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Statistical Computing Seminars
Logistic Regression with Stata

The purpose of this seminar is to help you increase your skills in using logistic regression analysis with Stata.  The seminar does not teach logistic regression, per se, but focuses on how to perform logistic regression analyses and interpret the results using Stata.  It is assumed that you are familiar with Logistic Regression (e.g. have had a class in logistic regression or have read about logistic regression, see our Statistics Books for Loan for books you can borrow on logistic regression).

In addition to the built-in Stata commands we will be demonstrating the use of a number on user-written ado's, in particular, listcoef, fitstat, prchange, prtab, prgen, etc. To find out more about these programs or to download them type findit followed by the program name in the Stata command window (example: findit listcoef). These add-on programs ease the running and interpretation of ordinal logistic models. Or, you can download the complete spostado package by typing the following in the Stata command window.:

We will use the hsb2 dataset. It doesn't have a binary response variable so we will create one. The variable hiwrite will indicate students with writing scores greater than or equal to 52. We will looks at some descriptive statistics before we begin our first logistic regression model.

use http://www.ats.ucla.edu/stat/stata/notes/hsb2, clear
generate hiwrite = write>=52

describe hiwrite read female prog
 
               storage  display     value
variable name   type   format      label      variable label
-------------------------------------------------------------------------------
hiwrite         float  %9.0g                  
read            float  %9.0g                  reading score
female          float  %9.0g       fl         
prog            float  %9.0g       sel        type of program

summarize hiwrite read female prog
 
    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
     hiwrite |       200         .63    .4840159          0          1
        read |       200       52.23    10.25294         28         76
      female |       200        .545    .4992205          0          1
        prog |       200       2.025    .6904772          1          3

tab1 hiwrite female prog
 
-> tabulation of hiwrite  

    hiwrite |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         74       37.00       37.00
          1 |        126       63.00      100.00
------------+-----------------------------------
      Total |        200      100.00

-> tabulation of female  

     female |      Freq.     Percent        Cum.
------------+-----------------------------------
       male |         91       45.50       45.50
     female |        109       54.50      100.00
------------+-----------------------------------
      Total |        200      100.00

-> tabulation of prog  

    type of |
    program |      Freq.     Percent        Cum.
------------+-----------------------------------
    general |         45       22.50       22.50
   academic |        105       52.50       75.00
   vocation |         50       25.00      100.00
------------+-----------------------------------
      Total |        200      100.00 

xi: logit hiwrite read female i.prog
i.prog            _Iprog_1-3          (naturally coded; _Iprog_1 omitted)

Iteration 0:   log likelihood = -131.79114
Iteration 1:   log likelihood = -91.787685
Iteration 2:   log likelihood = -87.382389
Iteration 3:   log likelihood = -87.017358
Iteration 4:   log likelihood = -87.013521
Iteration 5:   log likelihood = -87.013521

Logit estimates                                   Number of obs   =        200
                                                  LR chi2(4)      =      89.56
                                                  Prob > chi2     =     0.0000
Log likelihood = -87.013521                       Pseudo R2       =     0.3398

------------------------------------------------------------------------------
     hiwrite |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        read |   .1504846   .0269589     5.58   0.000     .0976462    .2033231
      female |   1.775335   .4176567     4.25   0.000     .9567429    2.593927
    _Iprog_2 |   .5915962   .4600557     1.29   0.198    -.3100963    1.493289
    _Iprog_3 |  -.8139846   .5073391    -1.60   0.109    -1.808351    .1803819
       _cons |  -8.053889   1.468961    -5.48   0.000      -10.933   -5.174778
------------------------------------------------------------------------------

estimates store M1

/* Wald test */
test _Iprog_2 _Iprog_3
 
 ( 1)  _Iprog_2 = 0
 ( 2)  _Iprog_3 = 0

           chi2(  2) =    9.03
         Prob > chi2 =    0.0110 

/* Likelihood ratio-test */
logit hiwrite read female, nolog
 
Logit estimates                                   Number of obs   =        200
                                                  LR chi2(2)      =      80.17
                                                  Prob > chi2     =     0.0000
Log likelihood = -91.703855                       Pseudo R2       =     0.3042

