Factor variables and value labels

A factor variable might be

• attitude measured on a scale of 1 to 5,

• agegrp recorded 1 to 4, 1 being 20-30, 2 being 31-40, ...

• region being 1 (North East), 2 (North Central), ...

When you fit a model, Stata allows factor-variable notation. You can type

i.attitude

to obtain the levels of factor variable attitude.

i.attitude#c.age

to obtain the levels of attitude interacted with continuous variable age

i.attitude##c.age

to mean i.attitude age i.attitude#c.age

i.attitude#i.agegrp

to obtain the levels of attitude interacted with the levels of agegrp

i.attitude##i.agegrp

to mean i.attitude i.agegrp i.attitude#i.agegrp

i.attitude#i.agegrp#i.region

to obtain the levels of attitude interacted with the levels of agegrp interacted with the levels of region

i.attitude##i.agegrp##i.region

to mean i.attitude i.agegrp i.region i.attitude#i.agegrp i.attitude#i.region i.agegrp#i.region i.attitude#i.agegrp#i.region

i.(attitude agegrp)

to mean i.attitude i.agegrp

i.(attitude agegrp)##i.region

to mean i.attitude##i.region i.agegrp##i.region

and so on.

Stata also has value labels. You might type

. label define region 1 "North east" 2 "North central" 3 "South" 4 "West"

. label values region region

In Stata, when you fit a model using factor-variable notation, the labels appear in the output:

. regress  y  i.attitude i.agegrp i.region


      Source 
 
       SS       df       MS   
             Number of obs =     400
                    
 
 
 
             F( 10, 389)   =   20.66

       Model 
 
  2827.06814    10  282.706814
             Prob > F      =  0.0000
    Residual 
 
   5323.1334   389  13.6841476
             R-squared     =  0.3469

 
 
 
             Adj R-squared =  0.3301

       Total 
 
  8150.20154   399  20.4265703
             Root MSE      =  3.6692





              y 
 
 Coefficient  Std. err.      t    P>|t|     [95% conf. interval]

 
 
 

       attitude 
 
 

      Disagree  
 
   1.249792   .5911202     2.11   0.035     .0876016    2.411982

       Neutral  
 
   1.556975   .6055619     2.57   0.011     .3663909    2.747558

         Agree  
 
   1.929689   .6013783     3.21   0.001     .7473308    3.112048

Strongly agree  
 
   3.449392   .5878003     5.87   0.000     2.293729    4.605055

                
 
 

         agegrp 
 
 

         31-40  
 
   1.876376   .5265159     3.56   0.000     .8412029    2.911549

         41-50  
 
   3.583126   .5174298     6.92   0.000     2.565817    4.600435

           50+  
 
     5.8832   .5266951    11.17   0.000     4.847675    6.918726

                
 
 

         region 
 
 

 North Central  
 
    .447837   .5133434     0.87   0.384    -.5614377    1.457112

         South  
 
  -1.397359   .5263279    -2.65   0.008    -2.432163   -.3625559

          West  
 
  -2.065611   .5209034    -3.97   0.000    -3.089749   -1.041473

                
 
 

          _cons 
 
   9.115172   .6209843    14.68   0.000     7.894266    10.33608

Value labels are also used by Stata's postestimation commands. Below we use pwcompare to compare y values for each pairing of the age groups:

. pwcompare agegrp

Pairwise comparisons of marginal linear predictions

Margins: asbalanced




                
 
                                 Unadjusted

                
 
   Contrast   Std. Err.     [95% Conf. Interval]

 
 
 

         agegrp 
 
 

31-40 vs 20-30  
 
   1.876376   .5265159      .8412029    2.911549

41-50 vs 20-30  
 
   3.583126   .5174298      2.565817    4.600435

  50+ vs 20-30  
 
     5.8832   .5266951      4.847675    6.918726

41-50 vs 31-40  
 
    1.70675   .5264024         .6718    2.741699

  50+ vs 31-40  
 
   4.006824   .5373647      2.950322    5.063327

  50+ vs 41-50  
 
   2.300075   .5304714      1.257125    3.343024

For instance, 31–40 year olds, have an average value of y that is 2.11 higher than that of 20–30 year olds, controlling for the other covariates in the model.