I want to estimate the causal relationship between two latent variables over time using structural equation modelling. both latent variables are measured according to different indicators (observed). the data is panel with N=21 and T=16 years.
after going through SEM estimation techniques, cross-lagged panel models seem to be the best option, however, given the small sample size where N=21. is cross-lagged panel applicable in this case? I noticed that cross-lagged models involve large N and small T (max 5 waves).
The obstacle I'm facing is the small sample size given the number of indicators.
Any ideas if cross-lagged models are applicable or are there other techniques? (please note that I am estimating two latent variables with many indicators)
- To my knowledge SEM requires (n>200), especially in complex models, which is the case with latent variables and cross-lagged panel modelling. For further explanations on sample size, see Kline (2011, 11ff).
- Also don't forget what the aim of CLPM, which is according to Newsom (2015: 122) : "The intention is generally to investigate which variable causally precedes the other, referred to as Granger causality in time series analysis (Granger, 1969)." So if you want to solely investigate on time trends (T=16), then CLPM might not be the best choice. Chapter 11 of the Newsom (2015) book provides explanation on "Time Series Models" maybe this helps.
Kline, R. B. (2011). Methodology in the Social Sciences.Principles and practice of structural equation modeling (3rd ed.). Guilford Press.
Newsom, J. T. (2015). Longitudinal structural equation modeling: A comprehensive introduction. Routledge.
Hi Tara,
given the large number of T's, a VAR model would probably be an alternative (which AFAIK) resembles the CLPM. Further, I would approach the analysis by running individual time series plots and methods to inspect the dynamics (e.g., seasons, autocorrelation, types of series, nonlinear trends):
Beard, E., Marsden, J., Brown, J., Tombor, I., Stapleton, J., Michie, S., & West, R. (2019). Understanding and using time series analyses in addiction research. Addiction, 114(10), 1866-1884.
Bringmann, L. F., Pe, M. L., Vissers, N., Ceulemans, E., Borsboom, D., Vanpaemel, W., . . . Kuppens, P. (2016). Assessing temporal emotion dynamics using networks. Assessment, 23(4), 425-435. doi:10.1177/1073191116645909
Hoffart, A., Langkaas, T. F., Øktedalen, T., & Johnson, S. U. (2019). The temporal dynamics of symptoms during exposure therapies of PTSD: A network approach. European Journal of Psychotraumatology, 10(1), 1-11.
Having said that please note that longitudinal models do not imply so many advantages compared to cross-sectional models referring the estimation of causal effects, as you still assume non-confounding, see
Papies, D., Ebbes, P., & Van Heerde, H. J. (2017). Addressing endogeneity in marketing models. In Advanced Methods for Modeling Markets (pp. 581-627). Cham: Springer.
VanderWeele, T. J., Jackson, J. W., & Li, S. (2016). Causal inference and longitudinal data: a case study of religion and mental health. Social Psychiatry and Psychiatric Epidemiology, 51(11), 1457-1466. doi:10.1007/s00127-016-1281-9
That is, you should think about confounders and include them as controls. If you do this as a multilevel model (what you should do IMHO) than using person-means across time as controls achieves controlling for person-trait-level confounders which is something at least, see
Antonakis, J., Bastardoz, N., & Rönkkö, M. (2019). On ignoring the random effects assumption in multilevel models: Review, critique, and recommendations. Organizational Research Methods. doi:10.1177/1094428119877457
Finally, the large number of T's will probably result in a nonlinear trend which could be an interesting side result of the study, especially when explaining it with between-subjects variables but also be part of the level 1 model. That is, a generalized additive mixed model would be an option. At present I don't know yet however, whether the GAMM (gen. add. mixed model) can be integrated with the VAR model but I guess it should be possible.
Andersen, R. (2009). Nonparametric methods for modeling nonlinearity in regression analysis. Annual Review of Sociology, 35(1), 67-85. doi:10.1146/annurev.soc.34.040507.134631
Jones, K., & Almond, S. (1992). Moving out of the linear rut: the possibilities of generalized additive models. Transactions of the Institute of British Geographers, 434-447.
HTH
--Holger
Significance of cross-lagged effects depends on the overall R2 of the model, and thus also on the size of the autoregressive effect. The latter will be low across long time lags, and so will be R2. I guess there is no chance (or only chance :-) to find a sign. cross-lagged effects in your case.
Holger Steinmetz Thank you so much for your detailed and clear explanation.
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