10(1) Example of Searching for Structure (Means Analysis)
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Research Question
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Explore the pattern of relationships between the time – involvement of
academic scientists and a set of contextual categorical variables: Rank,
institutional settings, scientific field, external funding of research.
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Methodology
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Classification and regression trees: SEARCH module: MEANS Analysis
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Dataset
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ANJU.DAT |
SYNTAX*
$RUN SEARCH
$FILES
PRINT = CART.LST
DICTIN = ANJU.DIC
DATAIN = ANJU.DAT
$SETUP
INCLUDE V9=1-3 AND V10=1,2 AND V12=1,2 AND V15=1,2
SEARCHING OF STRUCTURE
BADDATA=MD1 -
ANALYSIS=MEAN -
DEPVAR=V2 -
MINCASE=10 -
PRINT=(DICT, TRACW,TREE,FINAL)
VARS=(V9) TYPE=M
VARS=(V10,V12,V14,V15) TYPE=F
------------------------------------
Note : Search module does not recognize missing data or invalid
codes for the predictor variables. Hence, the filter Include has been used.
All options set at default values
EXTRACT FROM COMPUTER OUTPUT
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After filtering 1021 cases read from the input data file
The number of cases rejected is 16:
16 for missing data in the dependent variable
The number of processed cases is 1005
3 cases contained illegal characters and were treated according to
BADDATA specification
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Split 1 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
1 1005 .10050E+04 .41851E+02 .32525E+03 .32655E+06
Attempt to split group 1 Var= 326551.63
Predictor V9 v204:rank
Rank 1 Type M
Codes 1 2 3
Best split after code 1 Var expl= .25600360E+05
Predictor V10 v217:head? Rank 2 Type
F
Codes 1 2
Best split after code 1 Var expl= .71446650E+04
Predictor V12 v335:ext funds Rank 2 Type F
Codes 2 1
Best split after code 2 Var expl= .24188630E+05
Predictor V14 sv:inst type Rank
2 Type F
Codes 3 2 4 1
Best split after code 2 Var expl= .33990140E+05
Predictor V15 :field Rank 2 Type F
Codes 1 2
No eligible split
Best split for group 1 on predictor V14 sv:inst type Rank 1
Var expl= .33990140E+05
Split group 1 on V14 sv:inst type Var expl= .33990140E+05
Into group 2, codes 3 2
and group 3, codes 4 1
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Split 2 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
2 330 .33000E+03 .33533E+02 .24002E+03 .78966E+05
3 675 .67500E+03 .45917E+02 .31691E+03 .21360E+06
Attempt to split group 3 Var= 213595.36
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2 3
Best split after code 1 Var expl= .12996760E+05
Predictor V10 v217:head? Rank 2 Type F
Codes 1 2
Best split after code 1 Var expl= .61900730E+04
Predictor V12 v335:ext funds Rank 2 Type F
Codes 2 1
Best split after code 2 Var expl= .14340120E+05
Predictor V14 sv:inst type Rank 2 Type F
Codes 4 1
Best split after code 4 Var expl= .28903780E+04
Predictor V15 :field Rank 2 Type F
Codes 1 2
Best split after code 1 Var expl= .34723500E+04
Best split for group 3 on predictor V12 v335:ext funds Rank 1
Var expl= .14340120E+05
Split group 3 on V12 v335:ext funds Var expl= .14340120E+05
Into group 4, codes 2
and group 5, codes 1
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Split 3 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
2 330 .33000E+03 .33533E+02 .24002E+03 .78966E+05
4 297 .29700E+03 .40717E+02 .26587E+03 .78698E+05
5 378 .37800E+03 .50003E+02 .31978E+03 .12056E+06
Attempt to split group 5 Var= 120557.00
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2 3
Best split after code 2 Var expl= .29708200E+04
Predictor V10 v217:head? Rank 2 Type F
Codes 1 2
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 1
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 4 1
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 1 2
No eligible split
Best split for group 5 on predictor V9 v204:rank Rank 1
Var expl= .29708200E+04
Split group 5 on V9 v204:rank Var expl= .29708200E+04
Into group 6, codes 1 2
and group 7, codes 3
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Split 4 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
2 330 .33000E+03 .33533E+02 .24002E+03 .78966E+05
4 297 .29700E+03 .40717E+02 .26587E+03 .78698E+05
6 218 .21800E+03 .47601E+02 .28966E+03 .62856E+05
7 160 .16000E+03 .53275E+02 .34421E+03 .54730E+05
Attempt to split group 2 Var= 78966.133
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2 3
No eligible split
Predictor V10 v217:head? Rank 2 Type F
Codes 1 2
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 2 1
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 3 2
Best split after code 3 Var expl= .13163880E+05
Predictor V15 :field Rank 2 Type F
Codes 1 2
No eligible split
Best split for group 2 on predictor V14 sv:inst type Rank 1
Var expl= .13163880E+05
Split group 2 on V14 sv:inst type Var expl= .13163880E+05
Into group 8, codes 3
and group 9, codes 2
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Split 5 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
4 297 .29700E+03 .40717E+02 .26587E+03 .78698E+05
6 218 .21800E+03 .47601E+02 .28966E+03 .62856E+05
7 160 .16000E+03 .53275E+02 .34421E+03 .54730E+05
8 53 .53000E+02 .19094E+02 .98087E+02 .51005E+04
9 277 .27700E+03 .36296E+02 .21993E+03 .60702E+05
Attempt to split group 4 Var= 78698.242
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2 3
Best split after code 1 Var expl= .69443780E+04
Predictor V10 v217:head? Rank 2 Type F
Codes 1 2
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 2
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 4 1
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 1 2
Best split after code 1 Var expl= .46585620E+04
Best split for group 4 on predictor V9 v204:rank Rank 1
Var expl= .69443780E+04
Split group 4 on V9 v204:rank Var expl= .69443780E+04
Into group 10, codes 1
and group 11, codes 2 3
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Split 6 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
6 218 .21800E+03 .47601E+02 .28966E+03 .62856E+05
7 160 .16000E+03 .53275E+02 .34421E+03 .54730E+05
8 53 .53000E+02 .19094E+02 .98087E+02 .51005E+04
9 277 .27700E+03 .36296E+02 .21993E+03 .60702E+05
10 99 .99000E+02 .33879E+02 .19568E+03 .19177E+05
11 198 .19800E+03 .44136E+02 .26689E+03 .52577E+05
Attempt to split group 6 Var= 62856.281
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2
No eligible split
Predictor V10 v217:head? Rank 2 Type F
Codes 1 2
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 1
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 1 4
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 1 2
No eligible split
No eligible split for group 6
Split 6 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
7 160 .16000E+03 .53275E+02 .34421E+03 .54730E+05
8 53 .53000E+02 .19094E+02 .98087E+02 .51005E+04
9 277 .27700E+03 .36296E+02 .21993E+03 .60702E+05
10 99 .99000E+02 .33879E+02 .19568E+03 .19177E+05
11 198 .19800E+03 .44136E+02 .26689E+03 .52577E+05
Attempt to split group 9 Var= 60701.727
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2 3
No eligible split
Predictor V10 v217:head? Rank 2 Type F
Codes 1 2
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 2 1
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 2
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 2 1
No eligible split
No eligible split for group 9
1
Split 6 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
7 160 .16000E+03 .53275E+02 .34421E+03 .54730E+05
8 53 .53000E+02 .19094E+02 .98087E+02 .51005E+04
10 99 .99000E+02 .33879E+02 .19568E+03 .19177E+05
11 198 .19800E+03 .44136E+02 .26689E+03 .52577E+05
Attempt to split group 7 Var= 54729.898
Predictor V9 v204:rank Rank 1 Type M
