Probing a 3-way interaction - simple ... PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Brooke B posted on Friday, February 05, 2016 - 3:09 pm
I am attempting to use MPLUS to probe a 3-way interaction based on the approach put forth by Dawson & Richter (2006).

Specifically, using the MODEL CONSTRAINT command, I have created 4 new parameter estimates to calculate the simple slopes at 4 moderator "conditions" (Low/low, low/high, high/low, high, high).
I then created 6 pairwise differences among those 4 simple slopes, thereby creating 6 additional new "DIFF" parameter estimates.

The catch is, I'm not certain how MPLUS calculates the standard errors of these new "difference" parameters. The Dawson & Richter (2006) paper go into a lot of detail regarding what the formulas for those standard errors should be.

At this point, I DO get slightly different results when i use the Dawson excel spreadsheet to do the calculations by hand. I'm just not sure if I'm incorrectly filling out the excel spreadsheet (possible) or if MPLUS is not necessarily equipped/reliable for this specific use. Or if it is just a matter of different, but justifiable approaches.

Can you offer any insight as to how the standard errors are being calculated for a "DIFFERENCE in simple slopes" parameter that is created with the MODEL CONSTRAINT command?
 Bengt O. Muthen posted on Friday, February 05, 2016 - 5:52 pm
Standard errors for new parameters in Model Constraint are computed using the Delta method which gives asymptotically correct standard errors. That's probably how that paper got it. Note that ML and MLR give somewhat different results. If you like you can instead use bootstrap SEs, or Bayesian SEs.
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