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For my project, I am fitting a logistic regression to the some 'dummy' bank data. The head of the dataset looks like this

Obs counterparty_id data_period default age LTV
1   1               200712      1       15  120
2   1               200801      1       15  125
... ...             ...         ...     ... ...
100 10              200712      0       5   50
101 10              200801      0       5   50

And in the process, I have been told to fit a curve to age and LTV in order to find the best transformation, so I fit the curve and I get some results which look like this

Cubic transformation:

Score = beta_0 + beta_1*Age + beta_2*Age^2 + beta_3*Age^3
Score = 0.4    + 0.2*Age    + 0.15*Age^2   + 0.7*Age^3 

Quadratic transformation:

Score = beta_0 + beta_1*Age + beta_2*Age^2
Score = 0.1    + 0.13*Age    + 0.17*Age   

I understand the purpose of the curve fit in the logistic regression and I select the best transformation using Somers' D and R_sq_adj

However, now I am at the stage of preparing my variables for multi-factor-analysis, I unsure whether or not I apply just the cubic transformation to my raw data

Cubic_score = age^3

Or, I save the coefficients and then I apply this exact transformation to my variable

Cubic_score = 0.4    + 0.2*Age    + 0.15*Age^2   + 0.7*Age^3

So, my MFA regression would essentially look like this (I've left out LTV until now just to show the example of the process of selecting the best variables)

Option 1: Applying the transformation to the raw data

default = coefficient + age^3 + log(LTV)

Option 2: Applying the curve fit to the raw data

default = coefficient + (0.4 + 0.2*Age + 0.15*Age^2 + 0.7*Age^3) + (0.1 + 0.7* log(LTV))
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1 Answer 1

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Go for option 1. From what I see here, with option 2 you are trying to make coefficients as your independent variables.

But when going for option 1, include the original variable itself and not just the transformation. For example, using your notation: default = coefficient + age + age^2 + age^3 + log(LTV)

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    $\begingroup$ As your answer recognizes, the best coefficients for age and LTV as single predictors will typically be different from their coefficients in a model that includes both of them and possibly other predictors. So Option 1 is appropriate while Option 2 is not. Note, however, that a spline fit might be preferred to a polynomial fit, particularly if the Age values aren't expressed relative to some value within their typical range (e.g., mean or median). $\endgroup$
    – EdM
    Feb 5, 2019 at 16:32
  • $\begingroup$ Hello, thank you both for your input. Your advice makes sense! $\endgroup$
    – user235111
    Feb 6, 2019 at 7:51

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