Longitudinal change assessment

[Nick Frye]

Hello, SEM folks. I am reviewing a manuscript that has some SEM-related issues that I believe that this group can help clarify for me. This article claims to assess whether changes in variable A were longitudinally related to changes in variable B. The data included two time points, which were analyzed with a simple path model. The authors examined the Time 2 association between variables A and B while controlling for each variable’s Time 1 response; therefore, in the author’s mind they were examining assessments of change. My gut instinct tells me something wrong here (whether it be the language they’re using or the specific analysis conducted) but it’s been a while since I’ve dived into this topic. 

In addition for variable B (endogenous variable), the authors created factor scores derived from 3 manifest variables without provided any information about the CFA fit or loadings. Given that the authors did find a significant association between variable A and B, wouldn’t it be difficult to draw any conclusions based on this finding? For all I know the model could have a good fit but the loadings could be small and/or insignificant. Alternatively, one of the variables could be strongly associated with variable A whereas the others were not. 

Thank you for your time!

-Nicky

Sent from Yahoo Mail for iPhone

[Phil Wood]

Dear Nicky,

This is obviously something that I think about rather a bit. The basic idea that one time series observed on one construct can affect another series on another series goes by several names, such as the "cross-lagged panel correlation" where it came in from sociology studies of voting behavior. The analogous model for contingency tables goes by the name of the "lazarsfeld 16-fold cross tabulation table." More generally, though, the basic model you're looking at is most often talked about in the literature as "Granger causality" after Clive Granger's nobel prize-winning work in econometrics (yes, I know the economics prize isn't, technically speaking, a Nobel). If you'd like to read more about the most recent developments, take a look at the Vienna conference on the topic a few years bacK : https://onlinelibrary.wiley.com/doi/book/10.1002/9781118947074 (there's a chapter by yours truly talking about reciprocal and auto-causal effects as well).

There is, however, specific reason to be skeptical of such models as you say without going into dynamic systems. Specifically, the construct you're looking at could, for example, be a trait- a stable interindividual difference measured across several occasions. as such, assuming you had three or more measurement occasions, you could model each construct as a factor, estimate the correlation between the traits and, after that, look at whether cross-lagged effects still exist at the measurment occasion level. (I'd also correlate measurement errors within occasion across constructs.) 

As always, with any SEM model you should look for and consider the possibilty that there are outlying or influential observations and investigate the use of lowess regressions to check for the linearity assumptions assumed in any of these models. 

Just some off-hand comments- FWIW. Phil

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