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I'm considering an example where I'm creating a model to predict a binary categorical outcome to determine whether a tool will be successful (e.g. 1,0) over different periods of time. If I create an independent variable that is a composite of other independent variables (e.g. ALT = Tot_age-TSLT) then can I also still use the independent variables that created it? For example, can I have a model that looks like this:

Outcome=beta_0 + beta_1(TSLT) + beta_2(ASLT)

I have been told that you should not use composite variables and the variables that make up the composite variable in the same model. Is there a concrete reason why and does this apply to every case?

Variables:

  1. TSLT is time since last tested (The tool will be tested several times throughout its life in a simulated setting that is assumed to be as close to real life outcome as possible. Thus, if it is successful during simulated test, it is assumed it will be successful during real life. However, the further from the test date, the less certain of real life success you can be.)
  2. Tot_age is the age of the tool today based on its manufacture date
  3. ALT is age of the tool the last time it was tested
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There is absolutely no problem using composite variables, no matter if they are sums, products... or whatever you think of.

However you must be aware of the fact that if your composite variable is just a sum (or difference, or linear combination) of raw variables then the model you get is not more powerful than the model with raw variables.

In this case, the model $Out=\beta_0+\beta_1 TSLT+\beta_2ASLT$ is the same as the model $Out=\alpha_0+\alpha_1 TSLT+\alpha_2 Totage$ in the sense that regression will produce two formulae that predict exactly the same value for $Out$.

However, the coefficients will have a different meaning (and value), something that may be useful for your analysis.

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