------------------------------------------------------------------------------
     hiwrite |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        read |   .1656448   .0259864     6.37   0.000     .1147124    .2165771
      female |   1.667059   .3962125     4.21   0.000     .8904968    2.443621
       _cons |  -8.700539   1.388431    -6.27   0.000    -11.42181   -5.979264
------------------------------------------------------------------------------
 
lrtest M1
 
likelihood-ratio test                                  LR chi2(2)  =      9.38
(Assumption: . nested in M1)                           Prob > chi2 =    0.0092
  
/* rerun full model */
xi: logit hiwrite read female i.prog, nolog  /* displays coefficients */
i.prog            _Iprog_1-3          (naturally coded; _Iprog_1 omitted)

Logit estimates                                   Number of obs   =        200
                                                  LR chi2(4)      =      89.56
                                                  Prob > chi2     =     0.0000
Log likelihood = -87.013521                       Pseudo R2       =     0.3398

------------------------------------------------------------------------------
     hiwrite |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        read |   .1504846   .0269589     5.58   0.000     .0976462    .2033231
      female |   1.775335   .4176567     4.25   0.000     .9567429    2.593927
    _Iprog_2 |   .5915962   .4600557     1.29   0.198    -.3100963    1.493289
    _Iprog_3 |  -.8139846   .5073391    -1.60   0.109    -1.808351    .1803819
       _cons |  -8.053889   1.468961    -5.48   0.000      -10.933   -5.174778
------------------------------------------------------------------------------
 
xi: logistic hiwrite read female i.prog, nolog  /* displays odds ratios  */
i.prog            _Iprog_1-3          (naturally coded; _Iprog_1 omitted)

Logistic regression                               Number of obs   =        200
                                                  LR chi2(4)      =      89.56
                                                  Prob > chi2     =     0.0000
Log likelihood = -87.013521                       Pseudo R2       =     0.3398

------------------------------------------------------------------------------
     hiwrite | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        read |   1.162397   .0313369     5.58   0.000     1.102573    1.225468
      female |   5.902258   2.465117     4.25   0.000     2.603204    13.38222
    _Iprog_2 |    1.80687    .831261     1.29   0.198     .7333763    4.451712
    _Iprog_3 |    .443089   .2247964    -1.60   0.109     .1639242    1.197675
------------------------------------------------------------------------------
Now we will demonstrate some of the utilities developed by J. Scott Long & Jeremy Freese.
listcoef
 
logistic (N=200): Factor Change in Odds 

  Odds of: 1 vs 0

----------------------------------------------------------------------
     hiwrite |      b         z     P>|z|    e^b    e^bStdX      SDofX
-------------+--------------------------------------------------------
        read |   0.15048    5.582   0.000   1.1624   4.6782    10.2529
      female |   1.77533    4.251   0.000   5.9023   2.4261     0.4992
    _Iprog_2 |   0.59160    1.286   0.198   1.8069   1.3447     0.5006
    _Iprog_3 |  -0.81398   -1.604   0.109   0.4431   0.7023     0.4341
----------------------------------------------------------------------
  
listcoef, percent
 
logistic (N=200): Percentage Change in Odds 

  Odds of: 1 vs 0

----------------------------------------------------------------------
     hiwrite |      b         z     P>|z|      %      %StdX      SDofX
-------------+--------------------------------------------------------
        read |   0.15048    5.582   0.000     16.2    367.8    10.2529
      female |   1.77533    4.251   0.000    490.2    142.6     0.4992
    _Iprog_2 |   0.59160    1.286   0.198     80.7     34.5     0.5006
    _Iprog_3 |  -0.81398   -1.604   0.109    -55.7    -29.8     0.4341
----------------------------------------------------------------------
 
 fitstat
  
 Measures of Fit for logistic of hiwrite

Log-Lik Intercept Only:     -131.791     Log-Lik Full Model:          -87.014
D(195):                      174.027     LR(4):                        89.555
                                         Prob > LR:                     0.000
McFadden's R2:                 0.340     McFadden's Adj R2:             0.302
Maximum Likelihood R2:         0.361     Cragg & Uhler's R2:            0.493
McKelvey and Zavoina's R2:     0.556     Efron's R2:                    0.384
Variance of y*:                7.403     Variance of error:             3.290
Count R2:                      0.775     Adj Count R2:                  0.392
AIC:                           0.920     AIC*n:                       184.027
BIC:                        -859.145     BIC':                        -68.362
Another fit indicator is the Hosmer & Lemeshow goodness-of-fit given by the lfit command which is part of Stata.
lfit, group(10)

