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I am developing an early-warning GLM that predicts insurance claim severity based on characteristics such as industry, age, type of injury, etc. One of the fields that has proved most predictive, Variable X, is not known with certainty early enough in the life of the claim for me to use it in the model.

Would it be appropriate to develop a GLM to predict variable X, and then use this prediction as an input into the original early-warning model? If so, would I re-model the early-warning model with the predicted variable X data or use the original model coefficients based on the actual variable X data?

Thanks in advance.

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  • $\begingroup$ Sych model would not predict X but E(X) (see here), so you won't see any extreme values in the predicted X -- I guess that in early warning system you would be interested in the extreme values..? $\endgroup$
    – Tim
    Commented Nov 10, 2016 at 15:22
  • $\begingroup$ Trying to identify the top 20% of claims, so relatively extreme, yes. $\endgroup$
    – Frank H.
    Commented Nov 10, 2016 at 15:31
  • $\begingroup$ Why not just include any additional variables used for predicting $X$ directly within your early-warning GLM? $\endgroup$
    – whuber ♦
    Commented Nov 10, 2016 at 16:25
  • $\begingroup$ @whuber - Both models use the same variables but the ways each variable are categorized or transformed vary by model. Said another way, I tried just excluding variable X and the early-warning model loses significant predictive value. $\endgroup$
    – Frank H.
    Commented Nov 10, 2016 at 17:57
  • $\begingroup$ You asked for liks ... This is relevant to the multi-stage bootstrapping that I had previously referred to .... stats.stackexchange.com/questions/240728/… $\endgroup$
    – IrishStat
    Commented Nov 10, 2016 at 22:47

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If you are using data measured over time and you wish to obtain better estimates of X after a certain point in time you could "cheat" and predict that X from the other X's and if there is indeed identifiable divergence in X at the point of interest one could use the predicted X values as your new actuals for that X.

Now after identifying a useful model you might want to encode the uncertainty in your forecasts for all of your supporting/helping series . This can be done ( I have successfully programmed this via Monte Carlo methods !) and subsequentially the confidence limits on your forecasted Y become more robust and honest.

EDITED AFTER REQUEST FOR MORE DETAILS:

AR(1) forecasting contains a discussion . Essentially this is ground-breaking stuff where individual X's are forecasted either via a Delphi approach or statistically generating a pdf or frequency distribution (family) of forecasts for the forecast horizon. The second step is after constructing a useful model these forecasts for the X series are then used to drive a pdf of forecasts for the output series. Since each of the X's and the Y may have identified anomalies/pulses/exceptional/extreme values these can be used to populate the Y forecast yielding a forecast that incorporates a truer uncertainty in X. In this way volatility in the input series are recognized and used. If you wish to continue this dialogue you can either set up a chat room or contact me directly (preferred as I speak better than I type ).

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  • $\begingroup$ Can you provide more information about incorporating uncertainty? Any articles or links would be appreciated. $\endgroup$
    – Frank H.
    Commented Nov 10, 2016 at 15:32

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