Hi Saskia,

my first hunch would be to do some autoregressive modeling in a multilevel SEM perspective. Mplus can do this surely and perhaps OpenMx should also (lavaan not yet). I added some references about multilevel SEM and autoregressive models, that may be helpful. This should work with binary DVs, too. But that's beyond my knowledge.

That having said, you have to consider whether you really need a full blown multilevel model or if clustered SEs might not be suffiecient. There is a debate about that

Best,

Holger

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Preacher, K. J., Zyphur, M. J., & Zhang, Z. (2010). A general multilevel SEM framework for assessing multilevel mediation. Psychological Methods, 15(3), 209.

Mehta, P. D., & Neale, M. C. (2005). People are variables too: Multilevel structural equation modeling. Psychological Methods, 10(3), 259-284. doi:10.1037/1082-989X.10.3.259

McNeish, D., Stapleton, L. M., & Silverman, R. D. (2017). On the unnecessary ubiquity of hierarchical linear modeling. Psychological Methods, 22(1), 114-140. doi:10.1037/met0000078

Hamaker, E. L., Kuiper, R. M., & Grasman, R. P. P. P. (2015). A critique of the cross-lagged panel model. Psychological Methods, 20(1), 102-116.

Bollen, K. A., & Curran, P. J. (2004). Autoregressive latent trajectory (ALT) models A synthesis of two traditions. Sociological Methods & Research, 32(3), 336-383. doi:10.1177/0049124103260222

Frese, M., Garst, H., & Fay, D. (2007). Making things happen: Reciprocal relationships between work characteristics and personal initiative in a four-wave longitudinal structural equation model. Journal of Applied Psychology, 92(4), 1084-1102.

Zyphur, M. J., Allison, P. D., Tay, L., Voelkle, M. C., Preacher, K. J., Zhang, Z., . . . Koval, P. (forthcoming). From data to causes I: Building a general cross-lagged panel model (GCLM). Organizational Research Methods.

See Zyphur's Video about the GCLM approach: https://www.youtube.com/watch?v=tHnnaRNPbXs&feature=youtu.be

Zyphur, M. J., Voelkle, M. C., Tay, L., Allison, P. D., Preacher, K. J., Zhang, Z., . . . Koval, P. (forthcoming). From Data to Causes II: Comparing Approaches to Panel Data Analysis. Organizational Research Methods.

Thank you very much for your answer and all the helpful literature links, Holger Steinmetz . I was able to decide for a multilevel-SEM approach with your help and the literature. Thank you!

I would start simply and build in random effects multilevel models

e.g,

begin with 2-level model with repeated measures at level 1 and 'individuals' at level 2

then add in 3rd level to see if that complexity is needed by examining he size of the level 3 variance of the random effcets.

Then add time in - continuous time if you have it (it will have more power, cannot do with SEM) , first as linear and possibly quadratic ( I know you only have 3 time points but you may also have measured time in more detail)

The aim of this preliminary stage is to get a good idea of the nature of what needs to be explained. Then put in main effects of key variables starting with time varying variables with direct effects , then time invariant and finally the mediating variables.

We used MLwin's bootstrapping capability to estimate a mediating variable in this

Article Stressed out? An investigation of whether allostatic load me...

Kelvyn Jones thank you so much for your help. I like the idea of building the model stepwise and kind of adding more complexity to it step by step. I'll do some more research to see which procedure fits our data best. Now I have some starting points for finding out, which is great. Thanks!