Logistic model for hiwrite, goodness-of-fit test

  (Table collapsed on quantiles of estimated probabilities)

       number of observations =       200
             number of groups =        10
      Hosmer-Lemeshow chi2(8) =         7.08
                  Prob > chi2 =         0.5279
Let's look at some logistic regression diagnostics.
predict pprob            /* predicted probabilities */
predict r, resid         /* pearson residulas */
predict h, hat           /* leverage*/
predict db, dbeta        /* pregobon dbeta */
predict dx2, dx2         /* hosmer & lemeshow influence */                    

scatter h r, xline(0) msym(Oh) jitter(2) 



twoway (scatter dx2 pprob if hiwrite, msym(Oh) jitter(2)) ///
       (scatter dx2 pprob if ~hiwrite, msym(Oh) jitter(2)) 



scatter dx2 pprob if hiwrite [w=db], msym(Oh) jitter(2)


 
summarize pprob
 
    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
       pprob |       200         .63    .3032638   .0147326   .9968269
  
histogram pprob
(bin=14, start=.01473261, width=.0701496)

Some researchers find log-odds and odds ratios difficult to interpret and prefer to interpret their results in terms of predicted probabilities.
list hiwrite pprob in 1/30
 
     +--------------------+
     | hiwrite      pprob |
     |--------------------|
  1. |       1   .6280209 |
  2. |       1   .9585295 |
  3. |       0   .1926994 |
  4. |       0   .6485471 |
  5. |       1   .4038342 |
     |--------------------|
  6. |       1   .3013308 |
  7. |       1   .3705969 |
  8. |       0    .087399 |
  9. |       1   .8063778 |
 10. |       1   .7531218 |
     |--------------------|
 11. |       0   .5402142 |
 12. |       1   .7531218 |
 13. |       1   .9713376 |
 14. |       1    .660131 |
 15. |       1   .3339254 |
     |--------------------|
 16. |       0   .1501361 |
 17. |       1   .4038342 |
 18. |       1   .6280209 |
 19. |       1   .9410698 |
 20. |       0   .5554624 |
     |--------------------|
 21. |       0   .8063778 |
 22. |       1   .6485471 |
 23. |       0   .5154799 |
 24. |       1   .8273249 |
 25. |       0   .0355732 |
     |--------------------|
 26. |       0   .0229461 |
 27. |       1   .9104555 |
 28. |       1   .1424491 |
 29. |       0   .3013308 |
 30. |       0    .443076 |
     +--------------------+
Here is another utility (leastlikely) by Jeremy Freese that is not part of the spostado package.
leastlikely hiwrite read female prog 
 
Outcome: 0 

     +-----------------------------------------------+
     |     Prob   hiwrite   read   female       prog |
     |-----------------------------------------------|
 69. | .1173011         0     63     male   academic |
127. |  .137374         0     50   female   academic |
140. |  .105435         0     52   female   academic |
162. | .0526169         0     57   female   academic |
190. |  .137374         0     50   female   academic |
     |-----------------------------------------------|
198. |    .0912         0     57   female    general |
     +-----------------------------------------------+

Outcome: 1 

     +-----------------------------------------------+
     |     Prob   hiwrite   read   female       prog |
     |-----------------------------------------------|
  6. | .3013308         1     44     male   academic |
 28. | .1424491         1     47     male   vocation |
134. | .3160069         1     42   female   vocation |
158. | .3160069         1     42   female   vocation |
191. | .3160069         1     42   female   vocation |
     |-----------------------------------------------|
192. | .2971081         1     36   female    general |
     +-----------------------------------------------+
  
prchange
 

logit: Changes in Predicted Probabilities for hiwrite

          min->max      0->1     -+1/2    -+sd/2  MargEfct
    read    0.9293    0.0002    0.0312    0.3119    0.0312
  female    0.3657    0.3657    0.3560    0.1822    0.3678
_Iprog_2    0.1229    0.1229    0.1221    0.0613    0.1226
_Iprog_3   -0.1801   -0.1801   -0.1675   -0.0731   -0.1686

