next up previous

STAT 350: Lecture 26

Fitting Interactions: Two Way ANOVA
Influence of SCHOOL, REGION on STAY

data scenic;
 infile 'scenic.dat' firstobs=2;
 input Stay  Age Risk Culture Chest Beds 
          School Region Census Nurses Facil;
proc glm  data=scenic;
  class school region ;
  model Stay = School | Region / E 
          SOLUTION SS1 SS2 SS3 SS4 XPX INVERSE;
  output out=scout P=Fitted PRESS=PRESS H=HAT 
   RSTUDENT =EXTST R=RESID DFFITS=DFFITS COOKD=COOKD;
run ;
proc means data=scout;
  var stay;
  class school region;
run;
proc print data=scout;
EDITED SAS OUTPUT (Complete output)
Dependent Variable: STAY   
                                     Sum of            Mean
Source                  DF          Squares          Square   F Value     Pr > F
Model                    7     132.06558693     18.86651242      7.15     0.0001
Error                  105     277.14479360      2.63947422
Corrected Total        112     409.21038053
                  R-Square             C.V.        Root MSE            STAY Mean
                  0.322733         16.83864       1.6246459            9.6483186
Source                  DF        Type I SS     Mean Square   F Value     Pr > F
SCHOOL                   1      36.08413010     36.08413010     13.67     0.0003
REGION                   3      95.36410217     31.78803406     12.04     0.0001
SCHOOL*REGION            3       0.61735466      0.20578489      0.08     0.9718
Source                  DF       Type II SS     Mean Square   F Value     Pr > F
SCHOOL                   1      27.89404890     27.89404890     10.57     0.0015
REGION                   3      95.36410217     31.78803406     12.04     0.0001
SCHOOL*REGION            3       0.61735466      0.20578489      0.08     0.9718
Source                  DF      Type III SS     Mean Square   F Value     Pr > F
SCHOOL                   1      26.05955792     26.05955792      9.87     0.0022
REGION                   3      47.01938029     15.67312676      5.94     0.0009
SCHOOL*REGION            3       0.61735466      0.20578489      0.08     0.9718
Source                  DF       Type IV SS     Mean Square   F Value     Pr > F
SCHOOL                   1      26.05955792     26.05955792      9.87     0.0022
REGION                   3      47.01938029     15.67312676      5.94     0.0009
SCHOOL*REGION            3       0.61735466      0.20578489      0.08     0.9718

Output from SOLUTION option

                                        T for H0:    Pr > |T|   Std Error of
Parameter                  Estimate    Parameter=0                Estimate
INTERCEPT               7.890000000 B        18.17     0.0001     0.43420487
SCHOOL        1         1.790000000 B         1.46     0.1480     1.22811685
              2         0.000000000 B          .        .          .        
REGION        1         2.930434783 B         5.32     0.0001     0.55072100
              2         1.537200000 B         2.83     0.0055     0.54232171
              3         1.180588235 B         2.29     0.0241     0.51591227
              4         0.000000000 B          .        .          .        
SCHOOL*REGION 1 1      -0.286434783 B        -0.20     0.8455     1.46660342
              1 2      -0.618628571 B        -0.44     0.6620     1.41099883
              1 3      -0.300588235 B        -0.19     0.8486     1.57026346
              1 4       0.000000000 B          .        .          .        
SCHOOL*REGION 2 1       0.000000000 B          .        .          .        
              2 2       0.000000000 B          .        .          .        
              2 3       0.000000000 B          .        .          .        
              2 4       0.000000000 B          .        .          .        

