Contributor
Posts: 37

# Working with independent(exogenous) variables that are functions of one another

Hello,

I am working with a time series data set and am hoping someone can point me in the right direction for specifying a model considering my data.

My dependent variable is the number of web visits that hit a website on a daily interval for about 1.5 years ~500 observations.

My independent variables are the value of television dollars spent on about 250 different television stations. The television stations range from small reach stations to very large reach stations. Since I cannot place 250 independent variables into a regression anaysis with 500 observations I have chosen to group (cluster) stations together that are closely related in terms of reach or average price per television station. I have grouped my station variables into 7 different groups.

I am initially trying to  model this with an ARIMAX with distributed lags to pick up any drag behavior. However, what I am finding is that I am getting negative coeeficient for some of the group variables which theoritically does not make any sense. What I believe is happening is that the the regression is picking up the shift from an efficient TV group to a less efficient TV group; thus, it is showing me the net effect of dollars being shifted. What I am finding is that my "group" variables are additive functions of one another....as in

Cost_Group1 = Total Budget - Cost_Group2 Cost_Group3 Cost_Group4 Cost_Group5 Cost_Group6 Cost_Group7.

So if the true effect of 1 dollar (Group7)= 100 and the true effect of 1 dollar(Group1) = 10....then if there is a shift of dollars to Group1, the net effect is -90 and that's not actually true.

So it appears my independent variables are actually endogenous with one another....

any help?

Super User
Posts: 11,777

## Re: Working with independent(exogenous) variables that are functions of one another

Could you provide some examples of what your input data looks like. It need not be actual data if that is sensitive but maybe data with 2 or 3 records for each of 3 "grouped" values.

And the code that you ran.

It may be that you want a group type variable, class perhaps, but without out seeing your data it's a bit hard to see what may be going on.

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