Codes 3
No eligible split
Predictor V10 v217:head? Rank 2 Type F
Codes 2 1
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 1
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 4 1
Best split after code 4 Var expl= .27697110E+04
Var expl= .27697110E+04
Split group 7 on V14 sv:inst type Var expl= .27697110E+04
Into group 12, codes 4
Predictor V15 :field Rank 2 Type F
Codes 2 1
No eligible split
Best split for group 7 on predictor V14 sv:inst type Rank 1
and group 13, codes 1
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Split 7 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
8 53 .53000E+02 .19094E+02 .98087E+02 .51005E+04
10 99 .99000E+02 .33879E+02 .19568E+03 .19177E+05
11 198 .19800E+03 .44136E+02 .26689E+03 .52577E+05
12 67 .67000E+02 .48373E+02 .39621E+03 .26150E+05
13 93 .93000E+02 .56806E+02 .28055E+03 .25811E+05
Attempt to split group 11 Var= 52577.316
Predictor V9 v204:rank Rank 1 Type M
Codes 2 3
No eligible split
Predictor V10 v217:head? Rank 2 Type F
Codes 1 2
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 2
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 4 1
Best split after code 4 Var expl= .38634620E+04
Predictor V15 :field Rank 2 Type F
Codes 1 2
No eligible split
Best split for group 11 on predictor V14 sv:inst type Rank 1
Var expl= .38634620E+04
Split group 11 on V14 sv:inst type Var expl= .38634620E+04
Into group 14, codes 4
and group 15, codes 1
1
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Split 8 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
8 53 .53000E+02 .19094E+02 .98087E+02 .51005E+04
10 99 .99000E+02 .33879E+02 .19568E+03 .19177E+05
12 67 .67000E+02 .48373E+02 .39621E+03 .26150E+05
13 93 .93000E+02 .56806E+02 .28055E+03 .25811E+05
14 95 .95000E+02 .39537E+02 .19251E+03 .18096E+05
15 103 .10300E+03 .48379E+02 .30018E+03 .30618E+05
Attempt to split group 15 Var= 30618.232
Predictor V9 v204:rank Rank 1 Type M
Codes 2 3
No eligible split
Predictor V10 v217:head? Rank 2 Type F
Codes 2 1
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 2
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 1
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 1 2
No eligible split
No eligible split for group 15
Split 8 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
8 53 .53000E+02 .19094E+02 .98087E+02 .51005E+04
10 99 .99000E+02 .33879E+02 .19568E+03 .19177E+05
12 67 .67000E+02 .48373E+02 .39621E+03 .26150E+05
13 93 .93000E+02 .56806E+02 .28055E+03 .25811E+05
14 95 .95000E+02 .39537E+02 .19251E+03 .18096E+05
Attempt to split group 12 Var= 26149.672
Predictor V9 v204:rank Rank 1 Type M
Codes 3
No eligible split
Predictor V10 v217:head? Rank 2 Type F
Codes 2
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 1
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 4
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 2 1
No eligible split
No eligible split for group 12
Split 8 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
8 53 .53000E+02 .19094E+02 .98087E+02 .51005E+04
10 99 .99000E+02 .33879E+02 .19568E+03 .19177E+05
13 93 .93000E+02 .56806E+02 .28055E+03 .25811E+05
14 95 .95000E+02 .39537E+02 .19251E+03 .18096E+05
Attempt to split group 13 Var= 25810.516
Predictor V9 v204:rank Rank 1 Type M
Codes 3
No eligible split
Predictor V10 v217:head? Rank 2 Type F
Codes 1 2
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 1
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 1
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 1 2
No eligible split
No eligible split for group 13
1
Split 8 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
8 53 .53000E+02 .19094E+02 .98087E+02 .51005E+04
10 99 .99000E+02 .33879E+02 .19568E+03 .19177E+05
14 95 .95000E+02 .39537E+02 .19251E+03 .18096E+05
Attempt to split group 10 Var= 19176.545
Predictor V9 v204:rank Rank 1 Type M
Codes 1
No eligible split
Predictor V10 v217:head? Rank 2 Type F
Codes 1 2
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 2
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 1 4
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 1 2
No eligible split
No eligible split for group 10
1
Split 8 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
8 53 .53000E+02 .19094E+02 .98087E+02 .51005E+04
14 95 .95000E+02 .39537E+02 .19251E+03 .18096E+05
Attempt to split group 14 Var= 18095.621
Predictor V9 v204:rank Rank 1 Type M
Codes 2 3
No eligible split
Predictor V10 v217:head? Rank 2 Type F
Codes 1 2
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 2
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 4
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 1 2
No eligible split
No eligible split for group 14
1
Split 8 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
8 53 .53000E+02 .19094E+02 .98087E+02 .51005E+04
Attempt to split group 8 Var= 5100.5283
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2 3
No eligible split
Predictor V10 v217:head? Rank 2 Type F
Codes 1 2
No eligible split
Predictor V12 v335:ext funds Rank 2 Type F
Codes 2 1
No eligible split
Predictor V14 sv:inst type Rank 2 Type F
Codes 3
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 1 2
No eligible split
No eligible split for group 8
No splits possible
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The partitioning ends with 8 final groups
The variation explained is 23.9%
One-way analysis of final groups
Source Variation DF
Explained .78042510E+05 7
Error .24850910E+06 997
Total .32655160E+06 1004
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Split summary table
Group 1 1005 cases
Mean(Y)= .41850750E+02 Var(Y)= .32525060E+03 Variation= .32655160E+06
Split on V14 sv:inst type
Var expl= .33990140E+05
Into group 2, codes 3 2
and group 3, codes 4 1
Group 3 675 cases
Mean(Y)= .45917040E+02 Var(Y)= .31690700E+03 Variation= .21359540E+06
Split on V12 v335:ext funds
Var expl= .14340120E+05
Into group 4, codes 2
and group 5, codes 1
Group 5 378 cases
Mean(Y)= .50002650E+02 Var(Y)= .31977980E+03 Variation= .12055700E+06
Split on V9 v204:rank
Var expl= .29708200E+04
Into group 6, codes 1 2
and group 7, codes 3
Group 2 330 cases
Mean(Y)= .33533330E+02 Var(Y)= .24001860E+03 Variation= .78966130E+05
Split on V14 sv:inst type
Var expl= .13163880E+05
Into group 8, codes 3
and group 9, codes 2
Group 4 297 cases
Mean(Y)= .40717170E+02 Var(Y)= .26587240E+03 Variation= .78698240E+05
Split on V9 v204:rank
Var expl= .69443780E+04
Into group 10, codes 1
and group 11, codes 2 3
Group 7 160 cases
Mean(Y)= .53275000E+02 Var(Y)= .34421320E+03 Variation= .54729900E+05
Split on V14 sv:inst type
Var expl= .27697110E+04
Into group 12, codes 4
and group 13, codes 1
Group 11 198 cases
Mean(Y)= .44136360E+02 Var(Y)= .26689000E+03 Variation= .52577320E+05
Split on V14 sv:inst type
Var expl= .38634620E+04
Into group 14, codes 4
and group 15, codes 1
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Final group summary table
Group 6 218 cases
Mean(Y)= .47600920E+02 Var(Y)= .28966030E+03
Variation= .62856280E+05
Group 8 53 cases
Mean(Y)= .19094340E+02 Var(Y)= .98087080E+02
Variation= .51005280E+04
Group 9 277 cases
Mean(Y)= .36296030E+02 Var(Y)= .21993380E+03
Variation= .60701730E+05
Group 10 99 cases
Mean(Y)= .33878790E+02 Var(Y)= .19567900E+03
Variation= .19176540E+05
Group 12 67 cases
Mean(Y)= .48373130E+02 Var(Y)= .39620720E+03
Variation= .26149670E+05
Group 13 93 cases
Mean(Y)= .56806450E+02 Var(Y)= .28054910E+03
Variation= .25810520E+05
Group 14 95 cases
Mean(Y)= .39536840E+02 Var(Y)= .19250660E+03
Variation= .18095620E+05
Group 15 103 cases
Mean(Y)= .48378640E+02 Var(Y)= .30017870E+03
Variation= .30618230E+05
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INTERPRETATION
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IDAMS reports analysis specifications:
# Cases:1021 cases were read; 16
cases were rejected for missing data in the dependant variable.
