Possible to analyze cross lag panel data with regression alone (no SEM)?

#1
I have 2 (soon to be 4) waves of panel data. I have a relatively small sample size so I don't think I should use SEM - also I don't really understand SEM! Is there any effective way to analyze these data using only regression or correlation analyses? Preferably analyzed using SPSS if possible

Thanks in advance!
 

Lazar

Phineas Packard
#2
Yes. You can even do it with correlations if you like. You can do it with regression where:

Y1T2 = alpha + betaY1T1 + betaY2T1; and
Y2T2 = alpha + betaY2T1 + betaY1T1

where Y1 and Y2 are your analysis variables and T1 and T2 are your time waves. This is not perfect as you often get interesting information from the correlation of the residuals for Y1T2 and Y2T2 among other things. You can of course just use manifest variables (i.e. your scale scores not latent variables) in AMOS to run the crosslagged model. I think this would be the best approach.
 
#3
Thanks for the fast response! Can you elaborate more on what the model you posted means? Also - do you have a link to how to run a crosslagged model in AMOS? I've never used AMOS.
 

Lazar

Phineas Packard
#4
Lets run through the equations I gave you above first (also see link I gave you in the first post). The first one essentially looks at what the effect of variable 2 (Y2) on your variable Y1 after controlling for the effect of the Y1 variable at Time 1 predicting itself. So to put it clearly. Say we were interested in the effect of initial academic achievement on change in academic self-concept. What we want to know is whether achievement at Time 1 predicts self-concept at Time 2 after controlling for the participants initial levels of self-concept (i.e. self-concept at Time 1). Thus you get the effect of initial achievement on CHANGE in self-concept from Time 1 to Time 2. You can do the same thing looking at how initial self-cocnept predicts change in achievement. I give a much better explination of cross lagged models here http://onlinelibrary.wiley.com/doi/10.1111/j.1467-6494.2012.00766.x/abstract if you have access.

I've never used amos either but I assume you have it as it comes with SPSS. The SEM model with manifect variables is simple enough really you just have a model in which Time 1 variables predict each other and themselves at Time 2. Check out Figure 1 in the article I linked you to above.
 
#5
Thank you again. Your explanation of the regression models makes perfect sense. I'm a little confused, still, because in the paper you linked it seems your cross-lagged analyses were performed using SEM (that is how you get fit indices, right? Admittedly I know little about SEM). In your opinion, would reviewers have an issue with the basic regression equations you posted? Or the cross lag correlations? I had read the paper you linked re: correlations, but I was worried about using that method of analysis because I know reviewers typically prefer "fancier" analyses like SEM, which I doubt I can use because of my sample size.
 

Lazar

Phineas Packard
#6
My guess is that SEM would be asked for as this is the typical way of doing it now and thus regression might be looked down upon. Your model, if you use manifest not latent variables will be saturated and thus model fit will not apply to you.

It is relatively straight forward to do in but perhaps I can advice you better if I had some more details on your project. Can you give an idea of sample size and variables?
 

Lazar

Phineas Packard
#7
I should not that the Figure 1 in the paper I sent you is SEM. However, the causal logic behind it is what is important. You will not that it is the same figure more or less than those presented in the correlation paper.
 
#8
I am considering another way of analyzing these data. I have a main variable of interest (Y1) and four other DVs (Y2-Y5). I had initially considered running four separate cross lag panel analyses for Y1 and each of the DVs (as indicated above) but is it also possible to run 5 separate growth curve models with each Y as the DV at level 2 and the T1 value for the other four Ys at level 1?

I'm mainly interested in understanding the temporal ordering of increases in Y1 and increases in each of the other correlates (cross-sectional data suggest these variables are all correlated, now I would like to understand how they develop those relationships).