Conjoint Questions

EMSE 6035: Marketing Analytics for Design Decisions

John Paul Helveston

October 07, 2026

Some Quarto tips

Convert a data frame to a markdown table with `kable()`

library(tidyverse)

mtcars %>%
  kable()

	mpg	cyl	disp	hp	drat	wt	qsec	vs	am	gear	carb
Mazda RX4	21.0	6	160.0	110	3.90	2.620	16.46	0	1	4	4
Mazda RX4 Wag	21.0	6	160.0	110	3.90	2.875	17.02	0	1	4	4
Datsun 710	22.8	4	108.0	93	3.85	2.320	18.61	1	1	4	1
Hornet 4 Drive	21.4	6	258.0	110	3.08	3.215	19.44	1	0	3	1
Hornet Sportabout	18.7	8	360.0	175	3.15	3.440	17.02	0	0	3	2
Valiant	18.1	6	225.0	105	2.76	3.460	20.22	1	0	3	1
Duster 360	14.3	8	360.0	245	3.21	3.570	15.84	0	0	3	4
Merc 240D	24.4	4	146.7	62	3.69	3.190	20.00	1	0	4	2
Merc 230	22.8	4	140.8	95	3.92	3.150	22.90	1	0	4	2
Merc 280	19.2	6	167.6	123	3.92	3.440	18.30	1	0	4	4
Merc 280C	17.8	6	167.6	123	3.92	3.440	18.90	1	0	4	4
Merc 450SE	16.4	8	275.8	180	3.07	4.070	17.40	0	0	3	3
Merc 450SL	17.3	8	275.8	180	3.07	3.730	17.60	0	0	3	3
Merc 450SLC	15.2	8	275.8	180	3.07	3.780	18.00	0	0	3	3
Cadillac Fleetwood	10.4	8	472.0	205	2.93	5.250	17.98	0	0	3	4
Lincoln Continental	10.4	8	460.0	215	3.00	5.424	17.82	0	0	3	4
Chrysler Imperial	14.7	8	440.0	230	3.23	5.345	17.42	0	0	3	4
Fiat 128	32.4	4	78.7	66	4.08	2.200	19.47	1	1	4	1
Honda Civic	30.4	4	75.7	52	4.93	1.615	18.52	1	1	4	2
Toyota Corolla	33.9	4	71.1	65	4.22	1.835	19.90	1	1	4	1
Toyota Corona	21.5	4	120.1	97	3.70	2.465	20.01	1	0	3	1
Dodge Challenger	15.5	8	318.0	150	2.76	3.520	16.87	0	0	3	2
AMC Javelin	15.2	8	304.0	150	3.15	3.435	17.30	0	0	3	2
Camaro Z28	13.3	8	350.0	245	3.73	3.840	15.41	0	0	3	4
Pontiac Firebird	19.2	8	400.0	175	3.08	3.845	17.05	0	0	3	2
Fiat X1-9	27.3	4	79.0	66	4.08	1.935	18.90	1	1	4	1
Porsche 914-2	26.0	4	120.3	91	4.43	2.140	16.70	0	1	5	2
Lotus Europa	30.4	4	95.1	113	3.77	1.513	16.90	1	1	5	2
Ford Pantera L	15.8	8	351.0	264	4.22	3.170	14.50	0	1	5	4
Ferrari Dino	19.7	6	145.0	175	3.62	2.770	15.50	0	1	5	6
Maserati Bora	15.0	8	301.0	335	3.54	3.570	14.60	0	1	5	8
Volvo 142E	21.4	4	121.0	109	4.11	2.780	18.60	1	1	4	2

Example from last year

library(tidyverse)

df <- read_csv("competitors.csv")
df %>%
  kable()