NOTE: The X'X matrix has been found to be singular and a generalized inverse 
      was used to solve the normal equations.   Estimates followed by the 
      letter 'B' are biased, and are not unique estimators of the parameters.
      SCHOOL        REGION  N Obs    N          Mean       Std Dev       Minimum
--------------------------------------------------------------------------------
           1             1      5    5    12.3240000     3.3527198     9.7800000
                         2      7    7    10.5985714     1.1317454     8.2800000
                         3      3    3    10.5600000     0.7362744    10.1200000
                         4      2    2     9.6800000     0.6788225     9.2000000
           2             1     23   23    10.8204348     2.5061460     8.0300000
                         2     25   25     9.4272000     1.0978635     7.3900000
                         3     34   34     9.0705882     1.1911516     7.0800000
                         4     14   14     7.8900000     0.8332420     6.7000000
--------------------------------------------------------------------------------

Diagnostics for individual cases

  OBS  STAY  AGE RISK CULTURE CHEST BEDS SCHOOL REGION CENSUS NURSES FACIL
   23  9.78 52.3  5.0   17.6   95.9  270    1      1     240    198   57.1
   25  9.20 52.2  4.0   17.5   71.1  298    1      4     244    236   57.1
   26  8.28 49.5  3.9   12.0  113.1  546    1      2     413    436   57.1
   44 10.12 51.7  5.6   14.9   79.1  362    1      3     313    264   54.3
   46 10.16 54.2  4.6    8.4   51.5  831    1      4     581    629   74.3
   47 19.56 59.9  6.5   17.2  113.7  306    2      1     273    172   51.4
   74 10.05 52.0  4.5   36.7   87.5  184    1      1     144    151   68.6
   90 11.41 50.4  5.8   23.8   73.0  424    1      3     359    335   45.7
  100 10.15 51.9  6.2   16.4   59.2  568    1      3     452    371   62.9
  112 17.94 56.2  5.9   26.4   91.8  835    1      1     791    407   62.9
  OBS  FITTED     PRESS      HAT       EXTST      RESID     DFFITS     COOKD
   23 12.3240   -3.18000   0.20000   -1.76835   -2.54400   -0.88418   0.09578
   25  9.6800   -0.96000   0.50000   -0.41618   -0.48000   -0.41618   0.02182
   26 10.5986   -2.70500   0.14286   -1.55177   -2.31857   -0.63351   0.04950
   44 10.5600   -0.66000   0.33333   -0.33029   -0.44000   -0.23355   0.00688
   46  9.6800    0.96000   0.50000    0.41618    0.48000    0.41618   0.02182
   47 10.8204    9.13682   0.04348    6.48789    8.73957    1.38322   0.17189
   74 12.3240   -2.84250   0.20000   -1.57592   -2.27400   -0.78796   0.07653
   90 10.5600    1.27500   0.33333    0.63897    0.85000    0.45182   0.02566
  100 10.5600   -0.61500   0.33333   -0.30774   -0.41000   -0.21761   0.00597
  112 12.3240    7.02000   0.20000    4.15303    5.61600    2.07652   0.46676

Comments on code and results

Analysis of covariance example

Here I regress STAY on SCHOOL, REGION and FACILITIES. I begin by putting in all the possible interaction effects.

options pagesize=60 linesize=80;
data scenic;
 infile 'scenic.dat' firstobs=2;
 input Stay  Age Risk Culture Chest Beds 
    School Region Census Nurses Facil;
proc glm  data=scenic;
  class school region ;
  model Stay = School | Region | Facil 
           / SS1 SS2 SS3 ;
  output out=scout P=Fitted PRESS=PRESS H=HAT 
 RSTUDENT=EXTST R=RESID DFFITS=DFFITS COOKD=COOKD;
run ;
proc print data=scout;
proc glm  data=scenic;
  class school region ;
  model Stay = School | Region  Facil 
        / SS1 SS2 SS3 ;
run ;

