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Spline regression model | 11.65 KB |

Hello,

For my research, I would like to estimate the association between two latent variables using a spline/piecewise regression model with a single knot. The model should estimate two separate linear regression lines and the knot location (see attached image).

The two latent variables are anxiety and negative affectivity and both are measured with 7 indicators on a 1-5 Likert Scale.

On this forum, I read some topics about spline models in a growth model context, but I do not know whether such models can easily be transformed to spline models suitable for estimating associations between two latent variables using cross-sectional data.

I found an article by Jeffrey Harring (https://journals.sagepub.com/doi/pdf/10.1177/0013164413504295) that explains the mathematics of estimating such a model.

Is it possible to program this model in OpenMx?

Best wishes,

Paul

Possibly via bivariate normal integration over the two latent variables. I think you may need a user-defined fit function. The sign function may help. It is an interesting problem - will try to look at the paper too. Some ‘case’ { style functionality seems needed more generally.

Cheers

Mike

Thanks Mike! Good to know it is probably possible to estimate this model in Openmx.

I have no experience in specifying my own fit functions. Does this mean that I have to write an R function to compute the likelihood according to equations 16 and 17 in the paper?

I am also unsure how to add the non-linear regression parameters (e.g. knot location, two separate regression coefficients for the association between the two latent variables; see equation 4) to my model using either the mxMatrix or mxPath notation.

I greatly appreciate any help with these issues.

Best wishes,

Paul

You could write an arbitrary R function to evaluate the likelihood, and put an MxFitFunctionR into your MxModel. Alternately, if it's possible to express that function as an MxAlgebra, then you could do that, and use an MxFitFunctionAlgebra. The latter will be faster, but MxAlgebras aren't as general as R.