Deependent variable=V2 Predictor variables=V9 (monotonic), V10,V12,V14,V15
(Non-monotonic).
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Group – 1
Sum (wt) = # of cases
Mean for the entire sample = 41.851
Var = Variance = 0.32525E+.03
Variation = Sum of squares of the dependant variable = #
of cases ´ Var = .32655E+06
Attempt to split Group
– 1
Best splits for different predictors
Predictor code Cut-point Variance explained
V9(1,2,3) 1 0.25600360E+05
V10(1,2) 1 0.71446650E+04
V12(1,2) 1 0.24188630E+05
V14(3,2,4,1) 2 0.33990140E+05
V15(1,2) No eligible split
Best split for Group – 1 is on predictor V14 since it has the maximum
value of sum of squares
Group-1 is split on variable V14 into two groups:
Group-2: Codes 3, 2
Group-3: Codes 1, 4
Variance explained = 0.33990140E+05
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Split 2 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
2 330 .33000E+03 .33533E+02 .24002E+03 .78966E+05
3 675 .67500E+03 .45917E+02 .31691E+03 .21360E+06
Group 3 will be split first, because it has greater variance.
Best predictor and its cut-point for splitting Group 3 is selected in
the same manner as in Step 1.
Predictor V12 (1,2) at cut-point = 1 is found to be the best predictor,
since it explains greater variance compared to the best splits of other
predictors.
Group 3 is split into:
Group-4 Code: 1
Group-5 Code: 2
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Split 3 candidate groups
Group N Sum(WT) Mean Y Var Y Variation
2 330 .33000E+03 .33533E+02 .24002E+03 .78966E+05
4 297 .29700E+03 .40717E+02 .26587E+03 .78698E+05
5 378 .37800E+03 .50003E+02 .31978E+03 .12056E+06
Group 5 has the maximum variation = 120557 and hence it is selected
for further split.
All the predictor are again evaluated for their best splits and Predictor
V9 (1,2,3) is selected for splitting Group 4 at cut off : 1, 2. Note that
predictor V9 is monotonic.
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Split 4 candidate groups
Now the candidate groups for split area
Group-2, Group-5, Group-6 and Group-7
Group-2 will be split first since it explains the maximum variation (78966.13)
Again all candidate predictors are evaluated for splitting Group-2
V9(1,2,1) No
split meats the splitting criterion
V12(1,2) No
split meats the splitting criterion
V15(1,2) -to-
PredictorV14(3,2) is chosen for splitting Group-2
Group-2 is split into
Group-8 V14(Code:
3)
Group-9 V14(Code:
2)
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Split 5 candidate groups
Now candidate groups for split are:
Group-5, Group-6, Group-7, Group-8, Group-9.
Group-5 has the maximum sum of square (=786980) and is therefore chosen
for split.
Best predictor and cut-point value is selected in the same manner as
in the earlier steps.
Predictor V9(1,2,3) is found to be the best predictor, with cut-point
after code:1
Group-5 is split into groups:
Group-10
V9(Code: 1)
Group-11
V9(Code: 2,3)
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Split 6 candidate groups
Now, the candidate groups for further split are:
Group-6, Group-7, Group-8, Group-9 and Group-10, Group-11.
Group-6 has the maximum sum of squares (62856.201) and is therefore chosen
for further split.
Name of the predictor variables meats the eligibility criterion for splitting
Group-6.
Group-9 is now chosen for split, but none of the predictor (60701.727)
Variables meat the eligibility criterion for splitting this group.
Group-10 is now considered for further split, but none of the predictors
variables could split this group.
The remaining raps (viz. Group-8, Group-14) were considered for further
split, but none of the predictor variables could split any of these groups.
Group-7 is chosen for split. This group is split on predictor V14(4,1)
into two groups:
Group-12 V14(Code:4)
Group-13 V14(Code:1)
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Split 7 candidate groups
At this stage, there are 5 candidate groups for split
Group8, Group-10, Group-11, Group-12, Group-13.
Of these Group-11 is chosen for split, since it has the maximum value
of sum of squares: (52577.316).
Group-11 is now split into two groups on Predictor V14(4,1):
Group-14 V14(Code
= 4)
Group-15 V14(Code
= 1)
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Split 8 candidate groups
At this stage, there are 6 candidate groups for split:
Group-8, Group-10, Group-12, Group-13, Group-14, Group-15
Of these, Group-15 has the maximum value of sum of squares, hence considered
for further split:
None of the predictor variables is found to be eligible for further split
Group-12 is now considered for split, since it has the maximum variables
meet the eligibility criterion for splitting this group.
Group-10 is now considered for further split, but none of the predictor
variables could split this group.
The remaining raps (viz. Group-8, Group-14) were considered for further
split, but none of the predictor variables could split any of these groups.
The partition ends with 8 final groups (Variance explained = 23.9%)
Analysis of Variance Table
Sum of Square DF (No. of final groups -1)
Explained 78042.51 7
Error 248509.91 997
Total 326551.60 1004
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The foregoing results of partitioning the data set are summarized in
the summary table
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_______________
N=Number of cases | Group 1 |
Y=Dep. var. mean, v262:teaching | N=1005 |
C=Predictor codes |Y= 41.85075|
| Split 1 |
| on V14 |
|_____________|
|
_________________________________sv:inst type__________________________________
1
C=3,2 C=4,1
| |
_______|_______ _______|_______
| Group 2 | | Group 3 |
| N=330 | | N=675 |
|Y= 33.53333| |Y= 45.91704|
| Split 4 | | Split 2 |
| on V14 | | on V12 |
|_____________| |_____________|
| |
_________________sv:inst type__________________ ________________v335:ext funds_________________
C=3 C=2 C=1 C=2
| | | |
_______|_______ _______|_______ _______|_______ _______|_______
| Group 8 | | Group 9 | | Group 4 | | Group 5 |
| N=53 | | N=277 | | N=378 | | N=297 |
|Y= 19.09434| |Y= 36.29603| |Y= 50.00265| |Y= 40.71717|
| Final | | Final | | Split 3 | | Split 5 |
| | | | | on V9 | | on V9 |
|_____________| |_____________| |_____________| |_____________|
| |
___________v204:rank___________ ___________v204:rank___________
C=1,2 C=3 C=1 C=2,3
| | | |
_______|_______ _______|_______ _______|_______ _______|_______
| Group 6 | | Group 7 | | Group 10 | | Group 11 |
| N=218 | | N=160 | | N=99 | | N=198 |
|Y= 47.60092| |Y= 53.27500| |Y= 33.87879| |Y= 44.13636|
| Final | | Split 6 | | Final | | Split 7 |
| | | on V14 | | | | on V14 |
|_____________| |_____________| |_____________| |_____________|
| |
| |
1
|
_______|_______
N=Number of cases | Group 7 |
Y=Dep. var. mean, v262:teaching | N=160 |
C=Predictor codes |Y= 53.27500|
| Split 6 |
| on V14 |
|_____________|
|
_________________________________sv:inst type__________________________________
C=4 C=1
| |
_______|_______ _______|_______
| Group 12 | | Group 13 |
| N=67 | | N=93 |
|Y= 48.37313| |Y= 56.80645|
| Final | | Final |
| | | |
|_____________| |_____________|
1
|
_______|_______
N=Number of cases | Group 11 |
Y=Dep. var. mean, v262:teaching | N=198 |
C=Predictor codes |Y= 44.13636|
| Split 7 |
| on V14 |
|_____________|
|
