where the error terms need to be decomposed in the following manner; e(it)=u(i)+v(t)+w(it), where u(i) is the spatial error, v(t) is the temporal error and w(it) is the remaining residual or idiosyncratic error ...
Is there a way we can OUTPUT the three different errors which we use to calculate the variance of e(it)?
One of our final intention is to check the behavioral distribution of u(i) and v(t).
Could you kindly suggest me some references in this regards, and could we estimate the model using MPlus
Yes, this can be done in Mplus. I assume you have deemed this model identified; it seems like it is because all it does is to correlate the e residuals via the common source u. To do this in Mplus, you have to first define a factor u(i). In general, to define a factor you simply say, e.g.
I assume v(t) are constants, varying across time, but not across individuals. That changes the means of y over time which is the default. W(it) is the new residual. If y(ti) is your observed outcome, you then say
Thank you very much for the reply. It's very assuring to know that I can do it with Mplus. I was wondering how to handle the problem, since in econometrics we usually don't deal with this type of problem, and in fact no econometric software (to best of my knowledge) handles the problem the way we have to do for our paper. The closest I could do, for example with SAS or LIMDEP, is to fit a two-way (multi-way) random effect model.
Yes v(t) are constants, varying across time, but not across individuals.
to support our work we have to analyze the distribution of error terms (u(i) and v(t)) ... we have Y(s,d,c) observed over t time periods, where Y(.), a continuous variable is function of time only and "s" stands for State, "d" for special district and "c" for counties ... "c" is contained within "d" and further "d" is contained within "s" ... I was thinking to approach our problem from hierarchical linear two-way random effect perspective
I have two quick questions ...
Q1. I have Mplus 4.1 (base+mixture) ... could I estimate the model with this version of Mplus, or should I update it
Q2. could you suggest me a reference to start with
Q1. If you have a multilevel data structure as you indicate with s, d, c then you also need the Mplus multilevel module.
Q2. The model you describe - at least without the further multilevel aspect - is of a structural equation modeling type (e.g., Bollen's SEM book). The u factor can be seen as a "methods" factor. I discussed similar modeling, although not in ML, in an early paper available from my UCLA web site:
Muthén, B. (1983). Latent variable structural equation modeling with categorical data. Journal of Econometrics, 22, 48-65.