Designing Conjoint Surveys with {cbcTools}

---

## .center[Designing Conjoint Surveys with {cbcTools}]

]

### <svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M272 304h-96C78.8 304 0 382.8 0 480c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32C448 382.8 369.2 304 272 304zM48.99 464C56.89 400.9 110.8 352 176 352h96c65.16 0 119.1 48.95 127 112H48.99zM224 256c70.69 0 128-57.31 128-128c0-70.69-57.31-128-128-128S96 57.31 96 128C96 198.7 153.3 256 224 256zM224 48c44.11 0 80 35.89 80 80c0 44.11-35.89 80-80 80S144 172.1 144 128C144 83.89 179.9 48 224 48z"/></svg> John Paul Helveston
### <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M243.4 2.6l-224 96c-14 6-21.8 21-18.7 35.8S16.8 160 32 160v8c0 13.3 10.7 24 24 24H456c13.3 0 24-10.7 24-24v-8c15.2 0 28.3-10.7 31.3-25.6s-4.8-29.9-18.7-35.8l-224-96c-8.1-3.4-17.2-3.4-25.2 0zM128 224H64V420.3c-.6 .3-1.2 .7-1.8 1.1l-48 32c-11.7 7.8-17 22.4-12.9 35.9S17.9 512 32 512H480c14.1 0 26.5-9.2 30.6-22.7s-1.1-28.1-12.9-35.9l-48-32c-.6-.4-1.2-.7-1.8-1.1V224H384V416H344V224H280V416H232V224H168V416H128V224zm128-96c-17.7 0-32-14.3-32-32s14.3-32 32-32s32 14.3 32 32s-14.3 32-32 32z"/></svg> The George Washington University | Dept. of Engineering Management and Systems Engineering
### <svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M152 64H296V24C296 10.75 306.7 0 320 0C333.3 0 344 10.75 344 24V64H384C419.3 64 448 92.65 448 128V448C448 483.3 419.3 512 384 512H64C28.65 512 0 483.3 0 448V128C0 92.65 28.65 64 64 64H104V24C104 10.75 114.7 0 128 0C141.3 0 152 10.75 152 24V64zM48 248H128V192H48V248zM48 296V360H128V296H48zM176 296V360H272V296H176zM320 296V360H400V296H320zM400 192H320V248H400V192zM400 408H320V464H384C392.8 464 400 456.8 400 448V408zM272 408H176V464H272V408zM128 408H48V448C48 456.8 55.16 464 64 464H128V408zM272 192H176V248H272V192z"/></svg> June 15, 2023

]

---

### Designing a Choice-Based Conjoint Survey is Hard

---

### Designing a Choice-Based Conjoint Survey is Hard

---

### Designing a Choice-Based Conjoint Survey is Hard

---

# Many R packages for design of experiment

- [{cbcTools}](https://github.com/jhelvy/cbcTools)
- [{ExpertChoice}](https://github.com/JedStephens/ExpertChoice)
- [{support.CEs}](https://www.jstatsoft.org/article/view/v050c02)
- [{idefix}](https://www.jstatsoft.org/article/view/v096i03)
- [{choiceDes}](https://cran.r-project.org/web/packages/choiceDes/index.html)

---

# Many R packages for design of experiment

- [{cbcTools}](https://github.com/jhelvy/cbcTools) .red[<-- Does a lot more than just DOE!]
- [{ExpertChoice}](https://github.com/JedStephens/ExpertChoice)
- [{support.CEs}](https://www.jstatsoft.org/article/view/v050c02)
- [{idefix}](https://www.jstatsoft.org/article/view/v096i03)
- [{choiceDes}](https://cran.r-project.org/web/packages/choiceDes/index.html)

---

## .center[A systematic workflow for designing a CBC experiment]

---

## .center[A systematic workflow for designing a CBC experiment]

---

## .center[A systematic workflow for designing a CBC experiment]

---

]

---

---

## Example CBC question about apples

---

background-color: #fff

## .center[Define the attributes and levels]

<br>

]