_________________________________sv:inst type__________________________________
C=4 C=1
| |
_______|_______ _______|_______
| Group 14 | | Group 15 |
| N=95 | | N=103 |
|Y= 39.53684| |Y= 48.37864|
| Final | | Final |
| | | |
|_____________| |_____________|
N=Number of cases | Group 1 |
Y=Dep. var. mean, v262:teaching | N=1005 |
C=Predictor codes |Y= 41.85075|
| Split 1 |
| on V14 |
|_____________|
|
_________________________________sv:inst type__________________________________
1
C=3,2 C=4,1
| |
_______|_______ _______|_______
| Group 2 | | Group 3 |
| N=330 | | N=675 |
|Y= 33.53333| |Y= 45.91704|
| Split 4 | | Split 2 |
| on V14 | | on V12 |
|_____________| |_____________|
| |
_________________sv:inst type__________________ ________________v335:ext funds_________________
C=3 C=2 C=1 C=2
| | | |
_______|_______ _______|_______ _______|_______ _______|_______
| Group 8 | | Group 9 | | Group 4 | | Group 5 |
| N=53 | | N=277 | | N=378 | | N=297 |
|Y= 19.09434| |Y= 36.29603| |Y= 50.00265| |Y= 40.71717|
| Final | | Final | | Split 3 | | Split 5 |
| | | | | on V9 | | on V9 |
|_____________| |_____________| |_____________| |_____________|
| |
___________v204:rank___________ ___________v204:rank___________
C=1,2 C=3 C=1 C=2,3
| | | |
_______|_______ _______|_______ _______|_______ _______|_______
| Group 6 | | Group 7 | | Group 10 | | Group 11 |
| N=218 | | N=160 | | N=99 | | N=198 |
|Y= 47.60092| |Y= 53.27500| |Y= 33.87879| |Y= 44.13636|
| Final | | Split 6 | | Final | | Split 7 |
| | | on V14 | | | | on V14 |
|_____________| |_____________| |_____________| |_____________|
| |
| |
1
|
_______|_______
N=Number of cases | Group 7 |
Y=Dep. var. mean, v262:teaching | N=160 |
C=Predictor codes |Y= 53.27500|
| Split 6 |
| on V14 |
|_____________|
|
_________________________________sv:inst type__________________________________
C=4 C=1
| |
_______|_______ _______|_______
| Group 12 | | Group 13 |
| N=67 | | N=93 |
|Y= 48.37313| |Y= 56.80645|
| Final | | Final |
| | | |
|_____________| |_____________|
1
|
_______|_______
N=Number of cases | Group 11 |
Y=Dep. var. mean, v262:teaching | N=198 |
C=Predictor codes |Y= 44.13636|
| Split 7 |
| on V14 |
|_____________|
|
_________________________________sv:inst type__________________________________
C=4 C=1
| |
_______|_______ _______|_______
| Group 14 | | Group 15 |
| N=95 | | N=103 |
|Y= 39.53684| |Y= 48.37864|
| Final | | Final |
| | | |
|_____________| |_____________|
***** Normal termination of SEARCH
***** No more RUN statements in SETUP; step terminated
10(2) Searching for Structure : Regression Analysis
|
Research Question
|
:
|
How does the pattern of relationship between the time spent by on academic
scientist in contextual fac6tors?.
|
|
Methodology
|
:
|
Classification and regression trees: SEARCH module – Regression
analysis
|
|
Dataset
|
:
|
ANJU.DAT |
SYNTAX
$RUN SEARCH
$FILES
PRINT = SEARCH2.LST
DICTIN = ANJU.DIC
DATAIN = ANJU.DAT
$SETUP
INCLUDE V9=1-3 AND V15=1,2
SEARCHING OF STRUCTURE: REGRESSIN ANALYSIS
BADDATA=MD1 -
ANALYSIS=REGRESSION -
DEPVAR=V4 -
COVARIATE= V13 -
MINCASE=10 -
IDVAR=V1 -
PRINT=(TRACE, TABLE, TREE)
VARS= (V14, V15) TYPE=F
VARS= V9 TYPE=M
------------------------------------
Note : Search module does not recognize missing data or invalid
codes for the predictor variables. Hence, the filter Include has been used.
All options set at default values
EXTRACT FROM COMPUTER OUTPUT
|
|
Dependent variable: V4
Covariate
variable: V13
Identifier
variable: V1
After filtering
1039 cases read from the input data file
The number
of cases rejected is 23:
12
for missing data in the dependent variable
11 for missing data in the covariate
The number of processed cases is 1016
|
|
|
|
Split 1 candidate groups
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
1 1016 .10160E+04 .15990E+02 .14602E+03 .30705E+01 .11106E+06
.20010E+01 .38828E+01
Attempt to split group 1 Var= 111055.23
Predictor V14 sv:inst type Rank 2 Type F
Codes 3 2 4 1
Best split after code 3 Var expl= .82337250E+04
Predictor V15 :field Rank 2 Type F
Codes 2 1
Best split after code 2 Var expl= .90128400E+03
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2 3
Best split after code 2 Var expl= .30497740E+04
Best split for group 1 on predictor V14 sv:inst type Rank 1
Var expl= .82337250E+04
Split group 1 on V14 sv:inst type Var expl= .82337250E+04
Into group 2, codes 3
and group 3, codes 2 4 1
|
|
|
Split 2 candidate groups
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
2 57 .57000E+02 .31877E+02 .31175E+03 .21646E+01 .16436E+05
.34561E+01 .38954E+01
3 959 .95900E+03 .15046E+02 .12058E+03 .28464E+01 .86385E+05
.19145E+01 .37526E+01
Attempt to split group 3 Var= 86385.484
Predictor V14 sv:inst type Rank 2 Type F
Codes 2 4 1
Best split after code 4 Var expl= .14523170E+04
Predictor V15 :field Rank 2 Type F
Codes 2 1
No eligible split
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2 3
Best split after code 1 Var expl= .25520410E+04
Best split for group 3 on predictor V9 v204:rank Rank 1
Var expl= .25520410E+04
Split group 3 on V9 v204:rank Var expl= .25520410E+04
Into group 4, codes 1
and group 5, codes 2 3
|
|
|
Split 3 candidate groups
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
2 57 .57000E+02 .31877E+02 .31175E+03 .21646E+01 .16436E+05
.34561E+01 .38954E+01
4 317 .31700E+03 .18356E+02 .10762E+03 .17423E+01 .30268E+05
.26751E+01 .38973E+01
5 642 .64200E+03 .13411E+02 .11906E+03 .32997E+01 .53565E+05
.15389E+01 .32598E+01
Attempt to split group 5 Var= 53565.234
Predictor V14 sv:inst type Rank 2 Type F
Codes 2 4 1
Best split after code 4 Var expl= .20114190E+04
Predictor V15 :field Rank 2 Type F
Codes 2 1
No eligible split
Predictor V9 v204:rank Rank 1 Type M
Codes 2 3
No eligible split
Best split for group 5 on predictor V14 sv:inst type Rank 1
Var expl= .20114190E+04
Split group 5 on V14 sv:inst type Var expl= .20114190E+04
Into group 6, codes 2 4
and group 7, codes 1
|
|
|
Split 4 candidate groups
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
2 57 .57000E+02 .31877E+02 .31175E+03 .21646E+01 .16436E+05
.34561E+01 .38954E+01
4 317 .31700E+03 .18356E+02 .10762E+03 .17423E+01 .30268E+05
.26751E+01 .38973E+01
6 374 .37400E+03 .14513E+02 .12511E+03 .35936E+01 .34194E+05
.14305E+01 .25890E+01
7 268 .26800E+03 .11873E+02 .10697E+03 .31721E+01 .17360E+05
.16903E+01 .41696E+01
Attempt to split group 6 Var= 34194.266
Predictor V14 sv:inst type Rank 2 Type F
Codes 2 4
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 2 1
No eligible split
Predictor V9 v204:rank Rank 1 Type M
Codes 2 3
No eligible split
No eligible split for group 6
1
Split 4 candidate groups
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
2 57 .57000E+02 .31877E+02 .31175E+03 .21646E+01 .16436E+05
.34561E+01 .38954E+01
4 317 .31700E+03 .18356E+02 .10762E+03 .17423E+01 .30268E+05
.26751E+01 .38973E+01
7 268 .26800E+03 .11873E+02 .10697E+03 .31721E+01 .17360E+05
.16903E+01 .41696E+01
Attempt to split group 4 Var= 30268.211
Predictor V14 sv:inst type Rank 2 Type F
Codes 1 2 4
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 2 1
Best split after code 2 Var expl= .15842390E+04
Predictor V9 v204:rank Rank 1 Type M
Codes 1
No eligible split
Best split for group 4 on predictor V15 :field Rank 1
Var expl= .15842390E+04
Split group 4 on V15 :field Var expl= .15842390E+04
