Structural Equation Modeling

[#1]

@LauraCS 

Laura, I have a simple (hopefully) question.

I have two variables (x and y) that predict an outcome variable Z

The trouble is I think y depends on x

I'd like to set up a path analysis that shows me whether y has independent contribution to Z or is just serving as a proxy for x. When I do it the way I think I should, I don't get the answer I like

Thanks you so much for your guidance - 

Tim Roberts, Professor of Radiology, CHOP

[#2]

Hi Tim,

Thank you for your question! How are you setting up your model? Based on your description, I'd suggest fitting a model like this:

where Leadership = X, Conflict = Y, and Satisfaction = Z.

It sounds like the key coefficient you want to focus on is the one from Y --> Z. If that estimate is statistically and practically significant, then you'll know that Y has an independent contribution to Z above and beyond what X has. In the red triangle menu, you will also find the standardized estimates which are often used as effect sizes to quantify how large the effect is.

HTH,

~Laura

[#3]

Thanks. Luckily for us that was more or less what we were doing anyway. Sadly for us, it gives us an answer we don't like. But at least we are confident we did it right.

Interestingly when we break the connection between X and Y - i.e. have both X and Y independently go to Z we get ALMOST the same weights and p-values, but not exactly. Any idea why not exactly ?

Thx - Tim

[#4]

I'd expect the same unstandardized regression estimates but different standardized estimates. This is because standardized estimates depend on the model implied variance of the variables which does differ between these two models. If your unstandardized estimates are different, I'd need to look at the exact model. Feel free to DM me if you'd like to share your model/data or you could also send it to support@jmp.com 

Best,

~Laura

[#5]

I THINK that it comes down to the difference between SEM (when the model is a triangle) vs. multiple regression  (which I think this path reduces to when the x and y are connected too but not each other) ? Is that a reasonable interpretation? Thanks so much by the way

[#6]

sorry "x and y are connected to Z, but not each other"

[#7]

@LauraCS Two screen grabs of the models attached

 

 

[#8]

Thanks for sharing the screenshots. I wonder if there's something about the data that makes the estimation result in these small differences, especially given the large differences in variances. If you'd like to share your data (via tech support or DM) I could give you more details. However, what I'd expect to see is the same estimates. The attached script uses a simulated sample data table to fit the same two models and the results are as expected:

As a side note, you might consider adding covariances in these models, unless you truly expect those to be zero. Specifically, in the path model the residual covariance between GABA and FA might be needed, and in the regression model, the covariances between age, GABA, and FA, would be customary to include.

Best,

~Laura

[#9]

Thanks @LauraCS this is very helpful. What are the consequences of using the mediation model (straight lines) vs. the multiple regression model with covariance (curved lines) ?

[#10]

Glad it's helpful, @robertstpl!  The mediation model implies that Age has an effect on GABA and FA and that you're (perhaps) hypothesizing that Age has indirect effects on M50 that go through GABA and FA. The red triangle menu has an option for Indirect Effects so you can see what those are, if they're of interest. Thus, if there are significant indirect effects, the mediation model allows you to make statements like "Age affects M50 through GABA/FA above and beyond its direct effect on M50." The multiple regression model isn't making explicit hypotheses about how Age, GABA, and FA are associated; by adding the covariances, we simply assume they might be related but their associations aren't likely the key interest in that model.

HTH,

~Laura