EDITED SAS OUTPUT

Dependent Variable: STAY   
                                     Sum of            Mean
Source                  DF          Squares          Square   F Value     Pr > F
Model                   15     173.90201568     11.59346771      4.78     0.0001
Error                   97     235.30836485      2.42585943
Corrected Total        112     409.21038053
                  R-Square             C.V.        Root MSE            STAY Mean
                  0.424970         16.14289       1.5575171            9.6483186
Source                  DF        Type I SS     Mean Square   F Value     Pr > F
SCHOOL                   1      36.08413010     36.08413010     14.87     0.0002
REGION                   3      95.36410217     31.78803406     13.10     0.0001
SCHOOL*REGION            3       0.61735466      0.20578489      0.08     0.9682
FACIL                    1       9.52496125      9.52496125      3.93     0.0504
FACIL*SCHOOL             1       1.32686372      1.32686372      0.55     0.4613
FACIL*REGION             3      21.28634656      7.09544885      2.92     0.0377
FACIL*SCHOOL*REGION      3       9.69825722      3.23275241      1.33     0.2683
Source                  DF       Type II SS     Mean Square   F Value     Pr > F
SCHOOL                   1       4.73069924      4.73069924      1.95     0.1658
REGION                   3       8.16560072      2.72186691      1.12     0.3441
SCHOOL*REGION            3       7.04260265      2.34753422      0.97     0.4113
FACIL                    1       9.52496125      9.52496125      3.93     0.0504
FACIL*SCHOOL             1       3.76491803      3.76491803      1.55     0.2158
FACIL*REGION             3      21.28634656      7.09544885      2.92     0.0377
FACIL*SCHOOL*REGION      3       9.69825722      3.23275241      1.33     0.2683
Source                  DF      Type III SS     Mean Square   F Value     Pr > F
SCHOOL                   1       2.34679006      2.34679006      0.97     0.3278
REGION                   3       2.46002453      0.82000818      0.34     0.7979
SCHOOL*REGION            3       7.04260265      2.34753422      0.97     0.4113
FACIL                    1       0.70390965      0.70390965      0.29     0.5913
FACIL*SCHOOL             1       1.50831325      1.50831325      0.62     0.4323
FACIL*REGION             3       1.92051520      0.64017173      0.26     0.8513
FACIL*SCHOOL*REGION      3       9.69825722      3.23275241      1.33     0.2683
  OBS  STAY  AGE RISK CULTURE CHEST BEDS SCHOOL REGION CENSUS NURSES FACIL
   25  9.20 52.2  4.0   17.5   71.1  298    1      4     244    236   57.1
   46 10.16 54.2  4.6    8.4   51.5  831    1      4     581    629   74.3
   47 19.56 59.9  6.5   17.2  113.7  306    2      1     273    172   51.4
  OBS  FITTED     PRESS      HAT       EXTST      RESID     DFFITS     COOKD
   25  9.2000     .        1.00000     .        -0.00000     .         .     
   46 10.1600     .        1.00000     .         0.00000     .         .     
   47 11.8970    8.29701   0.07641    5.96177    7.66301    1.71483   0.13553

COMMENTS

Dependent Variable: STAY   
                                     Sum of            Mean
Source                  DF          Squares          Square   F Value     Pr > F
Model                    8     141.59054818     17.69881852      6.88     0.0001
Error                  104     267.61983235      2.57326762
Corrected Total        112     409.21038053
                  R-Square             C.V.        Root MSE            STAY Mean
                  0.346009         16.62612       1.6041408            9.6483186
Source                  DF        Type I SS     Mean Square   F Value     Pr > F
SCHOOL                   1      36.08413010     36.08413010     14.02     0.0003
REGION                   3      95.36410217     31.78803406     12.35     0.0001
SCHOOL*REGION            3       0.61735466      0.20578489      0.08     0.9708
FACIL                    1       9.52496125      9.52496125      3.70     0.0571
Source                  DF       Type II SS     Mean Square   F Value     Pr > F
SCHOOL                   1       8.66242211      8.66242211      3.37     0.0694
REGION                   3      82.48995156     27.49665052     10.69     0.0001
SCHOOL*REGION            3       0.48049197      0.16016399      0.06     0.9796
FACIL                    1       9.52496125      9.52496125      3.70     0.0571
Source                  DF      Type III SS     Mean Square   F Value     Pr > F
SCHOOL                   1       8.45264294      8.45264294      3.28     0.0728
REGION                   3      42.65719728     14.21906576      5.53     0.0015
SCHOOL*REGION            3       0.48049197      0.16016399      0.06     0.9796
FACIL                    1       9.52496125      9.52496125      3.70     0.0571


next up previous



Richard Lockhart
Wed Mar 5 22:48:46 PST 1997