<br>

- **Price ($/lb)**: 1.00, 1.50, 2.00, 2.50, 3.00, 3.50, 4.00

- **Type**: Fuji, Gala, Honeycrisp

- **Freshness**: Excellent, Average, Poor

]

---

---

# .center[Generate all possible profiles]

<br>

```r
profiles <- cbc_profiles(
  price     = seq(1, 4, 0.5), # $ per pound
  type      = c('Fuji', 'Gala', 'Honeycrisp'),
  freshness = c('Poor', 'Average', 'Excellent')
)
```

```r
head(profiles)
```

```
#>   profileID price type freshness
#> 1         1   1.0 Fuji      Poor
#> 2         2   1.5 Fuji      Poor
#> 3         3   2.0 Fuji      Poor
#> 4         4   2.5 Fuji      Poor
#> 5         5   3.0 Fuji      Poor
#> 6         6   3.5 Fuji      Poor
```

]

```r
tail(profiles)
```

```
#>    profileID price       type freshness
#> 58        58   1.5 Honeycrisp Excellent
#> 59        59   2.0 Honeycrisp Excellent
#> 60        60   2.5 Honeycrisp Excellent
#> 61        61   3.0 Honeycrisp Excellent
#> 62        62   3.5 Honeycrisp Excellent
#> 63        63   4.0 Honeycrisp Excellent
```

]

---

## .center[Generate a restricted set of profiles?]

> CAUTION: including restrictions in your designs can substantially reduce the statistical power of your design, so use them cautiously (and avoid them if possible).

```r
restricted_profiles <- cbc_restrict(
    profiles,
    type == "Gala" & price %in% c(1.5, 2.5, 3.5),
    type == "Honeycrisp" & price < 2,
    type == "Fuji" & freshness == "Poor"
)

dim(restricted_profiles)
```

```
#> [1] 41  4
```

---

---

# .center[Generate a survey design]

```r
design <- cbc_design( 
  profiles = profiles,
  n_resp   = 300, # Number of respondents
  n_alts   = 3,   # Number of alternatives per question
  n_q      = 6    # Number of questions per respondent
)
```

```r
head(design)
```

```
#>   profileID respID qID altID obsID price       type freshness
#> 1        53      1   1     1     1   2.5       Gala Excellent
#> 2        45      1   1     2     1   2.0       Fuji Excellent
#> 3        33      1   1     3     1   3.0       Gala   Average
#> 4        19      1   2     1     2   3.0 Honeycrisp      Poor
#> 5        14      1   2     2     2   4.0       Gala      Poor
#> 6        28      1   2     3     2   4.0       Fuji   Average
```

---

# .center[Include a "no choice" option]

```r
head(design)
```

```
#>   profileID respID qID altID obsID price type_Fuji type_Gala type_Honeycrisp freshness_Poor freshness_Average freshness_Excellent no_choice
#> 1         6      1   1     1     1   3.5         1         0               0              1                 0                   0         0
#> 2         1      1   1     2     1   1.0         1         0               0              1                 0                   0         0
#> 3        27      1   1     3     1   3.5         1         0               0              0                 1                   0         0
#> 4         0      1   1     4     1   0.0         0         0               0              0                 0                   0         1
#> 5        48      1   2     1     2   3.5         1         0               0              0                 0                   1         0
#> 6         1      1   2     2     2   1.0         1         0               0              1                 0                   0         0
```

---

## .center[Make a labeled design]

```r
head(design)
```

```
#>   profileID respID qID altID obsID price       type freshness
#> 1        22      1   1     1     1   1.0       Fuji   Average
#> 2        55      1   1     2     1   3.5       Gala Excellent
#> 3        63      1   1     3     1   4.0 Honeycrisp Excellent
#> 4        28      1   2     1     2   4.0       Fuji   Average
#> 5        54      1   2     2     2   3.0       Gala Excellent
#> 6        57      1   2     3     2   1.0 Honeycrisp Excellent
```

