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Math Help - Breaking up a variable

  1. #1
    Jun 2013

    Breaking up a variable

    Hi, I have a question about a regression I am running (actually an event history/survival analysis model, but my question should apply to all types of regression). In the original model, a variable--let's say the "geographic concentration of trees"--has a significant negative effect on the likelihood of the focal entity dying, given that it has survived so far. In the second model, I break up this variable into two exhaustive sub-variables: (1) the "geographic concentration of coniferous trees" and (2) the "geographic concentration of deciduous trees". Both these sub-variables have a negative coefficient but not a significant one.

    My question is: Can a variable have a significant effect but its sub-variables not have significant effects (even though the signs of the coefficients are the same as the sign on the original variable)?
    Last edited by turqwise; June 20th 2013 at 07:13 AM.
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  2. #2
    MHF Contributor
    Sep 2012

    Re: Breaking up a variable

    Hey turqwise.

    If you have two sub-variables you have somet cohing like B1*X1 + B2*X2 and with one sub-variable I'm assuming its B3*(X1+X2) = B3*X1 + B3*X2 for appropria scete co-efficients B1, B2, and B3.

    In the first scenario you are testing B1 = B2 = 0 for non-significant but in the second you are testing B3 = 0.

    If we consider a situation where test statistic for B1 = -1.5 and B2 = -1.5 then both will be in-significant but if B3 = -1.5 + -1.5 = -3.0 (assuming that can happen) then this will be significant.

    For more precise analyses you should consider the covariance between X1 and X2 and this relationship on the response variable.
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