              0       1
Pr(y|x)  0.2931  0.7069

            read    female  _Iprog_2  _Iprog_3
    x=     52.23      .545      .525       .25
sd(x)=   10.2529    .49922   .500628   .434099
 
prchange, fromto
 
logit: Changes in Predicted Probabilities for hiwrite

              from:       to:      dif:     from:       to:      dif:     from:       to:      dif:
             x=min     x=max  min->max       x=0       x=1      0->1     x-1/2     x+1/2     -+1/2
    read    0.0592    0.9885    0.9293    0.0009    0.0011    0.0002    0.6911    0.7223    0.0312
  female    0.4783    0.8440    0.3657    0.4783    0.8440    0.3657    0.4982    0.8542    0.3560
_Iprog_2    0.6388    0.7616    0.1229    0.6388    0.7616    0.1229    0.6422    0.7643    0.1221
_Iprog_3    0.7473    0.5671   -0.1801    0.7473    0.5671   -0.1801    0.7837    0.6162   -0.1675

              from:       to:      dif:          
           x-1/2sd   x+1/2sd    -+sd/2  MargEfct
    read    0.5273    0.8392    0.3119    0.0312
  female    0.6076    0.7898    0.1822    0.3678
_Iprog_2    0.6754    0.7367    0.0613    0.1226
_Iprog_3    0.7422    0.6691   -0.0731   -0.1686

              0       1
Pr(y|x)  0.2931  0.7069

            read    female  _Iprog_2  _Iprog_3
    x=     52.23      .545      .525       .25
sd(x)=   10.2529    .49922   .500628   .434099
 
prchange, x(_Iprog_2=0 _Iprog_3=0)
 
logit: Changes in Predicted Probabilities for hiwrite

          min->max      0->1     -+1/2    -+sd/2  MargEfct
    read    0.9337    0.0001    0.0325    0.3237    0.0325
  female    0.3778    0.3778    0.3689    0.1896    0.3835
_Iprog_2    0.1123    0.1123    0.1273    0.0639    0.1278
_Iprog_3   -0.1944   -0.1944   -0.1744   -0.0762   -0.1759

              0       1
Pr(y|x)  0.3157  0.6843

            read    female  _Iprog_2  _Iprog_3
    x=     52.23      .545         0         0
sd(x)=   10.2529    .49922   .500628   .434099

prchange, x(_Iprog_2=1 _Iprog_3=0)
 
logit: Changes in Predicted Probabilities for hiwrite

          min->max      0->1     -+1/2    -+sd/2  MargEfct
    read    0.9002    0.0002    0.0244    0.2502    0.0244
  female    0.2997    0.2997    0.2878    0.1437    0.2877
_Iprog_2    0.1123    0.1123    0.0959    0.0480    0.0959
_Iprog_3   -0.1622   -0.1622   -0.1320   -0.0573   -0.1319

              0       1
Pr(y|x)  0.2034  0.7966

            read    female  _Iprog_2  _Iprog_3
    x=     52.23      .545         1         0
sd(x)=   10.2529    .49922   .500628   .434099
 
prchange, x(_Iprog_2=0 _Iprog_3=1)
 
logit: Changes in Predicted Probabilities for hiwrite

          min->max      0->1     -+1/2    -+sd/2  MargEfct
    read    0.9473    0.0001    0.0376    0.3675    0.0376
  female    0.4156    0.4156    0.4167    0.2179    0.4437
_Iprog_2    0.1445    0.1445    0.1468    0.0739    0.1478
_Iprog_3   -0.1944   -0.1944   -0.2007   -0.0881   -0.2034

