how to standardize scores of a variable created from a principal component analysis?

[Eunhye Kang]

I did the principal component analysis and drew 2 components.
And I want to standardize the scales to 0-100 points for ease of interpretation.

By doing "predict pc1 pc2, score" I get 2 new variables of "pc1" and "pc2"

Now, how can I standardize their scores?


One more, can I use these variables for interaction effect? When I try it, Stata says " factor variables may not contain noninteger values"
What does this mean, and what would be the solution?

[Clyde Schechter]

"Standardizing" usually means adjusting so that the mean is zero and the standard deviation is 1. But it sounds like you want to transform these so that the scores range from 0 through 100.

foreach v of varlist pc1 pc2 {
    summ `v', meanonly
    gen `v'_100 = 100*(`v'-`r(min)')/(`r(max)'-`r(min)')
}

If you used pc1##pc2 for your interaction, Stata assumes, by default, that any variables specified in an interaction with # or ## are categorical variables. Categorical variables must have non-negative integer values. But pc1 and pc2 are continuous variables, so you have to tell Stata to override the default assumption. You do that with c.pc1##c.pc2.

[Nick Cox]

PCs are uncorrelated by construction, so looking for interactions is unnecessary and futile.

[Clyde Schechter]

Nick, that's not right. You can still have an interaction effect involving predictors that are independent of each other. Here's an artificial example:

. clear*

. set seed 1234

. set obs 100
number of observations (_N) was 0, now 100

. 
. gen x1 = rnormal()

. gen x2 = rnormal()

. corr x1 x2
(obs=100)

             |       x1       x2
-------------+------------------
          x1 |   1.0000
          x2 |  -0.0450   1.0000


. 
. gen xb = x1 + 2*x2 + 3*x1*x2

. gen y = xb + 0.5*rnormal()

. 
. regress y x1 x2

      Source |       SS           df       MS      Number of obs   =       100
-------------+----------------------------------   F(2, 97)        =     26.96
       Model |  391.682687         2  195.841344   Prob > F        =    0.0000
    Residual |  704.568718        97  7.26359503   R-squared       =    0.3573
-------------+----------------------------------   Adj R-squared   =    0.3440
       Total |   1096.2514        99  11.0732465   Root MSE        =    2.6951

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |    .483185   .2782382     1.74   0.086    -.0690408    1.035411
          x2 |   1.932138   .2681312     7.21   0.000     1.399972    2.464304
       _cons |  -.1104604   .2697883    -0.41   0.683    -.6459155    .4249946
------------------------------------------------------------------------------

. regress y c.x1##c.x2

      Source |       SS           df       MS      Number of obs   =       100
-------------+----------------------------------   F(3, 96)        =   1140.28
       Model |  1066.32678         3  355.442259   Prob > F        =    0.0000
    Residual |  29.9246276        96  .311714871   R-squared       =    0.9727
-------------+----------------------------------   Adj R-squared   =    0.9718
       Total |   1096.2514        99  11.0732465   Root MSE        =    .55831

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   .9777604   .0586116    16.68   0.000     .8614173    1.094104
          x2 |   2.004361   .0555674    36.07   0.000     1.894061    2.114661
             |
   c.x1#c.x2 |    3.02602   .0650449    46.52   0.000     2.896907    3.155133
             |
       _cons |   .0229037   .0559624     0.41   0.683    -.0881808    .1339883
------------------------------------------------------------------------------

[Nick Cox]

Clyde: Good point. Thanks.

A basic confusion on my part. Please ignore #3.