Into group 8, codes 2
and group 9, codes 1
|
|
|
Split 5 candidate groups
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
2 57 .57000E+02 .31877E+02 .31175E+03 .21646E+01 .16436E+05
.34561E+01 .38954E+01
7 268 .26800E+03 .11873E+02 .10697E+03 .31721E+01 .17360E+05
.16903E+01 .41696E+01
8 139 .13900E+03 .15302E+02 .86966E+02 .19206E+01 .10174E+05
.23022E+01 .35892E+01
9 178 .17800E+03 .20742E+02 .11128E+03 .13002E+01 .18510E+05
.29663E+01 .39650E+01
Attempt to split group 9 Var= 18509.781
Predictor V14 sv:inst type Rank 2 Type F
Codes 2 1 4
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 1
No eligible split
Predictor V9 v204:rank Rank 1 Type M
Codes 1
No eligible split
No eligible split for group 9
1
Split 5 candidate groups
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
2 57 .57000E+02 .31877E+02 .31175E+03 .21646E+01 .16436E+05
.34561E+01 .38954E+01
7 268 .26800E+03 .11873E+02 .10697E+03 .31721E+01 .17360E+05
.16903E+01 .41696E+01
8 139 .13900E+03 .15302E+02 .86966E+02 .19206E+01 .10174E+05
.23022E+01 .35892E+01
Attempt to split group 7 Var= 17359.549
Predictor V14 sv:inst type Rank 2 Type F
Codes 1
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 1 2
No eligible split
Predictor V9 v204:rank Rank 1 Type M
Codes 2 3
No eligible split
No eligible split for group 7
1
Split 5 candidate groups
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
2 57 .57000E+02 .31877E+02 .31175E+03 .21646E+01 .16436E+05
.34561E+01 .38954E+01
8 139 .13900E+03 .15302E+02 .86966E+02 .19206E+01 .10174E+05
.23022E+01 .35892E+01
Attempt to split group 2 Var= 16436.018
Predictor V14 sv:inst type Rank 2 Type F
Codes 3
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 2 1
Best split after code 2 Var expl= .10602170E+04
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2 3
No eligible split
Best split for group 2 on predictor V15 :field Rank 1
Var expl= .10602170E+04
Split group 2 on V15 :field Var expl= .10602170E+04
Into group 10, codes 2
and group 11, codes 1
|
|
|
Split 6 candidate groups
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
8 139 .13900E+03 .15302E+02 .86966E+02 .19206E+01 .10174E+05
.23022E+01 .35892E+01
10 25 .25000E+02 .27880E+02 .16594E+03 .40679E+00 .39657E+04
.32400E+01 .42733E+01
11 32 .32000E+02 .35000E+02 .41174E+03 .34537E+01 .11410E+05
.36250E+01 .36613E+01
Attempt to split group 11 Var= 11410.132
Predictor V14 sv:inst type Rank 2 Type F
Codes 3
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 1
No eligible split
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2
No eligible split
No eligible split for group 11
1
Split 6 candidate groups
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
8 139 .13900E+03 .15302E+02 .86966E+02 .19206E+01 .10174E+05
.23022E+01 .35892E+01
10 25 .25000E+02 .27880E+02 .16594E+03 .40679E+00 .39657E+04
.32400E+01 .42733E+01
Attempt to split group 8 Var= 10174.189
Predictor V14 sv:inst type Rank 2 Type F
Codes 4 1 2
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 2
No eligible split
Predictor V9 v204:rank Rank 1 Type M
Codes 1
No eligible split
No eligible split for group 8
1
Split 6 candidate groups
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
10 25 .25000E+02 .27880E+02 .16594E+03 .40679E+00 .39657E+04
.32400E+01 .42733E+01
Attempt to split group 10 Var= 3965.6689
Predictor V14 sv:inst type Rank 2 Type F
Codes 3
No eligible split
Predictor V15 :field Rank 2 Type F
Codes 2
No eligible split
Predictor V9 v204:rank Rank 1 Type M
Codes 1 2 3
No eligible split
No eligible split for group 10
No splits possible
|
|
|
The partitioning ends with 6 final groups
The variation explained is 13.9%
One-way analysis of final groups
Source Variation DF
Explained .15441640E+05 5
Error .95613590E+05 1010
Total .11105520E+06 1015
|
|
|
Split summary table
Group 1 1016 cases
Mean(Y)= .15990160E+02 Var(Y)= .14602160E+03
Mean(Z)= .20009840E+01 Var(Z)= .38827580E+01
Slope= .30705440E+01 Intercept= .98460470E+01
Corr= .50069920E+00 Variation= .11105520E+06
Split on V14 sv:inst type Var expl= .82337250E+04
Into group 2, codes 3
and group 3, codes 2 4 1
Group 3 959 cases
Mean(Y)= .15045880E+02 Var(Y)= .12057620E+03
Mean(Z)= .19144940E+01 Var(Z)= .37525980E+01
Slope= .28463960E+01 Intercept= .95964720E+01
Corr= .50214670E+00 Variation= .86385480E+05
Split on V9 v204:rank Var expl= .25520410E+04
Into group 4, codes 1
and group 5, codes 2 3
Group 5 642 cases
Mean(Y)= .13411210E+02 Var(Y)= .11905680E+03
Mean(Z)= .15389410E+01 Var(Z)= .32597920E+01
Slope= .32996560E+01 Intercept= .83332390E+01
Corr= .54599230E+00 Variation= .53565230E+05
Split on V14 sv:inst type Var expl= .20114190E+04
Into group 6, codes 2 4
and group 7, codes 1
Group 4 317 cases
Mean(Y)= .18356470E+02 Var(Y)= .10761620E+03
Mean(Z)= .26750790E+01 Var(Z)= .38972570E+01
Slope= .17423130E+01 Intercept= .13695640E+02
Corr= .33156360E+00 Variation= .30268210E+05
Split on V15 :field Var expl= .15842390E+04
Into group 8, codes 2
and group 9, codes 1
Group 2 57 cases
Mean(Y)= .31877190E+02 Var(Y)= .31175250E+03
Mean(Z)= .34561400E+01 Var(Z)= .38953630E+01
Slope= .21646290E+01 Intercept= .24395930E+02
Corr= .24196500E+00 Variation= .16436020E+05
Split on V15 :field Var expl= .10602170E+04
Into group 10, codes 2
and group 11, codes 1
1Final group summary table
Group 6 374 cases
Mean(Y)= .14513370E+02 Var(Y)= .12510840E+03
Mean(Z)= .14304810E+01 Var(Z)= .25889880E+01
Slope= .35936360E+01 Intercept= .93727400E+01
Corr= .51696E+00 Variation= .34194270E+05
Group 7 268 cases
Mean(Y)= .11873130E+02 Var(Y)= .10697260E+03
Mean(Z)= .16902990E+01 Var(Z)= .41696430E+01
Slope= .31720890E+01 Intercept= .65113570E+01
Corr= .62627E+00 Variation= .17359550E+05
Group 8 139 cases
Mean(Y)= .15302160E+02 Var(Y)= .86966010E+02
Mean(Z)= .23021580E+01 Var(Z)= .35891980E+01
Slope= .19206370E+01 Intercept= .10880550E+02
Corr= .39018E+00 Variation= .10174190E+05
Group 9 178 cases
Mean(Y)= .20741570E+02 Var(Y)= .11127750E+03
Mean(Z)= .29662920E+01 Var(Z)= .39649590E+01
Slope= .13001600E+01 Intercept= .16884920E+02
Corr= .24542E+00 Variation= .18509780E+05
Group 10 25 cases
Mean(Y)= .27880000E+02 Var(Y)= .16594330E+03
Mean(Z)= .32400000E+01 Var(Z)= .42733340E+01
Slope= .40678630E+00 Intercept= .26562010E+02
Corr= .65278E-01 Variation= .39656690E+04
Group 11 32 cases
Mean(Y)= .35000000E+02 Var(Y)= .41174190E+03
Mean(Z)= .36250000E+01 Var(Z)= .36612900E+01
Slope= .34537440E+01 Intercept= .22480180E+02
Corr= .32568E+00 Variation= .11410130E+05
|
INTERPRETATION
|
|
IDAM reports analysis specifications
No. of cases read
from the input data file = 1039
No. of cases rejected
for missing data = 23
No. of cases processed
= 1016
Dependent variable
= V4
Covariate variable=
V13
|
|
|
|
Group 1 (the entire sample)
N=Number of cases
SUM (WT) = Number of cases
Mean
Y = 15.990 (Mean of dependent variable)
Z = 2.001 (Mean of covariate variable)
Variance of
Y = Dependent variable
Z = Covariate variable
Slope = Slope of the dependent variable Y on the covariate Z in the
entire sample
Variation = Sum of squares of the dependent variable
|
|
|
Attempt to split Group 1
The algorithm attempts to make binary splits at different cut-off points
of all variables and selects the best cut-off, which results in maximum
difference in the slope between the parent group and the descendent group.
