﻿ 4 facet Interactions and Dummy Facets: Diving + Creativity

# 4 facet Interactions and Dummy Facets: Diving + Creativity

Dummy facets are facets intended only for investigating interactions, not for measuring main effects. All the elements of a dummy facet are anchored at 0.

Example 1: At the 1988 Illinois Boys Diving Competition, 12 divers performed 3 dives which were rated by 7 judges. The divers chose which types of dive to perform, so each diver did not perform most types of dive. Not all ratings were recorded. Thus, most of the data is "missing"! The original ratings were in the range 0 to 10 with half point increments, so all ratings have been doubled to make them integers. Previous analyses have been performed so that good starting logit values are known. One diver did the wrong dive by mistake - this is deliberately treated as missing data in this analysis.

Include clearly aberrant data, e.g., lucky guesses, if your purpose is to describe the past, e.g., for awarding a prize. Omit such data if your purpose is to predict the future, e.g., to discover examinee's ability to perform surgery or to obtain item difficulty calibrations for an item bank.

We are investigating if there is any judge-by-round (= rater by time-point) interaction.

Facets specifications and data (in file Divesb.txt)

title = 1988 Illinois Boys Diving Competition (Anne Wendt)

facets = 4 ; four facets are diver, dives, round, judges

Inter-rater = 4 ; facet 4 is the rater facet

noncenter = 1 ; diver measures float

positive = 1 ; only for divers does greater score mean greater measure

models = ; these models will be scanned in order until a match is found for each datum:

7,8,?,?,M ; make diver 7 on dive 8 missing - He did the wrong dive!

?,?,?B,?B,R20 ; "round"is a dummy facet for interaction with judges

; but round is checked for validity

*

labels=

1,Diver

;  diver          previous scores included in name for reference

1=Marty Turek    292.85 425.65        , 2.08 ; logit starting value of 2.08 after second ","

|  ; 10 other divers

12=Bryan Hanania   251.15              ,-1.19

*

2,Dives

; Each dives official weighted difficulty, e.g., 1.4, used as dive "name" after "="

1=1.4

| ; 6 other dives

8=2.6

9=2.4? ; unclear what dive this was

*

3,Round,A ; anchored at zero means dummy facet, does not affect measurement

1-3=,0 ; there were 3 rounds

*

4,Judges

1-7 ; there were 7 judges

*

data =

1,8,1,1,14 ; Diver 1, Marty, made a dive 8, a "2.6" dive, in round 1 rated by judge 1 with 7*2=14

| ; 136 other ratings

12,2,3,7,11 ; Bryan made a "1.7" dive in round 3 rated by judge 7 with 5.5*2=11

Largest judge by round interaction is:

Judge 1 was relatively lenient in Round 2 (+0.50 score points), but severe in Round 3 (-1.46 score points).

Example 2: In the Dives data, we suspect that there is an interaction between perceived diver ability (High and Low) and dive round. This is example dataset: Divesint.txt

Title = 1988 Illinois Boys Diving Competition (Anne Wendt)

Facets = 4 ; four facets are diver, dives, round, judges

Noncenter = 1 ; diver measures float

Positive = 1 ; only for divers does greater score mean greater measure

Models = ; these models will be scanned in order until a match is found for each datum:

7,8,?,?,?,M ; make diver 7 on dive 8 missing - He did the wrong dive!

; interaction between facet 3 (round) and facet 5 (perceived ability)

?,?,?B,?,?B,DoublePoints ; Round excluded for this analysis by X

*

Rating scale = DoublePoints,R20,Keep ; Keep unobserved intermediate categories

0  = 0.0

10 = 5.0 ; 5 on the original scoring

20 = 10.0

*

labels=

1,Diver

;  diver          previous scores

1, H: Marty Turek     292.85  ; previous scores

2, H: Tom Wright      279.95

3, L: Mike Gotkowski  249.9

4, L: Matt Paulson    244.55

5, L: Scott Ternovits 252.8

6, L: Ross Moyer      243.4

7, H: Curt Billings   266.25

8, H: Steve Hutchings 267.15

9, L: Larry Kirk      258.35

10, H: Kurt Becker     284.4

11, L: Lance Kleffman  259.6

12, L: Bryan Hanania   251.15

*

2,Dives

1-9

*

3,Round, D ; a dummy facet

1-3

*

4,Judges

1-7

*

5, Perceived ability, D ; a dummy facet

1, High previous score 260 up

2, Low previous score 259 down

*

Dvalues =

4, 1-7 ; the observations for the 7 judges are in Excel

5, 1, 1, 1 ; element label for facet 5 is first character of label in facet 1

*

Data = Dives.xls

; has this format:

 ; diver dive round judge 1 judge 2 judge 3 judge 4 judge 5 judge 6 judge 7 1 8 1 14 11 12 12 . . . 1 1 2 16 13 13 16 14 13 14 2 8 2 12 12 10 11 10 11 13

The interactions indicate a jump in ability in round 3 for those with perceived high ability. Do they handle the pressure of the final round better? Are the judges more lenient with them in the third round? Or ... This could be the start of an exciting investigation into competitive behavior of great interest to diving coaches.

Example 3: We want to investigate whether there is an interaction between judges and score-bands for the Creativity (Guilford) data. A dummy facet "score-band" is introduced into the data. It has 3 elements: 1, 4, 7, corresponding to the observed rating ranges 1-3, 4-6, 7-9.

Facets specifications and data (in file Guilfordsb.txt):

# ....

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