Growth models with varying time of in... PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 Anonymous posted on Thursday, June 30, 2005 - 7:33 pm
Hi Linda and Bengt:

I have monthly sales performance in dollars on 194 salespeople, along with their monthly use (in terms of pages viewed) of a Web-based learning system. I am interested in modeling the trajectories of sales performance as a function of time and website usage. Two noteworthy features of my data are:

1. I have an unbalanced panel dataset. The number of observations per salesperson ranges from a low of 7 to a high of 39.
2. The "intervention time" (ie, the month when each salesperson began using the Web-based system) VARIES across the sample, as salespeople choose when to begin using the system. As such, some may begin using the system the very first month they begin selling; others, in contrast, don't use the system until they have spent more than a year selling.

I understand that Miyazaki and Raudenbush's (2000) accelerated cohort design may be able to take care of point 1; However, I am yet to see a paper that allows for "varying time of intervention."

Would you please let me know if you are aware of any way of dealing with this kind of data? I would greatly appreciate any references/cites you might be able to provide.
 bmuthen posted on Sunday, July 03, 2005 - 12:19 am
Your situation reminds me of a model I proposed for alcohol use related to marital status, where a marital status change influences the growth curve for alcohol use. Marital status is a time-varying covariate, but it is the status change rather than the status that is predictive of change in the outcome. In this sense, I think of the website usage as a time-varying covariate. If you think this is relevant, you can consult a Curran-Muthen article in (I think) Journal of Studies on Alcohol say 5 years back.
 Anonymous posted on Friday, July 15, 2005 - 7:16 pm
Dear Bengt and Linda:

I am a "newbie" to MPLUS but have been using SEM techniques for some time now. I have data on the monthly sales performance of 116 employees over a time window ranging from 7 to 10 months of time. Using the "TYPE = MISSING" command, I have been able to model sales growth curves in MPLUS. However, I get very poor fit stats (CFI/TLI~=.5)when I attempt to fit a linear model and the following warning


when I try to include a quadratic term. Moreover, the model does not converge (NO CONVERGENCE. NUMBER OF ITERATIONS EXCEEDED.)when I try to freely estimate the growth factors or try to incorporate a cubic term in addition to the linear and quadratic growth factors.

My prelim data plots and descriptives indicate that this may be because I have very non-normal data (sales performance fluctuates wildly by month for each employee)and a zero-inflated distribution as well (each employee does have many months when they have zero sales). Taking a semi-log [y'=ln(1+y)]transform of the data has helped to smooth the sales curves, but I still have a preponderance of 0 values. I would greatly appreciate any tips you might have on dealing with this situation. Is 2-part growth modeling the answer? If so, could you please refer me to some good references on the method?

Also, how do I estimate the covariances between residual variances in MPLUS? I am sure this will help me increase the fit of my model.

Thanks for your time!
 bmuthen posted on Saturday, July 16, 2005 - 12:51 am
You can fit a quadratic growth model while having the quadratic factor variance fixed at zero so that it is a fixed effect, not random - this would get away from the warning message.

Yes, 2-part modeling can help here - see the Olsen-Schafer article in JASA from 2001 and the Brown et al application on the Mplus web site. Or, using the censored option (although that leads to heavier computations).

Residual covariances can be simply obtained by saying

y1 with y2;
y2 with y3;

 Sarah Cattan posted on Thursday, September 29, 2011 - 3:23 pm
Dear Linda and Bengt,

I observe individuals' wages at four points in time. My model for wage at time t is:
Wage(t) = b(t) * X(t) + e(t)
where X(t) are observed (time-varying and time-invariant) characteristics, b(t) are parameters, and e(t) is an error term.

I would like to allow the error terms to be correlated over time periods and would like to model this correlation with a latent factor, such that:
Wage(t) = b(t) * X(t) + a(t) * f + u(t)
where a(t) are factor loadings specific to each period and f is a time-invariant factor. u(t) is an error term that is uncorrelated across time.

This means that all the unobserved correlation in the wages over time is assumed to operate through the latent factor f.

I am interested in estimating the distribution of f and in estimating the factor loadings (under some normalization). How do you recommend that I program this in Mplus?

Thank you very much for your help,
 Linda K. Muthen posted on Thursday, September 29, 2011 - 7:31 pm
Let's say you have three timepoints and your outcome is w1, w2, and w3. You would say

f BY w1 w2 w3;

and use the FSCORES option of the SAVEDATA command.

Your data needs to be in wide format to do this.
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