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  • Mean Centering Variable for Interactioneffect

    Dear Statalists

    I'm in the final phase of my research and I want to look into the interaction effect of two variables.
    I'm having trouble with multicollinearity because of the interaction between one of the two variables and the interaction variable.

    I know mean centering variables is often used with this problem.
    However, I must be doing something wrong because my variable doesn't change after substracting the mean at every observation as well as my vif values do not change.
    I didn't know how to solve this in one step so I tried doing it with multiple steps.
    1) I asked for the mean value of the interaction variable
    2) I generated a new variable with this value in every cell/observation
    3) I substracted the initial interaction variable by the mean of the variable

    Am I doing something wrong here? Can someone please help me out.

    My coding process is below.

    Kind regards
    Kletser Jok



    Code:
    . gen Interaction= UAI* Altman_high
    
    . reg CAR_win Interaction UAI Altman_high LnSize Leverage LnDealValue Domestic Horizontal Japan US
    
          Source |       SS           df       MS      Number of obs   =       176
    -------------+----------------------------------   F(10, 165)      =      1.80
           Model |  .038689375        10  .003868937   Prob > F        =    0.0650
        Residual |  .355554565       165  .002154876   R-squared       =    0.0981
    -------------+----------------------------------   Adj R-squared   =    0.0435
           Total |  .394243939       175  .002252823   Root MSE        =    .04642
    
    ------------------------------------------------------------------------------
         CAR_win |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    -------------+----------------------------------------------------------------
     Interaction |  -.0000212   .0000375    -0.56   0.574    -.0000953     .000053
             UAI |   .0004438    .000323     1.37   0.171     -.000194    .0010816
     Altman_high |   .0003951   .0023014     0.17   0.864    -.0041489     .004939
          LnSize |  -.0047945   .0023444    -2.05   0.042    -.0094233   -.0001657
        Leverage |  -.0230251   .0208805    -1.10   0.272    -.0642525    .0182023
     LnDealValue |   .0052026   .0024621     2.11   0.036     .0003412     .010064
        Domestic |  -.0058679   .0095064    -0.62   0.538    -.0246378    .0129019
      Horizontal |  -.0071467   .0072896    -0.98   0.328    -.0215395    .0072462
           Japan |  -.0237803   .0124236    -1.91   0.057      -.04831    .0007493
              US |  -.0265029   .0131432    -2.02   0.045    -.0524535   -.0005522
           _cons |   .0488307   .0304801     1.60   0.111    -.0113505    .1090119
    ------------------------------------------------------------------------------
    
    . vif
    
        Variable |       VIF       1/VIF  
    -------------+----------------------
     Interaction |     10.29    0.097223
     Altman_high |     10.03    0.099713
             UAI |      4.12    0.242708
          LnSize |      3.70    0.270312
     LnDealValue |      3.29    0.304259
           Japan |      2.76    0.362260
        Leverage |      1.33    0.753473
              US |      1.30    0.771970
        Domestic |      1.15    0.869232
      Horizontal |      1.08    0.921773
    -------------+----------------------
        Mean VIF |      3.90
    
    . mean (Interaction)
    
    Mean estimation                   Number of obs   =        176
    
    --------------------------------------------------------------
                 |       Mean   Std. Err.     [95% Conf. Interval]
    -------------+------------------------------------------------
     Interaction |    243.902   22.60059      199.2972    288.5068
    --------------------------------------------------------------
    
    . gen Meaninteraction= 243.902
    
    . gen MC_Interaction=Interaction- Meaninteraction
    
    . reg CAR_win MC_Interaction UAI Altman_high LnSize Leverage LnDealValue Domestic Horizontal Japan US
    
          Source |       SS           df       MS      Number of obs   =       176
    -------------+----------------------------------   F(10, 165)      =      1.80
           Model |  .038689375        10  .003868937   Prob > F        =    0.0650
        Residual |  .355554565       165  .002154876   R-squared       =    0.0981
    -------------+----------------------------------   Adj R-squared   =    0.0435
           Total |  .394243939       175  .002252823   Root MSE        =    .04642
    
    --------------------------------------------------------------------------------
           CAR_win |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    ---------------+----------------------------------------------------------------
    MC_Interaction |  -.0000212   .0000375    -0.56   0.574    -.0000953     .000053
               UAI |   .0004438    .000323     1.37   0.171     -.000194    .0010816
       Altman_high |   .0003951   .0023014     0.17   0.864    -.0041489     .004939
            LnSize |  -.0047945   .0023444    -2.05   0.042    -.0094233   -.0001657
          Leverage |  -.0230251   .0208805    -1.10   0.272    -.0642525    .0182023
       LnDealValue |   .0052026   .0024621     2.11   0.036     .0003412     .010064
          Domestic |  -.0058679   .0095064    -0.62   0.538    -.0246378    .0129019
        Horizontal |  -.0071467   .0072896    -0.98   0.328    -.0215395    .0072462
             Japan |  -.0237803   .0124236    -1.91   0.057      -.04831    .0007493
                US |  -.0265029   .0131432    -2.02   0.045    -.0524535   -.0005522
             _cons |    .043672   .0328617     1.33   0.186    -.0212115    .1085556
    --------------------------------------------------------------------------------
    
    . vif
    
        Variable |       VIF       1/VIF  
    -------------+----------------------
    MC_Interac~n |     10.29    0.097223
     Altman_high |     10.03    0.099713
             UAI |      4.12    0.242708
          LnSize |      3.70    0.270312
     LnDealValue |      3.29    0.304259
           Japan |      2.76    0.362260
        Leverage |      1.33    0.753473
              US |      1.30    0.771970
        Domestic |      1.15    0.869232
      Horizontal |      1.08    0.921773
    -------------+----------------------
        Mean VIF |      3.90
    
    .

  • #2
    Mean-center the individual components that contribute to the interaction term, and not the interaction term, itself.
    Code:
    foreach var of varlist UAI Altman_high {
        summarize `var', meanonly
        generate double `var'_c = `var' - r(mean)
    }
    Also, use Stata's factor variable notation.
    Code:
    regress CAR_win ///
        c.UAI_c##c.Altman_high_c ///
        c.(LnSize Leverage LnDealValue) ///
        i.(Domestic Horizontal Japan US)

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