brand	volumeInOz	quantity	price	pricePerCup	biodegrability	opacity	logo
greatValue	9	50	$2.98	$0.06	FALSE	TRUE	FALSE
decorRack	9	50	$5.99	$0.12	FALSE	TRUE	FALSE
tigerChef	9	100	$7.99	$0.08	FALSE	TRUE	FALSE
smartly	9	80	$2.79	$0.03	FALSE	FALSE	FALSE
solo	9	50	$4.04	$0.08	FALSE	FALSE	FALSE
greatValue	9	100	$3.76	$0.04	FALSE	FALSE	FALSE
ecoProducts	9	1000	$187.69	$0.19	TRUE	FALSE	TRUE
worldCentric	9	2000	$220.00	$0.11	TRUE	FALSE	TRUE
hefty	18	50	$3.98	$0.08	FALSE	TRUE	FALSE
solo	18	50	$3.98	$0.08	FALSE	TRUE	FALSE
greatValue	18	120	$5.98	$0.05	FALSE	TRUE	FALSE
upAndUp	18	36	$2.49	$0.07	FALSE	TRUE	FALSE
greatValue	16	25	$1.98	$0.08	FALSE	FALSE	FALSE
solo	18	25	$3.05	$0.12	FALSE	FALSE	FALSE
upAndUp	18	28	$2.99	$0.11	FALSE	FALSE	FALSE
worldCentric	16	1000	$181.00	$0.18	TRUE	FALSE	TRUE
ecoProducts	16	1000	$279.85	$0.28	TRUE	FALSE	TRUE

More `kable()` formatting options:
{kableExtra} package

References

Simple approach: Insert a footnote with ^[]

This markdown…

The Eiffel Tower is 324 meters tall^[From the [Eiffel Tower wikipedia page](https://en.wikipedia.org/wiki
/Eiffel_Tower)]

…renders as this

The Eiffel Tower is 324 meters tall¹

¹From the Eiffel Tower wikipedia page

References

Complex (but more complete) approach: Use bibtex

https://quarto.org/docs/authoring/footnotes-and-citations.html

You can insert citations with [@citekey], and a “References” table will be automatically created.

Footnotes are perfectly fine for this class

Week 7: Conjoint Questions

1. Defining choice questions in R

2. Displaying choice questions in surveydown

Week 7: Conjoint Questions

1. Defining choice questions in R

2. Displaying choice questions in surveydown

1. Download today’s notes, then

2. Open the conjoint_buttons folder in Positron

We’ll be using the {cbcTools} package today

Install with:

remotes::install_github("jhelvy/cbcTools")

Choice question components

1. Generate `profiles` for each attribute and level

2. Create a survey `design` data frame from `profiles`

Basic Design

Any combination of attributes can be shown in each choice question

Question 1

Option:	1	2	3
Type:	Fuji	Pink Lady	Fuji
Price:	$4.00	$1.50	$2.50
Freshness:	Excellent	Poor	Average

Question 2

Option:	1	2	3
Type:	Pink Lady	Gala	Gala
Price:	$2.00	$4.00	$1.50
Freshness:	Excellent	Average	Average

This is exactly what’s in
`code/1_make_choice_questions.R`

profiles <- cbc_profiles(
  type = c("Fuji", "Gala", "Honeycrisp", "Pink Lady", "Red Delicious"),
  price = seq(1, 4, 0.5), # Price ($ / lb)
  freshness = c("Excellent", "Average", "Poor")
)

design <- cbc_design(
  profiles = profiles,
  n_resp = 2000, # Number of respondents
  n_alts = 3, # Number of alternatives per question
  n_q = 6 # Number of questions per respondent
)

Your Turn

Open the `conjoint_buttons` template folder in Positron

In code/1_make_choice_questions.R, replace the apple profiles with your own team’s attributes and levels

Leave cbc_design() at its default values for now - just get a basic design of your own running

Three design choices to consider

1. Regular or labeled?

2. Include a “none” option (outside good) or not?

3. Include restrictions?

1. Regular or labeled?

A labeled design fixes one attribute to a specific option position
e.g. Option 1 is always “Local”, option 2 is always “Imported”

Question 1

Option:	Local	Imported
Type:	Fuji	Honeycrisp
Price:	$2.50	$2.00
Miles traveled:	500 mi	1500 mi

Question 2

Option:	Local	Imported
Type:	Gala	Fuji
Price:	$2.00	$1.50
Miles traveled:	500 mi	3000 mi

Code: labeled design

design_labeled <- cbc_design(
  profiles = profiles,
  n_resp = 500,
  n_alts = 2, # must equal the # of levels in the label attribute
  n_q = 6,
  label = "sourcing"
)

Use a labeled design when respondents are really comparing named alternatives (brands, powertrains, sourcing…) rather than unlabeled bundles of attributes