              0       1
Pr(y|x)  0.5101  0.4899

            read    female  _Iprog_2  _Iprog_3
    x=     52.23      .545         0         1
sd(x)=   10.2529    .49922   .500628   .434099
 
prvalue, x(female=0 _Iprog_2=1 _Iprog_3=0) rest(mean)

logit: Predictions for hiwrite

  Pr(y=1|x):          0.5981   95% ci: (0.4424,0.7362)
  Pr(y=0|x):          0.4019   95% ci: (0.2638,0.5576)

        read    female  _Iprog_2  _Iprog_3
x=     52.23         0         1         0

prtab read
 
logit: Predicted probabilities of positive outcome for hiwrite

----------------------
reading   |
score     | Prediction
----------+-----------
       28 |     0.0592
       31 |     0.0900
       34 |     0.1344
       35 |     0.1529
       36 |     0.1734
       37 |     0.1960
       39 |     0.2478
       41 |     0.3080
       42 |     0.3410
       43 |     0.3756
       44 |     0.4115
       45 |     0.4483
       46 |     0.4858
       47 |     0.5234
       48 |     0.5607
       50 |     0.6330
       52 |     0.6997
       53 |     0.7304
       54 |     0.7589
       55 |     0.7854
       57 |     0.8318
       60 |     0.8859
       61 |     0.9003
       63 |     0.9242
       65 |     0.9428
       66 |     0.9504
       68 |     0.9628
       71 |     0.9760
       73 |     0.9821
       76 |     0.9885
----------------------

        read    female  _Iprog_2  _Iprog_3
x=     52.23      .545      .525       .25
 
prtab read female
 
logit: Predicted probabilities of positive outcome for hiwrite

--------------------------
reading   |     female    
score     |   male  female
----------+---------------
       28 | 0.0234  0.1237
       31 | 0.0362  0.1815
       34 | 0.0557  0.2583
       35 | 0.0642  0.2881
       36 | 0.0738  0.3199
       37 | 0.0848  0.3535
       39 | 0.1113  0.4249
       41 | 0.1447  0.4996
       42 | 0.1643  0.5372
       43 | 0.1860  0.5743
       44 | 0.2099  0.6106
       45 | 0.2360  0.6457
       46 | 0.2642  0.6794
       47 | 0.2944  0.7112
       48 | 0.3266  0.7411
       50 | 0.3959  0.7946
       52 | 0.4696  0.8394
       53 | 0.5072  0.8587
       54 | 0.5447  0.8760
       55 | 0.5817  0.8914
       57 | 0.6527  0.9173
       60 | 0.7469  0.9457
       61 | 0.7743  0.9529
       63 | 0.8226  0.9647
       65 | 0.8623  0.9737
       66 | 0.8792  0.9773
       68 | 0.9077  0.9831
       71 | 0.9392  0.9892
       73 | 0.9543  0.9919
       76 | 0.9704  0.9949
--------------------------

        read    female  _Iprog_2  _Iprog_3
x=     52.23      .545      .525       .25
 
prtab read female, x(_Iprog_2=1 _Iprog_3=0)
 
logit: Predicted probabilities of positive outcome for hiwrite

--------------------------
reading   |     female    
score     |   male  female
----------+---------------
       28 | 0.0374  0.1864
       31 | 0.0575  0.2647
       34 | 0.0874  0.3611
       35 | 0.1002  0.3965
       36 | 0.1146  0.4330
       37 | 0.1307  0.4703
       39 | 0.1689  0.5454
       41 | 0.2154  0.6184
       42 | 0.2420  0.6533
       43 | 0.2706  0.6865
       44 | 0.3013  0.7180
       45 | 0.3339  0.7474
       46 | 0.3682  0.7748
       47 | 0.4038  0.7999
       48 | 0.4405  0.8229
       50 | 0.5155  0.8626
       52 | 0.5897  0.8946
       53 | 0.6256  0.9079
       54 | 0.6601  0.9198
       55 | 0.6930  0.9302
       57 | 0.7531  0.9474
       60 | 0.8273  0.9658
       61 | 0.8478  0.9705
       63 | 0.8827  0.9780
       65 | 0.9105  0.9836
       66 | 0.9220  0.9859
       68 | 0.9411  0.9895
       71 | 0.9617  0.9933
       73 | 0.9713  0.9950
       76 | 0.9816  0.9968
--------------------------

        read    female  _Iprog_2  _Iprog_3
x=     52.23      .545         1         0
 
prgen read, from(0) to(100) gen(prg1) x(_Iprog_2=0 _Iprog_3=0 female=1) n(11)
prgen read, from(0) to(100) gen(prg2) x(_Iprog_2=1 _Iprog_3=0 female=1) n(11)
prgen read, from(0) to(100) gen(prg3) x(_Iprog_2=0 _Iprog_3=1 female=1) n(11)

graph twoway scatter prg1p1 prg2p1 prg3p1 prg1x, con(l l l) msym(O D S)