---

# .center[Make a Bayesian D-efficient design]

### .center[(Uses the [`idefix`](https://www.jstatsoft.org/article/view/v096i03) package to generate a design)]

```r
design <- cbc_design(
  profiles = profiles,
  n_resp   = 300, # Number of respondents
  n_alts   = 3,   # Number of alternatives per question
  n_q      = 6,   # Number of questions per respondent
* priors = list(
*   price     = -0.1, # Numeric, modeled as continuous
*   type      = c(0.1, 0.2), # Reference level: "Fuji"
*   freshness = c(0.1, 0.2) # Reference level: "Poor"
* )
)
```

Priors are defining the following model:

$$
u_j = -0.1p_j + 0.1t^{Gala}_j + 0.2t^{Honeycrisp}_j + 0.1f^{Ave}_j + 0.2f^{Excellent}_j + \varepsilon_j
$$

---

# .center[Import a design: .blue[Sawtooth] <svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:blue;overflow:visible;position:relative;"><path d="M438.6 278.6c12.5-12.5 12.5-32.8 0-45.3l-160-160c-12.5-12.5-32.8-12.5-45.3 0s-12.5 32.8 0 45.3L338.8 224 32 224c-17.7 0-32 14.3-32 32s14.3 32 32 32l306.7 0L233.4 393.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l160-160z"/></svg> <svg aria-hidden="true" role="img" viewBox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:blue;overflow:visible;position:relative;"><path d="M64 0C28.7 0 0 28.7 0 64V448c0 35.3 28.7 64 64 64H320c35.3 0 64-28.7 64-64V160H256c-17.7 0-32-14.3-32-32V0H64zM256 0V128H384L256 0zM80 224H96c22.1 0 40 17.9 40 40v8c0 8.8-7.2 16-16 16s-16-7.2-16-16v-8c0-4.4-3.6-8-8-8H80c-4.4 0-8 3.6-8 8v80c0 4.4 3.6 8 8 8H96c4.4 0 8-3.6 8-8v-8c0-8.8 7.2-16 16-16s16 7.2 16 16v8c0 22.1-17.9 40-40 40H80c-22.1 0-40-17.9-40-40V264c0-22.1 17.9-40 40-40zm72 46.4c0-25.6 20.8-46.4 46.4-46.4H216c8.8 0 16 7.2 16 16s-7.2 16-16 16H198.4c-7.9 0-14.4 6.4-14.4 14.4c0 5.2 2.8 9.9 7.2 12.5l25.4 14.5c14.4 8.3 23.4 23.6 23.4 40.3c0 25.6-20.8 46.4-46.4 46.4H168c-8.8 0-16-7.2-16-16s7.2-16 16-16h25.6c7.9 0 14.4-6.4 14.4-14.4c0-5.2-2.8-9.9-7.2-12.5l-25.4-14.5C160.9 302.4 152 287 152 270.4zM280 240v31.6c0 23 5.5 45.6 16 66c10.5-20.3 16-42.9 16-66V240c0-8.8 7.2-16 16-16s16 7.2 16 16v31.6c0 34.7-10.3 68.7-29.6 97.6l-5.1 7.7c-3 4.5-8 7.1-13.3 7.1s-10.3-2.7-13.3-7.1l-5.1-7.7c-19.3-28.9-29.6-62.9-29.6-97.6V240c0-8.8 7.2-16 16-16s16 7.2 16 16z"/></svg> <svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:blue;overflow:visible;position:relative;"><path d="M438.6 278.6c12.5-12.5 12.5-32.8 0-45.3l-160-160c-12.5-12.5-32.8-12.5-45.3 0s-12.5 32.8 0 45.3L338.8 224 32 224c-17.7 0-32 14.3-32 32s14.3 32 32 32l306.7 0L233.4 393.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l160-160z"/></svg> <svg aria-hidden="true" role="img" viewBox="0 0 581 512" style="height:1em;width:1.13em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:blue;overflow:visible;position:relative;"><path d="M581 226.6C581 119.1 450.9 32 290.5 32S0 119.1 0 226.6C0 322.4 103.3 402 239.4 418.1V480h99.1v-61.5c24.3-2.7 47.6-7.4 69.4-13.9L448 480h112l-67.4-113.7c54.5-35.4 88.4-84.9 88.4-139.7zm-466.8 14.5c0-73.5 98.9-133 220.8-133s211.9 40.7 211.9 133c0 50.1-26.5 85-70.3 106.4-2.4-1.6-4.7-2.9-6.4-3.7-10.2-5.2-27.8-10.5-27.8-10.5s86.6-6.4 86.6-92.7-90.6-87.9-90.6-87.9h-199V361c-74.1-21.5-125.2-67.1-125.2-119.9zm225.1 38.3v-55.6c57.8 0 87.8-6.8 87.8 27.3 0 36.5-38.2 28.3-87.8 28.3zm-.9 72.5H365c10.8 0 18.9 11.7 24 19.2-16.1 1.9-33 2.8-50.6 2.9v-22.1z"/></svg>]

```r
library(readr)

design <- read_csv('design.csv')

head(design)
```

```
#>   respID qID altID obsID price       type freshness
#> 1      1   1     1     1   1.0       Fuji   Average
#> 2      1   1     2     1   3.5       Gala Excellent
#> 3      1   1     3     1   4.0 Honeycrisp Excellent
#> 4      1   2     1     2   4.0       Fuji   Average
#> 5      1   2     2     2   3.0       Gala Excellent
#> 6      1   2     3     2   1.0 Honeycrisp Excellent
```

