Nonlinear regression in weighted samples
Message/Author
 Stian Lydersen posted on Friday, June 27, 2014 - 4:38 am
We have a weighted sample, weighted as follows: The sampling was carried out in four strata, with sampling probabilities .37, .48, .70 and 0.89, respectively. We want to carry out a nonlinear regression analysis. In SPSS ans Stata, this seems to be possible only for nonweighted samples.

1. Is nonlinear regression possible in Mplus?

2. If yes, can this be done with our weighted sample?
 Linda K. Muthen posted on Friday, June 27, 2014 - 6:26 am
What do you mean by nonlinear regression. What is the model?
 Stian Lydersen posted on Monday, June 30, 2014 - 1:52 am
Y = A0 + B1*(X1 - C) +B3*((X1 - C)*D2) + E

Where X1 and D are covariates, D is dichotomous, E is the error term, and A0, B1,B3, and C are parameters.

This is actually a reparametrization of the linear regression with an interaction term:

Y = B0 + B1*X1 + B2*D + B3(X1*D) + E

We are particularly interested in the estimate and confidence interval for C, which is the X1-value where the regression lines for D=0 and D=1 cross. (The model is eqn 15 in the ref below.)

Widaman, K.F., Helm, J.L., Castro-Schilo, L., Pluess, M., Stallings, M.C., & Belsky, J. 2012. Distinguishing ordinal and disordinal interactions. Psychol.Methods, 17, (4) 615-622
 Bengt O. Muthen posted on Monday, June 30, 2014 - 10:32 am
See plots connected with UG ex 3.18 and also "Mediation" in the the left margin website section Special Mplus Topics.
 Stian Lydersen posted on Monday, June 30, 2014 - 11:19 pm
The reference to UG ex 3.18 and also "Mediation" seem to relate to the standard parametrization of interaction, which is not difficult. Our problem is statistical inference for C in the reparametrized model. This requires use of the nonlinear regression equation we stated first:

Y = A0 + B1*(X1 - C) +B3*((X1 - C)*D2) + E
 Bengt O. Muthen posted on Tuesday, July 01, 2014 - 6:00 am
You can express C as a "NEW" parameter in terms of the model parameters using Model Constraint. This then gives you the SE and CI for C.
 Stian Lydersen posted on Wednesday, July 02, 2014 - 3:42 am
Thank you. This seems to work:

MODEL CONSTRAINT:
NEW (C);
C = -B2/B3;

Parts of the results for C are:
Estimate = 0.820
S.E. = 0.387
Confidence interval lower 2.5% = 0.061
Confidence interval upper 2.5% = 1.458

If I compute a 95% confidence interval as estimate +-1.96S.E., I get (0.046 to 1.594). Suprisingly, the interval reported by Mplus is narrower. Can that be correct?
 Linda K. Muthen posted on Wednesday, July 02, 2014 - 9:50 am
 Stian Lydersen posted on Monday, July 07, 2014 - 12:37 am
Thanks to Linda Muthen for pointing out in an email to me that the results provided in the Mplus output are correct. I had mistakenly computed an approximate c.i. as estimate +- 2SE, while Mplus provides a c.i. using estimate +-1.96SE.
 Frode Stenseng posted on Wednesday, August 20, 2014 - 3:20 am
Ref. Prof. Lydersen's question:

"We are particularly interested in the estimate and confidence interval for C, which is the X1-value where the regression lines for D=0 and D=1 cross. (The model is eqn 15 in the ref below.)

Widaman, K.F., Helm, J.L., Castro-Schilo, L., Pluess, M., Stallings, M.C., & Belsky, J. 2012. Distinguishing ordinal and disordinal interactions. Psychol.Methods, 17, (4) 615-622"

My colleague Lydersen succeeded in testing this by computing the interaction term in SPSS and then using the model constraints function.

I want to perform the same test, but I use latent variables, so I am not able to compute an interaction term in SPSS to use in the model. I also use the grouping function (Satorra-Bentler)to test for moderation and not the xwith.

So, my question is: Is it possible to do this test in Mplus using latent variables and the grouping function?

If yes, I would be very grateful for a description on how to perform this test.

Best regards,

Frode Stenseng
 Linda K. Muthen posted on Wednesday, August 20, 2014 - 4:09 pm
You can use the XWITH option for latent variable interactions. See Example 5.13.

Please note you can create observed variable interactions in Mplus using the DEFINE command. It is not necessary to do this outside of Mplus.
 Dan Cloney posted on Sunday, October 19, 2014 - 8:32 pm
Hi,

I want to include an orthogonal polynomial (of an observed continuous variable) as a predictor in a model.

In R, there is a function to define orthogonal polynomials - e.g., poly(x, degree = n)) will produce an m by n matrix of the 1...n degrees of x.

Is there a similar function in MPlus that I can use e.g., in the DEFINE command? I can't see anything in the UG.

(sorry if this isn't the best place to post my question - I realise this is a more general question).
 Bengt O. Muthen posted on Monday, October 20, 2014 - 6:05 am
No, there is not such a function in Mplus.