> Whilst the plm graph are linear, why the rest of them have u shape?
> Is this because of the logic behind each procedures are different of I have done in wrong way round?
Yes. It is because the procedures treat the explanatory variable differently.
The first model in your code is a LINEAR model in PROC LOGISTIC that uses only age as the explanatory variable. It is plotted by using the EFFECTPLOT stmt in PROC PLM. By definition, this model will be a logistic curve ("sigmoid shape"). Because age does not have a large effect when predicting Health, the sigmoid curve is very flat and looks almost linear.
The second model is ADAPTIVEREG, which uses spline regression and uses an algorithm to automatically choose knots (thus the "adaptive" part of the name). Age is not represented as a single variable, but as several spline effects. Therefore, this model can result in a U-shaped fit.
The third model is LOGISTIC with spline effects (although I think you misspecified the MODEL stmt, which should be MODEL HEALTH=SPL). This model uses a basic of cubic and 5 interior knots. Again, because Age is represented by multiple spline effects, this model can result in a U-shaped fit.
> Major concern is that proc plm gave me a probability with CI, which I wanted to have
Confidence limits for predicted values are created under the assumption that the model is correctly specified. If you use a linear model to fit data that do not look like the model, the CLs are useless. I think in your case, the data indicate a nonlinear effect of Age. Therefore you should not use the linear LOGISTIC model.
... View more
