Correcting for measurement error in logistic regression?

CB

Super Moderator
#1
Hi guys,

Myself and a co-author have recently submitted a journal article assessing a particular criminological theory's adequacy in terms of predicting academic dishonesty. The main analysis involved a logistic regression predicting presence of academic dishonesty (yes/no) in a follow-up period, with the IV's being the subscales of an attitudinal test administered at time zero.

We chose to use the subscales (4 items each) of this particular test as predictors rather than the full scale due to very poor factorial fit for a one factor model, but good fit for a multifactorial model based on the test subscales. One of the reviewers highlighted the low-ish internal consistency reliability of these subscales (~0.6+), and suggested looking at a correction for attenuation in relationships due to measurement error.

I've read a little about corrections for measurement error in logistic regression, but have ended up a bit confused. Thoreson and Laake seem to suggest that maximum likelihood estimation is the optimum option to deal with this. As I understand it SPSS uses ML for the estimation of logistic regression models, but surely this is something a bit different? I can't see how the automatic SPSS estimation procedure could correct for measurement error.

Has anyone had any experience with measurement error corrections in logistic regression? Any suggestions for correction methods that are reasonably easy to execute?
 

Link

Ninja say what!?!
#2
Measurement error is an entire field in itself in epidemiology. There are two main ways I remember of adjusting for measurement error. The first is to do an analysis with a "gold standard", the gold standard being the tool you trust the most to be free from measurement error. The second is to do a calibration of the tool itself. Maybe you might be able to find more if you google.

Hope that helps.
 
#3
"and suggested looking at a correction for attenuation in relationships due to measurement error."

What I think this is referring to is the Spearman correction for attenuation. The formula is on wiki. What the correction attempts to do is "correct" the validity coefficient (correlation between x and y, where (say) y is critereon as Link said above). The thought is that if x and/or y is not measured very accurately (with good reliability) then what worth is the validity coefficient. So, if you have published reliability coefficients (correlation of x and x again, correlation of y and y again), you can correct the validity coefficient - making it stronger.

The question is - how do you do that with your subscale? Also, I'm not sure what this has to do with Chronbach's alpha. I hope that helps - a little anyways.
 
#4
Sorry CowboyBear,
I seemed to have gone down the wrong path with my comment. I now see what you are asking for. SEM actually does this. I don't know about logistic regression or another method for dichotomous outcomes.
 

CB

Super Moderator
#5
Sorry CowboyBear,
I seemed to have gone down the wrong path with my comment. I now see what you are asking for. SEM actually does this. I don't know about logistic regression or another method for dichotomous outcomes.
No worries! Yep, I've been thinking that it'd be ideal to use SEM - the issue then is how to incorporate logistic regression (or some other appropriate way to deal with a dichotomous DV) into an SEM model. Fun...
 

CB

Super Moderator
#6
Measurement error is an entire field in itself in epidemiology. There are two main ways I remember of adjusting for measurement error. The first is to do an analysis with a "gold standard", the gold standard being the tool you trust the most to be free from measurement error. The second is to do a calibration of the tool itself. Maybe you might be able to find more if you google.

Hope that helps.
Hi Link, thanks for your comment. I've read a little about measurement error corrections in epidemiology. What confuses me a bit is that measurement error in epidemiology seems to be conceptually a quite different thing than in psychometrics. In epidemiology it seems to be possible to actually measure true scores with a gold standard (or even an "alloyed gold standard" ;)) - whereas in psychometrics, true scores can't be directly measured, even for a calibration sample. Rather, measurement error is usually conceptualised as scale variation occurring due to unique variation in individual items. So I'm a little perplexed as to whether measurement error corrections from epidemiology can be implemented in my case (and also, admittedly, how to do them if they can be!)