Greetings. Following a qualitative exploration of my research topic, I am embarking on the quantitative follow-up phase of my research. I want to test the relationships between 10 predictor variables and 2 outcome variables. All 12 variables are latent constructs. The construct items will be derived from literature wherever possible but some modification is necessary. As a statistical notice what are the options? Is multiple regression an option? Many of the papers in the field have used CFA in AMOS etc but this look fairly daunting at my current level slowly working my way through SPSS guides by Field and Pallant. Many thanks for any advice.
Dear Nick,
a while ago I wrote an extensive recommendation for starters in SEM.
Perhaps you take a look and its list of references as a start:
https://www.researchgate.net/post/Dear_scholars_how_to_design_a_Structural_Equation_Modeling_surveys#view=5c0cdaf3c7d8ab762f591a75
12 variables are a lot of and its extremely important that you get these terms and implications right both in order to not waste space in your survey as well to not "over-load" the measurement model part of your overall SEM. I would aim at identifying 2-3 superclear indicators of a latent variable and to test the respective structures in a CFA. The goal should be to get a non-significant chi-square. After that, one option could be to go to a single-indicator latent model with either composites of the CFA (with fixed error variances to control the measurement error) or using the best indicators from the CFA per latent and to fix the error to the value of the error variance found in the CFA. All of this is not optimal but going in to a full SEM with measurement models and structural effect has its costs, too, namely a) bias of effects in samples sizes of N
Thanks Holger. To clarify, my model currently has 12 latent constructs (' e.g. technical quality, functional quality, trust etc), each to be represented by ~3 indicators. Does that sound feasible?
Hi,
the problem with large models is the immense number of testable implications which will most likely result in a misfitting model. Hence, it may be better to concentrate on one or two specific causal effects in the structural model and build a necessary part of the model around that focus. Doing that requires a bit of knowledge about graphical identification rules. As the most feasible approach, I routinely start with drawing a model in the dagitty.net software. This is a browser program in which you can draw a focal path model and, step by step, build around a net of those variables who (a) either effect the IVs or b) the DV or both. By then thinking about the relationship among those "auxiliary variables" who can find out (the software prints that) which of these variables have to be incorporated in you empirical model in order to be controlled for to identify the effect. Perhaps you want to much by focusing on all 12 variables and the real deal is only a subset of them.
Here's a video in which a researcher applies dagitty in this regard
https://www.youtube.com/watch?v=pJhU4fimHBQ&t=1849s
Here's a nice paper (a rarity, unfortunately) in which the authors had one essential causal effect and built around that the model.
Vahratian, A., Siega-Riz, A. M., Savitz, D. A., & Zhang, J. (2005). Maternal pre-pregnancy overweight and obesity and the risk of cesarean delivery in nulliparous women. Annals of epidemiology, 15(7), 467-474.
Below please find the best references that take a look onto SEM from a "graph theory" lense which underlies the aforementioned approaches.
With regard to the 12 latent variables: Be sure to select 3 really super clear indicators that make the essential assumptions of the common factor model most plausible (see my linked posting above).
HTH
Holger
Chen, B., & Pearl, J. (2014). Graphical tools for linear structural equation modeling. 1-23.
Chen, B., Pearl, J., & Kline, R. B. (forthcoming). Graphical tools for linear path models. Psychometrika.
Elwert, F. (2013). Graphical causal models. In S. L. Morgan (Ed.), Handbook of causal analysis for social research. (pp. 245-273). Dordrecht Heidelberg New York London: Springer.
Hernan, M. A. (2018). The c-word: Scientific euphemisms do not improve causal inference from observational data. American Journal of Public Health, 108(5), 616-619. doi:10.2105/ajph.2018.304337
Pearl, J., Glymour, C., & Jewell, N. P. (2016). Causal inference in statistics: A primer: Wiley.
Pearl, J., & MacKenzie, D. (2018). The book of why. New York: Basic books.
Shipley, B. (2004). Cause and correlation in biology. A user's guide to path analysis, structural equations and causal inference. Cambridge UK: Cambridge University Press.
Thoemmes, F., Rosseel, Y., & Textor, J. (2018). Local fit evaluation of structural equation models using graphical criteria. Psychological Methods, 23(1), 27-41. doi:10.1037/met0000147
Dawid, A. P. (2010). Beware of the DAG! NIPS Causality: Objectives and Assessment(2000), 59-86. doi:10.2459/JCM.0b013e32833dadd5
Thoemmes, F. (2015). Reversing arrows in mediation models does not distinguish plausible models. Basic and Applied Social Psychology, 37(4), 226-234. doi:10.1080/01973533.2015.1049351
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