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tbates / umx

Making Structural Equation Modeling (SEM) in R quick & powerful
https://tbates.github.io/
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means: Allow residualizeContinuousVars=TRUE #116

Open tbates opened 4 years ago

tbates commented 4 years ago

Only apply definition approach to ordinals in selCovs

In mixed cases, residualizing continuous variables and reserving definition approach for ordinals can be a win if there are many covariates

make optional with residualizeContinuousVars=TRUE

Originally posted by @mcneale in https://github.com/tbates/umx/issues/21#issuecomment-616629010

tbates commented 4 years ago

Thinking this through prior to implementing: Won't the beta weights for the continuous covariates be biased high because they get first bite at the cherry? And ordinal covariates which would have dominated a type-III sums of squares regression will be biased downward? I guess it just amounts to two-part Type-I sums of squares, with ordinal entered as a last block?

tbates commented 4 years ago

Q: What, if anything, would be wrong with running the full regression in glm (including ordinal variables with the correct link function), then plugging the resulting beta weights into the means model but as free=FALSE?

That way all the betas are estimated jointly and speedily, and we'd still have the non-regressed ordinal DV in the data, as required for the thresholded covariance model to work.

mcneale commented 4 years ago

The estimate of beta would be assumed to have no error. To the extent that this beta covaries with other model parameters, their errors would be biased, I think (might be rendered moot by being entirely exogenous). See Pearson-Aitken selection formula & function in OpenMx :). The other thing is that we still need to be sure that covariates are just that - external causes of our trait of interest. If causation guess is wrong, all hell breaks loose :). Oh yeah, it did that a couple of months ago...

Does glm have normal ogive link function that works with ordinal measures? Does it agree with including covariate in threshold model in OpenMx? Easy enough to experiment to ensure equality.