I used Ordinary least square (OLS), Generalized linear modelling (GLM) and Multivariable fractional polynomials (MFP) methods to develop a prediction model and all 3 models produced identical predictions. Can anyone give an explanation for this?
Thanks
Sameera, what kind of analysis did you do?
If you have a standard regression analysis (and assumptions are met), usually the results (parameter estimates (Beta's)) of OLS and GLM (Maximum Likelihood) are (theoretically) identical. If the parameters are identical, the predictions will also be identical.
I do not know about MFP. Does MFP give the same parameters and are the functions identical (no polynomials with power 2)?
Well old and GLM are equivalent so that is not surprising. I know nothing about the third. Best, David Booy
Thanks Peter Moorer and David Eugene Booth.
My paper is "Mapping of Minnesota Living with Heart Failure questionnaire (MLHFQ) to EQ-5D-5L in patients with heart failure". I have attached a similar paper from the literature. I developed several regression models to predict EQ 5D 5L using MLHFQ and the best model was selected using couple of validation parameters. The analysis was done using STATA and OLS, GLM and MFP predicted the same values! This is the first time that i have used GLM and MFP, thus was a bit worried whether i have made a mistake. So according to your answers, i assume my results are quite possible
Thanks!
Sameera -
I'm guessing that for your GLM software to do something other than OLS, you have to instruct it to do so.
Have you tried WLS? You might consider this for regression of form y = y* + e:
https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression
There is this, with references noted in it: https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx
The WLS regression coefficients are often very close to those for OLS, but the prediction intervals associated with smaller predictions would be shorter, and the prediction intervals associated with larger predictions would be longer, often much longer.
If the sample size is small, the regression coefficients would be more likely to differ more substantially from the OLS ones, but then we would be less sure of the regression weights. But with smaller samples there is more uncertainty, so that is to be expected. Choosing OLS when that is obviously not correct would not help. Sometimes it can be reasonable though. Model and data issues may cause that to be the case.
Cheers - Jim
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