Predictor Cut-off Variance explained
(After code)
V14 (3,2,4,1) 3 8233.725
V15 (2,1) 2 901.284
V9 (1,2,3) 2 3049.774
Best split for Group 1 on predictor V14
2 57 .57000E+02 .31877E+02 .31175E+03 .21646E+01 .16436E+05
.34561E+01 .38954E+01
3 959 .95900E+03 .15046E+02 .12058E+03 .28464E+01 .86385E+05
.19145E+01 .37526E+01
Group-3 is selected for further split since its slope is greater than
that of Group-2
All the predictors are examined for their best splits.
Predictor Cut-off Variance explained
(After code)
V14 (2,4,1) 4 1452.317
V15 (2,1) No eligible split
V9 (1,2,3) 1 2552.041
Group-3 is now spilt on V9 into two groups:
Group-4 V9(Code 1)
Group-5 V9(Code 2, 3)
|
|
|
Split 3
Now the candidate group are:
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
2 57 .57000E+02 .31877E+02 .31175E+03 .21646E+01 .16436E+05
34561E+01 .38954E+01
4 317 .31700E+03 .18356E+02 .10762E+03 .17423E+01 .30268E+05
.26751E+01 .38973E+01
5 642 .64200E+03 .13411E+02 .11906E+03 .32997E+01 .53565E+05
.15389E+01 .32598E+01
Group 5 is selected for forth split, since it accounts for the largest
value of the slope and variance.
All predictors are evaluated for splitting Group-5.
Predictor Cut-off Variance explained
(After code)
V14 (2,4,1) 4 2011.419
V15 (2,1) No eligible split
V9 (2,3) 1 No eligible split
Group-5 is now split on V14 into two groups:
Group-6V14(2, 4)
Group-7V14(1)
|
|
|
Split 4
At this stage, there are 4 candidates groups for further splits.
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
2 57 .57000E+02 .31877E+02 .31175E+03 .21646E+01 .16436E+05
.34561E+01 .38954E+01
4 317 .31700E+03 .18356E+02 .10762E+03 .17423E+01 .30268E+05
.26751E+01 .38973E+01
6 374 .37400E+03 .14513E+02 .12511E+03 .35936E+01 .34194E+05
.14305E+01 .25890E+01
7 268 .26800E+03 .11873E+02 .10697E+03 .31721E+01 .17360E+05
.16903E+01 .41696E+01
Group-6 is selected for further split since it has the largest value
of the slope (variance explained).
No eligible split for Group-6 is found.
Group-4 is then considered for possible split. All the predictor variables
were evaluated for splitting this group. Predictors V9 and V14 did not
meet the eligibility criterion for split.
Hence, this group was split on variable V15 (1, 2) into two groups:
Group-8V15(Code: 2)
Group-9V15(Code: 1)
|
|
|
At this stage there are 4 candidate groups for further split
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
2 57 .57000E+02 .31877E+02 .31175E+03 .21646E+01 .16436E+05
.34561E+01 .38954E+01
7 268 .26800E+03 .11873E+02 .10697E+03 .31721E+01 .17360E+05
.16903E+01 .41696E+01
8 139 .13900E+03 .15302E+02 .86966E+02 .19206E+01 .10174E+05
.23022E+01 .35892E+01
9 178 .17800E+03 .20742E+02 .11128E+03 .13002E+01 .18510E+05
.29663E+01 .39650E+01
Group-9, Group-7 were sequentially evaluated for further split, but none
of the predictor met the eligibility criterion to split any of these groups.
Group 2 was considered for further split. Only one variable i.e.V15
met the eligibility criterion, and hence this group was split into two
groups:
Group-10V15(Code: 2)
Group-11V15(Code: 1)
|
|
|
At this stage there are three candidate groups for further split:
Group-8, Group-10 and Group-11
Group N Sum(WT) Mean Y,Z Var Y,Z Slope Variation
8 139 .13900E+03 .15302E+02 .86966E+02 .19206E+01 .10174E+05
.23022E+01 .35892E+01
10 25 .25000E+02 .27880E+02 .16594E+03 .40679E+00 .39657E+04
.32400E+01 .42733E+01
11 32 .32000E+02 .35000E+02 .41174E+03 .34537E+01 .11410E+05
.36250E+01 .36613E+01
These groups were considered sequentially for further split, but none
of the predictor variables met the eligibility criterion for splitting
any of these groups.
|
|
|
The partition ends with 6 terminal groups
Group-10, Group-11, Group-8, Group-9, Group-6 and Group-7.
This partition explains 13.9% of the total variance
Analysis of variance Table
Source Variation DF
Explained .15441640E+05 5
Error .95613590E+05 1010
Total .11105520E+06 1015
|
|
|
History of the splitting process.
|
|
|
Graphical representation of the splitting process.
|
_______________
N=Number of cases | Group 1 |
Y=Dep. var. mean, v264:supervsn | N=1016 |
Z=Covariate mean |Y= 15.99016|
S=Slope |Z= 2.00098|
C=Predictor codes |S= 3.07054|
| Split 1 |
| on V14 |
|_____________|
|
_________________________________sv:inst type__________________________________
C=3 C=2,4,1
| |
_______|_______ _______|_______
| Group 2 | | Group 3 |
| N=57 | | N=959 |
|Y= 31.87719| |Y= 15.04588|
|Z= 3.45614| |Z= 1.91449|
|S= 2.16463| |S= 2.84640|
| Split 5 | | Split 2 |
| on V15 | | on V9 |
|_____________| |_____________|
| |
____________________:field_____________________ ___________________v204:rank___________________
C=2 C=1 C=1 C=2,3
| | | |
_______|_______ _______|_______ _______|_______ _______|_______
| Group 10 | | Group 11 | | Group 4 | | Group 5 |
| N=25 | | N=32 | | N=317 | | N=642 |
|Y= 27.88000| |Y= 35.00000| |Y= 18.35647| |Y= 13.41121|
|Z= 3.24000| |Z= 3.62500| |Z= 2.67508| |Z= 1.53894|
|S= .40679| |S= 3.45374| |S= 1.74231| |S= 3.29966|
| Final | | Final | | Split 4 | | Split 3 |
| | | | | on V15 | | on V14 |
|_____________| |_____________| |_____________| |_____________|
| |
____________:field_____________ _________sv:inst type__________
C=2 C=1 C=2,4 C=1
| | | |
_______|_______ _______|_______ _______|_______ _______|_______
| Group 8 | | Group 9 | | Group 6 | | Group 7 |
| N=139 | | N=178 | | N=374 | | N=268 |
|Y= 15.30216| |Y= 20.74157| |Y= 14.51337| |Y= 11.87313|
|Z= 2.30216| |Z= 2.96629| |Z= 1.43048| |Z= 1.69030|
|S= 1.92064| |S= 1.30016| |S= 3.59364| |S= 3.17209|
| Final | | Final | | Final | | Final |
| | | | | | | |
|_____________| |_____________| |_____________| |_____________|
10.3 Searching for Structure: CHI Analysis
|
Research Question
|
:
|
Explore the pattern of relationships between the time – involvement
of academic scientists in teaching ( coded as; 1=Low, 2= Averagr, 3= Above
averagre, 4= High) and a set of contextual variables: Rank, institutional
settings, scientific field, external funding of research.