In the next section we will by using the commands xi3 and postgr3 developed by Michael Mitchell of ATS. You can obtain these commands by typing findit xi3 and findit postgr3 at the Stata command line. Note these also require the spostado package by typing findit spostado.
xi3: logit hiwrite read female i.prog
i.prog            _Iprog_1-3          (naturally coded; _Iprog_1 omitted)

Iteration 0:   log likelihood = -131.79114
Iteration 1:   log likelihood = -91.787685
Iteration 2:   log likelihood = -87.382389
Iteration 3:   log likelihood = -87.017358
Iteration 4:   log likelihood = -87.013521
Iteration 5:   log likelihood = -87.013521

Logit estimates                                   Number of obs   =        200
                                                  LR chi2(4)      =      89.56
                                                  Prob > chi2     =     0.0000
Log likelihood = -87.013521                       Pseudo R2       =     0.3398

------------------------------------------------------------------------------
     hiwrite |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        read |   .1504846   .0269589     5.58   0.000     .0976462    .2033231
      female |   1.775335   .4176567     4.25   0.000     .9567429    2.593927
    _Iprog_2 |   .5915962   .4600557     1.29   0.198    -.3100963    1.493289
    _Iprog_3 |  -.8139846   .5073391    -1.60   0.109    -1.808351    .1803819
       _cons |  -8.053889   1.468961    -5.48   0.000      -10.933   -5.174778
------------------------------------------------------------------------------
 
postgr3 read, by(prog) x(female=1)

Next, we will demonstrate some alternative coding systems using xi3.
xi: logit hiwrite i.ses
i.ses             _Ises_1-3           (naturally coded; _Ises_1 omitted)

Iteration 0:   log likelihood = -131.79114
Iteration 1:   log likelihood = -126.42346
Iteration 2:   log likelihood = -126.38058
Iteration 3:   log likelihood = -126.38056

Logit estimates                                   Number of obs   =        200
                                                  LR chi2(2)      =      10.82
                                                  Prob > chi2     =     0.0045
Log likelihood = -126.38056                       Pseudo R2       =     0.0411

------------------------------------------------------------------------------
     hiwrite |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     _Ises_2 |   .6218519   .3608067     1.72   0.085    -.0853163     1.32902
     _Ises_3 |   1.369547   .4296508     3.19   0.001     .5274464    2.211647
       _cons |  -.1278334   .2923261    -0.44   0.662     -.700782    .4451152
------------------------------------------------------------------------------

test _Ises_2 _Ises_3
 
 ( 1)  _Ises_2 = 0
 ( 2)  _Ises_3 = 0

           chi2(  2) =   10.16
         Prob > chi2 =    0.0062
 
xi3: logit hiwrite o.ses
o.ses             _Ises_1-3           (_Ises_3 for ses==3 omitted)

Iteration 0:   log likelihood = -131.79114
Iteration 1:   log likelihood = -126.42346
Iteration 2:   log likelihood = -126.38058
Iteration 3:   log likelihood = -126.38056

Logit estimates                                   Number of obs   =        200
                                                  LR chi2(2)      =      10.82
                                                  Prob > chi2     =     0.0045
Log likelihood = -126.38056                       Pseudo R2       =     0.0411

------------------------------------------------------------------------------
     hiwrite |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     _Ises_1 |   .4970091   .1561627     3.18   0.001     .1909359    .8030823
     _Ises_2 |   .0313389   .1501452     0.21   0.835    -.2629404    .3256181
       _cons |   .5647148   .1521475     3.71   0.000     .2665112    .8629183
------------------------------------------------------------------------------

describe _Ises_1 _Ises_2
 
              storage  display     value
variable name   type   format      label      variable label
-------------------------------------------------------------------------------
_Ises_1         double %10.0g                 deg=1 orth. poly. for ses
_Ises_2         double %10.0g                 deg=2 orth. poly. for ses
 
test _Ises_1 _Ises_2
 
 ( 1)  _Ises_1 = 0
 ( 2)  _Ises_2 = 0

           chi2(  2) =   10.16
         Prob > chi2 =    0.0062
We continue with the use of xi3 with categorical predictors. These models are logistic equivalents of analysis of variance models. The next example is the logistic equivalent of a 3-by-2 factorial anova and is followed by the equivalent of a 3-by-2 factorial ancova.
xi3: logit hiwrite g.prog*g.female
g.prog            _Iprog_1-3          (naturally coded; _Iprog_1 omitted)
g.female          _Ifemale_0-1        (naturally coded; _Ifemale_0 omitted)

