As far as my understanding goes, the LLP model works by assuming linear relationship between variables for every small kernel. Hence for n observations there will be n different linear models.
If this is the case won’t it be difficult to quantify the significance of a parameter/ variable on the model outcome.
What I want is:
If there are x independent variables in LLP regression leading to an outcome, is there a way to assign a significance to the input variables such that variable 1 is more important than variable 2 and can ultimately be dropped from the equation!
Dear Samyadeep,
yes by using SA you can reduce the number of important parameters (input quantities of interest) by factor fixing with small influence on output quantity of interest. Doing so you can reduce the dimensionality of the problem. However using LSA is only possible for independent input quantity of interest, if they depend on each other or if the problem is nonlinear you should use global sensitivity analysis, which gives you also the interdependence plus a ranking of most important parameters. The LSA has further limitations, as it does only give correct results if the parameter space used is sufficiently small, if you want to see global effects for a large parameter space you also need to use GSA. See our paper on LSA and GSA.
Best wishes,
Stefan
The LLP model is based on OLS which is based on the assumptions underlying the error term. LLP will give a better prediction with noisy data as compared to OLS that have a large variance with noisy data. Using LLP with autoregressive models does not mean changing assumptions as it is done in sensitivity analysis, therefore, in answering your question " Is it possible to perform a sensitivity analysis on a local linear prediction model? " I would say NO!
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