Contexts in Which Best and Worst CBC are Most Valuable: Application to School Choice
Joel Huber: Duke UniversityNamika Sagara: Duke University
Angelyn Fairchild: Research Triangle Institute
Why Study School Choice?
• School choice is an increasingly difficult reality for parents.
• It is possible to mimic aspects of the actual choices
• There are many analyses of actual school choices but few published conjoint studies
• Positive and negative reaction to features makes school choice ideal for Best/Worst choice based conjoint
Our process
• Identified attributes differentiating public schools in actual choices
• Pretested these to make sure we covered the most important ones with 4 continuous attributes and 4 binary ones
• Built a fixed B/W CBC design • Ran the study on a national sample of 150
parents with a child entering grades 6-11.
Our Sample• Sample: Parent of a child age 11 to 17 attending
public school– 57% Female– 59% Caucasian– 59% had at least some college– Median income was between $50,001 and $75,000
• “Think about your youngest child that is more than 11 years old.”– Age and gender– School grade– Select five important characteristics for child’s school (e.g., close to home)
An Important One-time Decision
• “Suppose you just moved to a new area where families are able to choose which school they would most like their children to attend.”
• Introduction to attributes and practice questions– We defined ranges of each attribute and asked relative
importance– We built up gradually to more complex, realistic choices
Ultimate choice task
Attribute 1: Distance
Travel time to school
Bus Ride 5 min 15 min 30 min 45 min
“About how many minutes does it take for your child to get to school now?”
Attribute 2: Academic Quality
School Attributes
Travel time 5 min 15 min 30 min 45 min
% under Grade Level 15% 25% 35% 45%
“At your child's current school, what percent do you think are below grade level?”
Warm up Choice 1“Next we will ask you to choose between two schools with different travel time and percent of students below grade level.
Imagine that only two school options are available for your child, and the schools are the same except for the differences shown below.”
Attribute 3: Income
School Attributes
Travel time 5 min 15 min 30 min 45 min
% under Grade Level 15% 25% 35% 45%
% Economically Disadvantaged 10% 30% 50% 70%
“At your child’s current school, what percent of students are economically disadvantaged?”
Attribute 4: Diversity
School Attributes
Travel time 5 min 15 min 30 min 45 min
% under Grade Level 15% 25% 35% 45%
% Economically Disadvantaged 10% 30% 50% 70%
PercentMinority 25% 40% 55% 70%
“At your child's current school, about what percent of students are minorities?”
Warm up Question 2
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International Baccalaureate (IB) Program
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International Baccalaureate (IB) Program
Science, Technology, Engineering and Math (S.T.E.M)
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International Baccalaureate (IB) Program
Science, Technology, Engineering and Math (S.T.E.M)
Expanded Arts Program
Featured Programs
International Baccalaureate (IB) Program
Science, Technology, Engineering and Math (S.T.E.M)
Expanded Arts Program
Promote Sports Teams
One of 8 Best/Worst Choice Tasks
“Best” Schools
15 25 35 45 5 15 30 45 10 30 50 70 25 40 55 70
-150
-100
-50
0
50
100
150
% Below Grade Level
Travel Time
Arts Sports STEMIB%
Minority
% Economically
Disadvantaged
“Worst” Schools
15 25 35 45 5 15 30 45 10 30 50 70 25 40 55 70
-150
-100
-50
0
50
100
150
% Below Grade Level
Travel TimeArts
% Economically Disadvantaged
Sports STEMIB%
Minority
What is important in a school?
-1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
Academic quality
Travel time
Income
% Minority
Arts
STEM
Sports
What is important in a School?
-1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
Academic quality
Travel time
Income
% Minority
Sports
IB
Arts
STEM
Who cares?
-1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
Academic quality
Travel time
Income
% Minority
Sports
IB
Arts
STEM
Educated Parent
Nonwhite
Older child
Lower incomePart time
Who cares?
-1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
Academic quality
Travel time
Income
% Minority
Sports
IB
Arts
STEM
Educated Parent
Nonwhite
Older child
Lower incomePart time
Employed full time
Higher income
Younger Child
White
Less educated parent
What we learned
• By building complexity gradually it is possible to generate reliable responses for a difficult and important choice
• 8 choices is sufficient to separate those with quite different values
• B/W provides both insight into what is desired and feared, and generates stable individual estimates
Simple individual level estimation
• All the analysis used standard Sawtooth Software HB analysis
• Can we generate a simplified model that can allow feedback to subjects on the fly?
• Concert 4-level variables to linear, producing 4 linear, 4 binary variables from 8 Best and 8 Worst choices
• This follows from work by Saigal and Dahan (Sawtooth Software Proceedings 2012)
Individual Linear Choice Using Simple Vector Product
• Choice vector Y has 32 items, 4 for each choice set, code Best as a 1, Worst as -1 and Zero otherwise
• Design matrix X(32,8) is zero centered within each choice set
• B-hat = (X’X)-1X’Y• Since we use a fixed design X we multiply
(X’X)-1X’ (8 x32) by Y(32x1) to get B(8x1)
Correlation between HB and linear choice model
% Under Grade Sports STEM Arts Minority Bustime IB Poverty0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Correlation of HB and Linear with Self Explicated
Academic Bustime STEM Poverty Arts Minority IB Sports0.00
0.10
0.20
0.30
0.40
0.50
0.60
Effective use of Best/Worst Choice Based Conjoint
• Best/Worst is appropriate for choices with levels people avoid or fear
• Where there is both attraction and avoidance, combining Best + Worst choices results in better results
• Analyzing Best + Worst with a linear model generates results reasonably close to HB analysis
Thank you!
What is important in a school?
-1.0 -0.5 0.0 0.5 1.0
-1.0
-0.5
0.0
0.5
1.0
Academic quality
Travel time
Income
Income
% Minority
Sports
IB
Arts
STEM
STEM
Correspondence between HB and linear estimates
HB Importance Estimates