2. Include a “none” option?

A “none” option lets respondents say “I wouldn’t buy any of these”

Question 1

Option:	1	2	3	None
Type:	Honeycrisp	Gala	Fuji
Price:	$4.00	$2.00	$1.00
Freshness:	Average	Average	Poor

Question 2

Option:	1	2	3	None
Type:	Pink Lady	Honeycrisp	Gala
Price:	$1.50	$3.50	$3.50
Freshness:	Poor	Poor	Excellent

Code: a “none” option

design_no_choice <- cbc_design(
  profiles = profiles,
  n_resp = 2000,
  n_alts = 3,
  n_q = 6,
  no_choice = TRUE
)

Without this, respondents are forced to pick one of the alternatives shown, even if they wouldn’t choose any of them in real life

Attribute-specific features

Some attributes may only be valid for certain levels of other attributes

Example: “Miles traveled” only makes sense for imported apples (locally grown apples don’t really have a meaningful travel distance).

To implement this, add restrictions to your profiles with cbc_restrict()

Code: restrictions

profiles <- cbc_profiles(
  type = c("Fuji", "Gala", "Honeycrisp"),
  price = seq(1, 4, 0.5),
  sourcing = c("Local", "Imported"),
  milesTraveled = c(50, 500, 1500, 3000)
)

# Local apples only get the lowest ("~0") miles traveled value
profiles_restricted <- profiles %>%
  cbc_restrict(
    sourcing == "Local" & milesTraveled > 50
  )

Warning: Restrictions can lead to imbalances

Design the questions from the restricted profiles…

design_restricted <- cbc_design(
  profiles = profiles_restricted,
  n_resp = 500,
  n_alts = 2,
  n_q = 6
)

#> 
#>    Local Imported 
#>     1171     4829

“Imported” apples show up far more often, since they have more valid attribute combinations left after restricting

Fix imbalances with `balance_by`

design_balanced <- cbc_design(
  profiles = profiles_restricted,
  n_resp = 500,
  n_alts = 2,
  n_q = 6,
  balance_by = "sourcing"
)

#> 
#>    Local Imported 
#>     3011     2989

Now “Local” and “Imported” show up about equally often

Your Turn

With your team, discuss the specific choice question design for your project

Regular or labeled?
Include a “none” option (outside good) or not?
Include restrictions?

Then update code/1_make_choice_questions.R to match

Week 7: Conjoint Questions

1. Defining choice questions in R

2. Displaying choice questions in surveydown

Displaying choice questions in your survey

1. Read in the design file (`choice_questions.csv`)

2. Sample and store a random respondent ID

3. Filter the design for the respondentID

4. Define a function to create question options

5. Create the options for each choice question

6. Create each choice question (6 in total)

1. Read in the design file (`choice_questions.csv`)

design <- readr::read_csv("choice_questions.csv")

2. Sample and store a random respondent ID

Sample a random respondentID

respondentID <- sample(design$respID, 1)

Store the respondentID

sd_store_value(respondentID, "respID")

In your survey data, you will have a respID column

3. Filter the design for the respondentID

df <- design %>%
  filter(respID == respondentID) %>%
  mutate(image = paste0("images/", image))

Images are stored in "images" folder, so we paste on that path

Result looks like this:

head(df)

#> # A tibble: 6 × 9
#>   profileID respID   qID altID obsID type          price freshness image                  
#>       <dbl>  <dbl> <dbl> <dbl> <dbl> <chr>         <dbl> <chr>     <chr>                  
#> 1        45     28     1     1   163 Red Delicious   1.5 Average   images/redDelicious.jpg
#> 2        77     28     1     2   163 Gala            1.5 Poor      images/gala.jpg        
#> 3        94     28     1     3   163 Pink Lady       3   Poor      images/pinkLady.jpg    
#> 4         8     28     2     1   164 Honeycrisp      1.5 Excellent images/honeycrisp.jpg  
#> 5        85     28     2     2   164 Red Delicious   2   Poor      images/redDelicious.jpg
#> 6        80     28     2     3   164 Red Delicious   1.5 Poor      images/redDelicious.jpg