|
|
Methodology
|
:
|
Classification and regression trees: SEARCH module – CHI analysis
|
|
Dataset
|
:
|
PSN.DAT
|
SYNTAX*
$RUN SEARCH
$FILES
PRINT = PSN.LST
DICTIN = PSN.DIC
DATAIN = PSN.DAT
$SETUP
INCLUDE V2=1-3 AND V3=1-2 AND V5 =1,2 AND V6=1-4
SEARCHING OF STRUCTURE
BADDATA=MD1 -
ANALYSIS=CHI -
DEPVAR=V6 CODE= (1-4) -
MINCASE=10 -
PRINT=(TREE,DICT,TRACE,FINAL)
VARS=V2 TYPE=M
VARS=(V3,V4, V5) TYPE=F
------------------------------------
Note : Search module does not recognize missing data or invalid
codes for the predictor variables. Hence, the filter Include has been used.
All options set at default values
EXTRACTION FROM COMPUTER OUTPUT
|
|
After filtering 1011 cases read from the input data file
1 cases contained illegal characters on filter variables and were skipped
|
|
|
|
Split 1 candidate groups
Group N Sum(WT) Variation
1 1011 .10110E+04 .27381E+04
Attempt to split group 1 Var= 2738.0928
Predictor V2 RANK Rank 1 Type M
Codes 1 2 3
Best split after code 1 Var expl= .87576360E+02
Predictor V3 FUNDING Rank 2 Type F
Codes 1 2
Best split after code 1 Var expl= .84713570E+02
Predictor V4 INSTYP Rank 2 Type F
Codes 3 4 2 1
Best split after code 3 Var expl= .86131580E+02
Predictor V5 FIELD Rank 2 Type F
Codes 2 1
No eligible split
Best split for group 1 on predictor V2 RANK Rank 1
Var expl= .87576360E+02
Split group 1 on V2 RANK Var expl= .87576360E+02
Into group 2, codes 1
and group 3, codes 2 3
|
|
|
Split 2 candidate groups
Group N Sum(WT) Variation
2 356 .35600E+03 .85404E+03
3 655 .65500E+03 .17965E+04
Attempt to split group 3 Var= 1796.4799
Predictor V2 RANK Rank 1 Type M
Codes 2 3
Best split after code 2 Var expl= .23601020E+02
Predictor V3 FUNDING Rank 2 Type F
Codes 2 1
Best split after code 2 Var expl= .31537450E+02
Predictor V4 INSTYP Rank 2 Type F
Codes 2 3 4 1
Best split after code 3 Var expl= .54556970E+02
Predictor V5 FIELD Rank 2 Type F
Codes 2 1
No eligible split
Best split for group 3 on predictor V4 INSTYP Rank 1
Var expl= .54556970E+02
Split group 3 on V4 INSTYP Var expl= .54556970E+02
Into group 4, codes 2 3
and group 5, codes 4 1
|
|
|
Split 3 candidate groups
Group N Sum(WT) Variation
2 356 .35600E+03 .85404E+03
4 152 .15200E+03 .38393E+03
5 503 .50300E+03 .13580E+04
Attempt to split group 5 Var= 1357.9944
Predictor V2 RANK Rank 1 Type M
Codes 2 3
No eligible split
Predictor V3 FUNDING Rank 2 Type F
Codes 2 1
No eligible split
Predictor V4 INSTYP Rank 2 Type F
Codes 4 1
No eligible split
Predictor V5 FIELD Rank 2 Type F
Codes 2 1
No eligible split
No eligible split for group 5
Split 3 candidate groups
Group N Sum(WT) Variation
2 356 .35600E+03 .85404E+03
4 152 .15200E+03 .38393E+03
Attempt to split group 2 Var= 854.03656
Predictor V2 RANK Rank 1 Type M
Codes 1
No eligible split
Predictor V3 FUNDING Rank 2 Type F
Codes 1 2
Best split after code 1 Var expl= .31131080E+02
Predictor V4 INSTYP Rank 2 Type F
Codes 3 4 1 2
Best split after code 3 Var expl= .42759830E+02
Predictor V5 FIELD Rank 2 Type F
Codes 2 1
No eligible split
Best split for group 2 on predictor V4 INSTYP Rank 1
Var expl= .42759830E+02
Split group 2 on V4 INSTYP Var expl= .42759830E+02
Into group 6, codes 3
and group 7, codes 4 1 2
|
|
|
Split 4 candidate groups
Group N Sum(WT) Variation
4 152 .15200E+03 .38393E+03
6 36 .36000E+02 .91390E+01
7 320 .32000E+03 .80214E+03
Attempt to split group 7 Var= 802.13776
Predictor V2 RANK Rank 1 Type M
Codes 1
No eligible split
Predictor V3 FUNDING Rank 2 Type F
Codes 1 2
Best split after code 1 Var expl= .24340890E+02
Predictor V4 INSTYP Rank 2 Type F
Codes 4 1 2
No eligible split
Predictor V5 FIELD Rank 2 Type F
Codes 2 1
No eligible split
Best split for group 7 on predictor V3 FUNDING Rank 1
Var expl= .24340890E+02
Split group 7 on V3 FUNDING Var expl= .24340890E+02
Into group 8, codes 1
and group 9, codes 2
|
|
|
Split 5 candidate groups
Group N Sum(WT) Variation
4 152 .15200E+03 .38393E+03
6 36 .36000E+02 .91390E+01
8 120 .12000E+03 .32932E+03
9 200 .20000E+03 .44848E+03
Attempt to split group 9 Var= 448.47726
Predictor V2 RANK Rank 1 Type M
Codes 1
No eligible split
Predictor V3 FUNDING Rank 2 Type F
Codes 2
No eligible split
Predictor V4 INSTYP Rank 2 Type F
Codes 1 4 2
No eligible split
Predictor V5 FIELD Rank 2 Type F
Codes 1 2
No eligible split
No eligible split for group 9
Split 5 candidate groups
Group N Sum(WT) Variation
4 152 .15200E+03 .38393E+03
6 36 .36000E+02 .91390E+01
8 120 .12000E+03 .32932E+03
Attempt to split group 4 Var= 383.92853
Predictor V2 RANK Rank 1 Type M
Codes 2 3
No eligible split
Predictor V3 FUNDING Rank 2 Type F
Codes 1 2
No eligible split
Predictor V4 INSTYP Rank 2 Type F
Codes 3 2
No eligible split
Predictor V5 FIELD Rank 2 Type F
Codes 1 2
No eligible split
No eligible split for group 4
1
Split 5 candidate groups
Group N Sum(WT) Variation
6 36 .36000E+02 .91390E+01
8 120 .12000E+03 .32932E+03
Attempt to split group 8 Var= 329.31958
Predictor V2 RANK Rank 1 Type M
Codes 1
No eligible split
Predictor V3 FUNDING Rank 2 Type F
Codes 1
No eligible split
Predictor V4 INSTYP Rank 2 Type F
Codes 4 1 2
No eligible split
Predictor V5 FIELD Rank 2 Type F
Codes 2 1
No eligible split
No eligible split for group 8
1
Split 5 candidate groups
Group N Sum(WT) Variation
6 36 .36000E+02 .91390E+01
Attempt to split group 6 Var= 9.1389990
Predictor V2 RANK Rank 1 Type M
Codes 1
No eligible split
Predictor V3 FUNDING Rank 2 Type F
Codes 1 2
No eligible split
Predictor V4 INSTYP Rank 2 Type F
Codes 3
No eligible split
Predictor V5 FIELD Rank 2 Type F
Codes 2 1
No eligible split
No eligible split for group 6
No splits possible
|
|
|
The partitioning ends with 5 final groups
The variation explained is 7.6%
One-way analysis of final groups
Source Variation DF
Explained .20923410E+03 4
Error .25288590E+04 1006
Total .27380930E+04 1010
|
|
|
Split summary table
Group 1 1011 cases Variation= .27380930E+04
Split on V2 RANK Var expl= .87576360E+02
