We have just completed data collection for a study examining individuals' propensity to adopt "really new services" (in this case, 12 new wireless services), using a 13-item battery to examine such constructs as "newness," skepticism, etc.
We would like to fit a measurement model to the 13 items, but the analysis is complicated by two aspects, including: 1. (Replications of) Within-subject measures - each R rated multiple services (8) on the 13-item battery 2. Missingness - in order to reduce respondent burden, each respondent rated a randomly selected subset of services (8, out of the 12 services shown across the sample. The overall sample size is n = 406, so on avg n = 270 rated each service on the 13 items.
We are not sure how to handle (1) and (2) within Mplus. Any suggestions would be very much appreciated.
The fact that people answered more than one item is handled by the multivariate analysis. You can use missing data estimation to handle the fact that not all respondent answered all items. In Version 4, this would be TYPE=MISSING. This is the default in Version 5.
But respondents rated multiple services (8) on each of the 13 items. So, we have a conventional CFM (13 items), but 8 replications for each respondent (8 services x 13 ratings x 406 respondents). The ratings across the 8 services (within a respondent) are clearly not independent... so, given the replications across services, I'm still not clear how to structure this in Mplus.
Eventually, we wish to draw inferences about: 1. The LV means, by service 2. The effect the LV's have on selected dep vars (such as Purchase Intent) 3. Derive latent classes, using a Factor Mixture model (e.g., based on propensity to adopt)
You have 104 variables for each person (8 times 13) with a total of 156 (12 times 13. Your dataset will have 156 columns and 406 rows. Missing value flags will be given for the variables each respondent did not answer. If you want to compare the services, you would not do that using multiple group analysis because the groups need to contain independent observations. Instead, you would compare the means of the services as though they were repeated measures across time. See Example 6.14 but without the growth model. The multivariate modeling takes care of the non-independence of observations.
An alternative would be to sort the observations into independent groups who have taken the same 104 items and do a multiple group analysis.
Linda, thank you very much. I think I'm beginning to see the logic of your approach, but let me confirm to be sure.
I was initially concerned that the specification you've suggested would result in each LV being defined as it relates to the corresponding service, e.g., LV1 x SVCA; LV1 x SVCB; etc., which is clearly not very parsimonious. Ideally, we would like to test for and (hopefully) establish that the CFM for a given LV is at least partially invariant across services, which would clearly yield a more parsimonious model.
To that end, we had briefly considered "stacking" the observations (406 respondents x 8 services = 3,248 cases), analogous to Muthén and Satorra (1995 - I realize that isn't exactly what they did). Of course, the cases are not independent, so this approach is problematic.
So, to confirm, with the approach you've suggested, would we test for measurement invariance by constraining the measurement parameters for a given LV, across services, and testing the constrained model vs. a model in which the parameters are allowed to vary across services? If so, I'm assuming we could employ the same approach in the structural model and test to see whether the effects of a particular LV vary by service - is that correct?
One more (seemingly) related question - we also expect different groups of individuals (e.g., early adopters vs. later adopters) to possess very different views and propensities to adopt, so we would also like to uncover and distinguish these segments. We were initially planning a mixture model, but with the specification you've suggested I could also envision a CFM with second order factors (e.g., defined across services) - for example, we might have a "skepticism" second order factor obtained from respondents' ratings across the 8 services they rated. This would allow us to scale (and perhaps cluster) respondents on the basis of the second order factors.
Given the specification you've suggested, which I believe would permit us to extract second order factors, any thoughts on how and when to incorporate the second order factors with a mixture model?
No, we would be attempting to cluster respondents on the basis of their responses to combinations of the LV's (within/across services: Familiarity, Skepticism, Curiosity, etc.). There is a sizable # that has "limited interest" in any of the svcs (the LV we wish to predict).
We had originally planned to use a Factor Mixture model to uncover homogeneous segments, and examine them in an across-group model.
Based on the CFM you suggested, we are now also considering a model with second-order factors on the LV's across services, and including these second-order LV's in the SEM.
Not sure whether one or the other of the approaches, or some combination, makes the most sense.