4. Define a function to create question options

make_cbc_options <- function(df) {
  alt1 <- df |> filter(altID == 1)
  alt2 <- df |> filter(altID == 2)
  alt3 <- df |> filter(altID == 3)

  options <- c("option_1", "option_2", "option_3")

  names(options) <- c(
    glue(
      "
      **Option 1**<br>
      <img src='{alt1$image}' width=100><br>
      **Type**: {alt1$type}<br>
      **Price**: $ {alt1$price} / lb
    "
    ),
    glue(
      "
      **Option 2**<br>
      <img src='{alt2$image}' width=100><br>
      **Type**: {alt2$type}<br>
      **Price**: $ {alt2$price} / lb
    "
    ),
    glue(
      "
      **Option 3**<br>
      <img src='{alt3$image}' width=100><br>
      **Type**: {alt3$type}<br>
      **Price**: $ {alt3$price} / lb
    "
    )
  )
  return(options)
}

4. Define a function to create question options

Make one-row data frames for each alternative.

For example, alt1 looks like this:

#> Rows: 1
#> Columns: 9
#> $ profileID <dbl> 45
#> $ respID    <dbl> 28
#> $ qID       <dbl> 1
#> $ altID     <dbl> 1
#> $ obsID     <dbl> 163
#> $ type      <chr> "Red Delicious"
#> $ price     <dbl> 1.5
#> $ freshness <chr> "Average"
#> $ image     <chr> "images/redDelicious.jpg"

make_cbc_options <- function(df) {
  alt1 <- df |> filter(altID == 1)
  alt2 <- df |> filter(altID == 2)
  alt3 <- df |> filter(altID == 3)

  options <- c("option_1", "option_2", "option_3")

  names(options) <- c(
    glue(
      "
      **Option 1**<br>
      <img src='{alt1$image}' width=100><br>
      **Type**: {alt1$type}<br>
      **Price**: $ {alt1$price} / lb
    "
    ),
    glue(
      "
      **Option 2**<br>
      <img src='{alt2$image}' width=100><br>
      **Type**: {alt2$type}<br>
      **Price**: $ {alt2$price} / lb
    "
    ),
    glue(
      "
      **Option 3**<br>
      <img src='{alt3$image}' width=100><br>
      **Type**: {alt3$type}<br>
      **Price**: $ {alt3$price} / lb
    "
    )
  )
  return(options)
}

4. Define a function to create question options

alt1[c('image', 'type', 'price')]

#> # A tibble: 1 × 3
#>   image                   type          price
#>   <chr>                   <chr>         <dbl>
#> 1 images/redDelicious.jpg Red Delicious   1.5

Renders as:

#> **Option 1**<br>
#> <img src='images/redDelicious.jpg' width=100><br>
#> **Type**: Red Delicious<br>
#> **Price**: $ 1.5 / lb

make_cbc_options <- function(df) {
  alt1 <- df |> filter(altID == 1)
  alt2 <- df |> filter(altID == 2)
  alt3 <- df |> filter(altID == 3)

  options <- c("option_1", "option_2", "option_3")

  names(options) <- c(
    glue(
      "
      **Option 1**<br>
      <img src='{alt1$image}' width=100><br>
      **Type**: {alt1$type}<br>
      **Price**: $ {alt1$price} / lb
    "
    ),
    glue(
      "
      **Option 2**<br>
      <img src='{alt2$image}' width=100><br>
      **Type**: {alt2$type}<br>
      **Price**: $ {alt2$price} / lb
    "
    ),
    glue(
      "
      **Option 3**<br>
      <img src='{alt3$image}' width=100><br>
      **Type**: {alt3$type}<br>
      **Price**: $ {alt3$price} / lb
    "
    )
  )
  return(options)
}

5. Create the options for each choice question

cbc1_options <- make_cbc_options(df |> filter(qID == 1))

Value stored in your data:

#> option_1

Label:

#> [1] "  **Option 1**<br>\n  <img src='images/redDelicious.jpg' width=100><br>\n  **Type**: Red Delicious<br>\n  **Price**: $ 1.5 / lb"

Renders as:

**Option 1**

**Type**: Red Delicious
**Price**: $ 1.5 / lb

5. Create the options for each choice question

Now make the options for each question

cbc1_options <- make_cbc_options(df |> filter(qID == 1))
cbc2_options <- make_cbc_options(df |> filter(qID == 2))
cbc3_options <- make_cbc_options(df |> filter(qID == 3))
cbc4_options <- make_cbc_options(df |> filter(qID == 4))
cbc5_options <- make_cbc_options(df |> filter(qID == 5))
cbc6_options <- make_cbc_options(df |> filter(qID == 6))