Iteration 0:   log likelihood = -131.79114
Iteration 1:   log likelihood = -108.03058
Iteration 2:   log likelihood = -107.54459
Iteration 3:   log likelihood = -107.53451
Iteration 4:   log likelihood =  -107.5345

Logit estimates                                   Number of obs   =        200
                                                  LR chi2(5)      =      48.51
                                                  Prob > chi2     =     0.0000
Log likelihood =  -107.5345                       Pseudo R2       =     0.1841

------------------------------------------------------------------------------
     hiwrite |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    _Iprog_2 |   1.019718   .3965045     2.57   0.010     .2425836    1.796853
    _Iprog_3 |  -1.363926   .5229104    -2.61   0.009    -2.388812   -.3390409
  _Ifemale_1 |   1.415893   .3839096     3.69   0.000     .6634439    2.168342
   _Ipr2Xfe1 |  -.6768107   .7930089    -0.85   0.393     -2.23108    .8774582
   _Ipr3Xfe1 |   1.399533   1.045821     1.34   0.181    -.6502375    3.449304
       _cons |   .1850745   .1919548     0.96   0.335      -.19115    .5612989
------------------------------------------------------------------------------

test _Iprog_2 _Iprog_3
 
 ( 1)  _Iprog_2 = 0
 ( 2)  _Iprog_3 = 0

           chi2(  2) =   25.69
         Prob > chi2 =    0.0000
 
test _Ipr2Xfe1 _Ipr3Xfe1
 
 ( 1)  _Ipr2Xfe1 = 0
 ( 2)  _Ipr3Xfe1 = 0

           chi2(  2) =    4.68
         Prob > chi2 =    0.0965
 
postgr3 prog, by(female)



xi3: logit hiwrite g.prog*g.female read
g.prog            _Iprog_1-3          (naturally coded; _Iprog_1 omitted)
g.female          _Ifemale_0-1        (naturally coded; _Ifemale_0 omitted)

Iteration 0:   log likelihood = -131.79114
Iteration 1:   log likelihood = -88.489831
Iteration 2:   log likelihood = -83.519038
Iteration 3:   log likelihood = -82.980688
Iteration 4:   log likelihood = -82.970372
Iteration 5:   log likelihood = -82.970367

Logit estimates                                   Number of obs   =        200
                                                  LR chi2(6)      =      97.64
                                                  Prob > chi2     =     0.0000
Log likelihood = -82.970367                       Pseudo R2       =     0.3704

------------------------------------------------------------------------------
     hiwrite |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    _Iprog_2 |   .5592136   .4655076     1.20   0.230    -.3531645    1.471592
    _Iprog_3 |  -1.114651   .5972121    -1.87   0.062    -2.285165    .0558632
  _Ifemale_1 |    2.24037   .4921306     4.55   0.000     1.275812    3.204929
   _Ipr2Xfe1 |   -1.83987   .9600167    -1.92   0.055    -3.721468    .0417287
   _Ipr3Xfe1 |     .85677   1.194374     0.72   0.473    -1.484161      3.1977
        read |   .1637165   .0291826     5.61   0.000     .1065197    .2209134
       _cons |   -8.04175   1.476084    -5.45   0.000    -10.93482   -5.148679
------------------------------------------------------------------------------


test _Iprog_2 _Iprog_3
 
 ( 1)  _Iprog_2 = 0
 ( 2)  _Iprog_3 = 0

           chi2(  2) =    9.68
         Prob > chi2 =    0.0079
 
test _Ipr2Xfe1 _Ipr3Xfe1
 
 ( 1)  _Ipr2Xfe1 = 0
 ( 2)  _Ipr3Xfe1 = 0

           chi2(  2) =    7.32
         Prob > chi2 =    0.0258
 
postgr3 prog, by(female)



postgr3 prog, by(female) x(read=42)



postgr3 prog, by(female) x(read=62)


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