Nonlinear regression in weighted samples PreviousNext
Mplus Discussion > Multilevel Data/Complex Sample >
 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:

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
Please send the output and your license number to Please be sure you are using Version 7.2.
 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.
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