Into group 2, codes 1
and group 3, codes 2 3
Group 3 655 cases Variation= .17964800E+04
Split on V4 INSTYP Var expl= .54556970E+02
Into group 4, codes 2 3
and group 5, codes 4 1
Group 2 356 cases Variation= .85403660E+03
Split on V4 INSTYP Var expl= .42759830E+02
Into group 6, codes 3
and group 7, codes 4 1 2
Group 7 320 cases Variation= .80213780E+03
Split on V3 FUNDING Var expl= .24340890E+02
Into group 8, codes 1
and group 9, codes 2
|
|
|
Final group summary table
Group 4 152 cases
Variation= .38392850E+03
Group 5 503 cases
Variation= .13579940E+04
Group 6 36 cases
Variation= .91389990E+01
Group 8 120 cases
Variation= .32931960E+03
Group 9 200 cases
Variation= .44847730E+03
Dependent variable percent distribution for each group (*=Final groups)
1 2 3 4* 5* 6* 7 8* 9*
Code= 1 36.10 52.25 27.33 42.11 22.86 97.22 47.19 31.67 56.50
Code= 2 19.09 20.51 18.32 22.37 17.10 2.78 22.50 25.00 21.00
Code= 3 21.96 16.85 24.73 26.97 24.06 .00 18.75 23.33 16.00
Code= 4 22.85 10.39 29.62 8.55 35.98 .00 11.56 20.00 6.50
|
INTERPRETATION
|
|
IDAMS reports that 1011 cases were read from the input data file.
|
|
|
|
Split: 1
At this stage, the candidate group is Group-1 comprising all the cases.
N = Number of cases
Sum (weight) = Number of cases
Variation = 2738.0928
This is the entropy of the whole group.
Attempt to split Group-1
All the predictors are evaluated, one by one, for their best splits.
Predictor Cut-off Entropy
After code
V2 (1, 2, 3) 1 87.57636
V3 (1, 2) 1 84.71357
V4 (3,4,2,1) 3 86.13158
V5 (2, 1) No eligible split
Best split for Group-1 on predictor V2 since it accounts for the maximum
entropy.
Group-1 is split on V2 into the following groups:
Group – 2V2 (Code: 1)
Group – 3V2 (Code: 2, 3)
|
|
|
Split 2
At this stage there are two candidate groups.
Group N Sum(WT) Variation
2 356 .35600E+03 .85404E+03
3 655 .65500E+703 .1965E+04
Group – 3 is considered first for split, since it accounts for the
maximum entropy.
Best predictors and their cut-off values are as follows:
Predictor Cut-off Entropy
After code
V2 ( 2, 3) 2 23.60102
V3 (2, 1) No eligible split
V4 (2, 3,4,1) 3 54.556970
V5 (2, 1) No eligible split
Best split for Group-3 is on predictor V4 since it has the maximum value
of entropy. This group is split into two groups on variable V4:
Group – 4V4 (Code: 2, 3)
Group – 5V4 (Code: 4, 1)
|
|
|
Split 3
At this stage there are three candidate groups for further splitting:
Group N Sum(WT) Variation
2 356 .35600E+03 .85404E+03
4 152 .15200E+03 .38393E+03
5 503 .50300E+03 .13580E+04
It can be easily seen that Group-5 has the maximum value of entropy and
would be considered first for possible split.
All the predictors are evaluated in the same manner as for the earlier
splits. None of the predictor variable met the eligibility criterion for
splitting this group.
Hereafter Group-2 was considered for further split, since it accounted
for greater entropy than Group-4.
All the predictors were evaluated for splitting Group-2. Predictor V4
(3,4,1,2) was found to be the best predictor at cut-off value (code 3).
Hence, Group-2 was partitioned into the following groups:
Group – 6V4 (Code: 3)
Group – 7V4 (Code: 4, 1, 2)
|
|
|
Split – 4
At this stage there are three candidate groups for possible splits
Group N Sum(WT) Variation
4 152 .15200E+03 .38393E+03
6 36 .36000E+02 .91390E+01
7 320 .32000E+03 .80214E+03
Group-7 has the maximum value of entropy and was considered first for
a possible split.
All the predictors were evaluated for splitting Group-7, Variable V3
was found to be the best splitter at cut-off value = 1. Hence, Group-7
is split into the following groups on this predictor:
Group – 8V3(Code:1)
Group – 9V3(Code:2)
|
|
|
Split 5
At this stage, there are 4 candidate groups for possible splits.
Group N Sum(WT) Variation
4 152 .15200E+03 .38393E+03
6 36 .36000E+02 .91390E+01
8 120 .12000E+03 .32932E+03
9 200 .20000E+03 .44848E+03
Group-9 has the highest value of entropy, and is, therefore, considered
first for possible split. However, none of the predictor variable could
meet the eligibility criterion for splitting this group.
Thereafter, Group-4, Group-8 and Group-6 were considered one after the
other for possible split. However, none of the predictors was able to
split any of these groups.
|
|
|
The partitioning ends with 5 final groups, Group-6, Group-8, Group-9,
Group-4, Group-5.
7.6 of the total variance is explained by the partition.
One-way analysis of final groups
Source Variation DF
Explained .20923410E+03 4
Error .25288590E+04 1006
Total .27380930E+04 1010
|
|
|
Summary table
This is a history of partitioning of the data on various predictors.
|
|
|
Final group summary table
The size and entropy of the final groups.
Frequency distribution (%) of different categories of the dependent variable
in each of the nine groups created by the algorithm.
Find groups are identified by*
Graphical representation of the splitting process summarized at
.
|
|
|
|
_______________
N=Number of cases | Group 1 |
C=Predictor codes | N=1011 |
| Split 1 |
| on V2 |
|_____________|
|
_____________________________________RANK______________________________________
C=1 C=2,3
| |
_______|_______ _______|_______
| Group 2 | | Group 3 |
| N=356 | | N=655 |
| Split 3 | | Split 2 |
| on V4 | | on V4 |
|_____________| |_____________|
| |
____________________INSTYP_____________________ ____________________INSTYP_____________________
C=3 C=4,1,2 C=2,3 C=4,1
_______|_______ _______|_______ _______|_______ _______|_______
| Group 6 | | Group 7 | | Group 4 | | Group 5 |
| N=36 | | N=320 | | N=152 | | N=503 |
| Final | | Split 4 | | Final | | Final |
| | | on V3 | | | | |
|_____________| |_____________| |_____________| |_____________|
|
____________FUNDING____________
C=1 C=2
| |
_______|_______ _______|_______
| Group 8 | | Group 9 |
| N=120 | | N=200 |
| Final | | Final |
| | | |
|_____________| |_____________|