Transforming Independent Variables

[Yawo Kokuvi]

Hello,

good morning. I am looking for some guidance on transforming (or not) of a set of independent variables that I will be using for a logit model. Most of these variables, particularly proportions and density - have true meaningful zeros. The temptation is for a log transformation but that will not deal with the zero issue.

Thanks for any assistance.

cheers, Cy

                      Age at interview
-------------------------------------------------------------
      Percentiles      Smallest
 1%           16             15
 5%           19             15
10%           21             16       Obs                 595
25%           25             16       Sum of Wgt.         595

50%           30                      Mean           30.61513
                        Largest       Std. Dev.       8.64633
75%           35             65
90%           41             65       Variance       74.75903
95%           46             72       Skewness       1.217693
99%           61             74       Kurtosis       5.868338

              Highest grade in school completed
-------------------------------------------------------------
      Percentiles      Smallest
 1%            7              2
 5%            8              5
10%            9              5       Obs                 588
25%           11              7       Sum of Wgt.         588

50%           12                      Mean           11.87075
                        Largest       Std. Dev.      2.198876
75%           13             18
90%           14             18       Variance       4.835054
95%           16             20       Skewness       .1317919
99%           18             22       Kurtosis       4.874681

           Score out of 11 on KAB qnnaire section
-------------------------------------------------------------
      Percentiles      Smallest
 1%            8              7
 5%            9              7
10%            9              7       Obs                 422
25%           10              7       Sum of Wgt.         422

50%           10                      Mean           10.13507
                        Largest       Std. Dev.      .8599024
75%           11             11
90%           11             11       Variance       .7394322
95%           11             11       Skewness      -.8235116
99%           11             11       Kurtosis       3.482594

                       SH:Density_Know
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            0              0
10%         .014              0       Obs                 562
25%         .092              0       Sum of Wgt.         562

50%           .2                      Mean           .2290338
                        Largest       Std. Dev.      .1633596
75%         .356             .5
90%           .5             .5       Variance       .0266864
95%           .5             .5       Skewness        .296762
99%           .5             .5       Kurtosis       1.866217

                       SH:Density_Drug
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            0              0
10%            0              0       Obs                 562
25%            0              0       Sum of Wgt.         562

50%         .027                      Mean           .0689609
                        Largest       Std. Dev.      .0986219
75%         .107             .5
90%         .186             .5       Variance       .0097263
95%         .286             .5       Skewness       2.062268
99%           .5             .5       Kurtosis       7.724059

                       SH:Density_Sex
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            0              0
10%            0              0       Obs                 562
25%            0              0       Sum of Wgt.         562

50%         .005                      Mean           .0140801
                        Largest       Std. Dev.      .0253859
75%         .018           .107
90%         .036           .167       Variance       .0006444
95%         .053           .167       Skewness       5.274151
99%         .107           .333       Kurtosis       52.14508

                   
mean size ego network
-------------------------------------------------------------
      Percentiles      Smallest
 1%            1              1
 5%            2              1
10%            3              1       Obs                 589
25%            6              1       Sum of Wgt.         589

50%            9                      Mean           11.11205
                        Largest       Std. Dev.      8.034429
75%           15             40
90%           21             44       Variance       64.55205
95%           27             54       Skewness       1.737934
99%           38             66       Kurtosis        8.57792

               proportion of gender homophily
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            0              0
10%            0              0       Obs                 589
25%           .2              0       Sum of Wgt.         589

50%     .3846154                      Mean           .3687123
                        Largest       Std. Dev.      .2372442
75%     .5384615              1
90%     .6666667              1       Variance       .0562848
95%     .7307692              1       Skewness      -.0105412
99%         .875              1       Kurtosis       2.254534

              proportion of behavcat homophily
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            0              0
10%            0              0       Obs                 589
25%            0              0       Sum of Wgt.         589

50%            0                      Mean           .0959932
                        Largest       Std. Dev.      .1599062
75%          .15             .8
90%     .3333333              1       Variance         .02557
95%           .4              1       Skewness       2.299208
99%          .75              1       Kurtosis       9.709863

                proportion of race homophily
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            0              0
10%     .1111111              0       Obs                 589
25%     .4545455              0       Sum of Wgt.         589

50%          .75                      Mean           .6676776
                        Largest       Std. Dev.      .3243566
75%            1              1
90%            1              1       Variance       .1052072
95%            1              1       Skewness       -.756955
99%            1              1       Kurtosis       2.355689

                mean absolute age difference
-------------------------------------------------------------
      Percentiles      Smallest
 1%          1.5              0
 5%            3              0
10%     3.851852              0       Obs                 589
25%         5.75              0       Sum of Wgt.         589

50%        8.875                      Mean           9.974443
                        Largest       Std. Dev.      6.615875
75%     12.55556       40.63636
90%           17             43       Variance        43.7698
95%           20             54       Skewness       3.008487
99%     36.33333             72       Kurtosis       21.36231

               Number of sexual contacts (est)
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            1              0
10%            1              0       Obs                 549
25%            1              0       Sum of Wgt.         549

50%            2                      Mean           60.49909
                        Largest       Std. Dev.      337.1342
75%            6           2001
90%           51           2700       Variance       113659.5
95%          200           3001       Skewness       10.48025
99%         1802           5401       Kurtosis       138.0463

[Nick Cox]

Square roots, cube roots and neglog are all available for right-skewed distributions with possible outliers. The aim of transformation, however, is better if it is to handle nonlinearity and/or outliers rather than to attain symmetric marginal distributions. (There is a myth in many corners that predictors should be normally distributed.)

[Phil Bromiley]

You need to think hard about your variables before making a bunch of arbitrary transformations. Transforming iv's changes the model being estimated and can make it harder to interpret.

Glancing at your descriptive statistics, it is not obvious why you'd want to transform most of your variables. In others, some serious consideration of the relations might be worthwhile. For example, with some like "proportion of behavcat homophily" you might wonder whether there is a different relation for all the zeros and the non-zero values. On the other hand, sexual contacts does look like a few observations with extremely high values have a disproportionate influence on an estimation. How to handle such observations (often termed outliers) is a source of substantial disagreement among folks who do applied statistical analysis.