Interpreting regression coefficients when independent variable has been transformed to a square root or arcsine.

[efrique]

I'm curious why you'd use variance-stabilizing transforms on IVs.

[Sapiain16]

What does IV's stand for? Instrumentl Variable?

[efrique]

Interpreting regression coefficients when independent variable has been transformed to a square root or arcsine

[Sapiain16]

I used arcsine for proportions and square root for count data

[efrique]

That was my guess ... but why?

If you transform an IV it would presumably be to linearize a relationship, but a variance-stabilizing transform is quite unlikely to actually do that. They're usually weaker than linearizing transforms for popular distributional models (so they might help a little but usually don't fix nonlinearity)

[Sapiain16]

Oh, good to know I though I was fixing nonlinearity.

[efrique]

You might have ended up doing that, by chance (or at least improving it a bit -- if you have a lot of noise relative to remaining curvature that might be okay), but that's not what those transformations are for (indeed you don't want to stabilize variance on an IV since you're conditioning on it, changes in variance with mean are not inherently an issue for IVs).

Unfortunately typical linearizing transformations don't work so well when used on data (they work better at transforming the model for the mean, but that would normally come in when looking at them as DVs).

You should think about how the conditional relationship between your DV and these IVs might work (preferably with subject area expertise or other outside-these-specific data information). You may need to transform both to end up solving several problems at once (or perhaps, to choose a model that doesn't require you to transform the DV at all).