I specialise in the insurance industry. I spend my days building GLM models and calculating the Technical Premium. I just started a new position in a new company and I am becoming extremely confused.
In my previous company, we used WTW Emblem software, which was not cheap but very handy to use.
My manager at the time suggested to use the so called CU line which is explained as "toggles the display of the current model unsimplified approximate, which is defined in Linear Predictor space as Current Model + Observed Average - Current Average. Where the model has a log link function this is equivalent to
Current Model * (Observed Average / Current Average). This gives an indication of the fit to the data, scaled to the model prediction. Comparing this line to the Current Model can give an indication of the mix adjusted fit of the model".
What I was looking in this CU line was a monotonous trend either going up or down.
In my current company we are using R for glm modelling and we dont have CU like as such. We are using average observed and average fitted lines.
What I am truly confused is that my new colleagues are looking into this average observed line, and they are happy to fit it into a model even if its not monotonous trend, even when there are quite a bit of data in each of the levels. Lets say, engine power as a rating factor which is shown below (an extremely simplified example). X axis is the engine power.
They would be happy to fit this variable in a way so the fitted line would closely follow the observed line.
And this is what makes me extremely confused. Are we not looking the for same monotonic trend in the observed variable to decide whether we want to fit it or not. This example if from an insurance industry, but I am sure same principles are applied in other sectors as well.