6. Create each choice question (6 in total)

Code:

sd_question(
  type = 'mc_buttons',
  id = 'cbc_q1',
  label = "(1 of 6) If these were your only options, which would you choose?",
  option = cbc1_options
)

Renders as:

TABLE layout: Show options in a table with `kable()`

library(dplyr)

alts <- df %>%
  filter(qID == 1) %>%
  mutate(
    # Add $ sign to price and html code for image path
    price = paste(scales::dollar(price), "/ lb"),
    image = paste0('<img src="', image, '" width=100>')
  ) %>%
  # Make nicer attribute labels
  select(
    `Option:` = altID,
    ` ` = image,
    `Price:` = price,
    `Type:` = type,
    `Freshness:` = freshness
  )

# Drop row names
row.names(alts) <- NULL

Option: Show options in a table with `kable()`

Display the transpose, t(alts)

kbl(t(alts), escape = FALSE) %>%
  kable_styling(
    bootstrap_options = c("striped", "hover", "condensed"),
    full_width = FALSE,
    position = "center"
  )

Option:	1	2	3

Price:	$1.50 / lb	$1.50 / lb	$3.00 / lb
Type:	Red Delicious	Gala	Pink Lady
Freshness:	Average	Poor	Poor

TABLE layout: Show options in a table with `kable()`

Your choice question can be defined in the survey.qmd
file as it is just choosing one of three options:

Your Turn

With your team, choose a format to work with (buttons or table) for your choice question, then modify the example survey to match your project.

Some Quarto tips

Convert a data frame to a markdown table with kable()

Example from last year

More kable() formatting options:{kableExtra} package

References

References

Week 7: Conjoint Questions

1. Defining choice questions in R

2. Displaying choice questions in surveydown

Week 7: Conjoint Questions

1. Defining choice questions in R

2. Displaying choice questions in surveydown

We’ll be using the {cbcTools} package today

Choice question components

1. Generate profiles for each attribute and level

2. Create a survey design data frame from profiles

Basic Design

This is exactly what’s incode/1_make_choice_questions.R

Your Turn

Open the conjoint_buttons template folder in Positron

Three design choices to consider

Three design choices to consider

1. Regular or labeled?

2. Include a “none” option (outside good) or not?

3. Include restrictions?

1. Regular or labeled?

Code: labeled design

2. Include a “none” option?

Code: a “none” option

Attribute-specific features

Code: restrictions

Warning: Restrictions can lead to imbalances

Fix imbalances with balance_by

Your Turn

Week 7: Conjoint Questions

1. Defining choice questions in R

2. Displaying choice questions in surveydown

Displaying choice questions in your survey

1. Read in the design file (choice_questions.csv)

2. Sample and store a random respondent ID

3. Filter the design for the respondentID

4. Define a function to create question options

5. Create the options for each choice question

6. Create each choice question (6 in total)

1. Read in the design file (choice_questions.csv)

2. Sample and store a random respondent ID

3. Filter the design for the respondentID

5. Create the options for each choice question

5. Create the options for each choice question

6. Create each choice question (6 in total)

TABLE layout: Show options in a table with kable()

Option: Show options in a table with kable()

TABLE layout: Show options in a table with kable()

Your Turn

Versions:

Buttons layout: conjoint_buttons

Table layout: conjoint_tables

Convert a data frame to a markdown table with `kable()`

More `kable()` formatting options:
{kableExtra} package

1. Generate `profiles` for each attribute and level

2. Create a survey `design` data frame from `profiles`

This is exactly what’s in
`code/1_make_choice_questions.R`

Open the `conjoint_buttons` template folder in Positron

Fix imbalances with `balance_by`

1. Read in the design file (`choice_questions.csv`)

1. Read in the design file (`choice_questions.csv`)

TABLE layout: Show options in a table with `kable()`

Option: Show options in a table with `kable()`

TABLE layout: Show options in a table with `kable()`

Buttons layout: `conjoint_buttons`

Table layout: `conjoint_tables`