Jon Heron posted on Monday, July 25, 2016 - 1:10 am
I am attempting to model a nominal mediator observed with error + from your causal-mediation manuscript (p32) I see that the way to deal with this is to use knownclass.
As I usually model nominal variables with error as part of a manual implementation of r3step I thought a good starting point would be to reproduce an r3step result using the knownclass set-up before moving on to mediation.
Progress thus far: with a 4-category latent variable, the logit classification matrix - defining the link between error-prone W and error-free C - contains 12 non-zero parameters. In order to introduce W using KNOWNCLASS the bottom row of this matrix becomes the intercepts for C to define the latent class distribution, and if I subtract this bottom row from the other three I obtain the 9 log-odds parameter constraints with which I can link C and W. I then regress error-free C on my covariate.
This is where things fall apart. I think this issue lies in the fact that linking C and W in this manner requires me to specify intercepts for C rather than intercepts for W within classes of C. However since the end-goal is to regress C on a covariate, the meaning of these C-intercepts changes. I have tried centering the covariate but my estimates are still wrong. I should add that I am however reproducing the correct likelihood.
See Table 8.35. This approach can also be used for a truly latent class variable situation with error-prone indicators.
Jon Heron posted on Tuesday, July 26, 2016 - 1:50 am
I redrafted that post a few times but it still wasn't very clear.
8.35 is for a manifest nominal mediator, and the other one you mention - truly latent class variable situation - is given in Figure 17 in your manuscript.
I am attempting a third type. In your manuscript you refer to a nominal mediator being "observed with error". Hence I assumed it would be possible to perform a bias-adjusted 3-step method and incorporate a previously-derived grouping along with information derived from the classification matrix.
As this seemed rather complex I thought I would start off by trying to reproduce an r3step result using the knownclass formulation.
I can't find any code for Figure 17 as I have a feeling that that in itself would be really helpful. Do you perhaps have that?