---

---

# .center[Check design **balance**]

```r
cbc_balance(design)
```

```
Individual attribute level counts

price:

1 1.5   2 2.5   3 3.5   4 
784 755 759 741 776 827 758

type:

Fuji       Gala Honeycrisp 
      1800       1800       1800

freshness:

Poor   Average Excellent 
     1845      1767      1788 
```

]

```
Pairwise attribute level counts

price x type:

Fuji Gala Honeycrisp
     NA 1800 1800       1800
1   784  260  256        268
1.5 755  248  254        253
2   759  259  240        260
2.5 741  239  254        248
3   776  263  286        227
3.5 827  264  258        305
4   758  267  252        239
```

]

---

# .center[Check design **overlap**]

```r
cbc_overlap(design)
```

```
Counts of attribute overlap:
(# of questions with N unique levels)

price:

1    2    3 
    31  630 1139

type:

1    2    3 
   156 1248  396

freshness:

1    2    3 
   175 1189  436 
```

]

---

---

# .center[Simulate random choices]

```r
data <- cbc_choices(
  design = design,
  obsID  = "obsID"
)
```

```r
head(data)
```

```
#>   profileID respID qID altID obsID price       type freshness choice
#> 1        22      1   1     1     1   1.0       Fuji   Average      0
#> 2        55      1   1     2     1   3.5       Gala Excellent      0
#> 3        63      1   1     3     1   4.0 Honeycrisp Excellent      1
#> 4        28      1   2     1     2   4.0       Fuji   Average      1
#> 5        54      1   2     2     2   3.0       Gala Excellent      0
#> 6        57      1   2     3     2   1.0 Honeycrisp Excellent      0
```

---

## .center[Simulate choices according to a prior]

```r
data <- cbc_choices(
  design = design,
  obsID = "obsID",
* priors = list(
*   price     = -0.1,
*   type      = c(0.1, 0.2),
*   freshness = c(0.1, -0.2)
* )
)
```

]

Attribute | Level | Utility 
----------|-----------
**Price** | Continuous | -0.1
**Type**  | Fuji | 0
          | Gala | 0.1
          | Honeycrisp  | 0.2
**Freshness**  | Average | 0
               | Excellent | 0.1
               | Poor  | -0.2

]

---

## .center[Simulate choices according to a prior]

```r
data <- cbc_choices(
  design = design,
  obsID = "obsID",
  priors = list(  
    price = -0.1, 
*   type = randN(
*     mu    = c(0.1, 0.2),
*     sigma = c(0.5, 1)
*   ),
    freshness = c(0.1, -0.2) 
  ) 
)
```

]

Attribute | Level | Utility 
----------|-----------
**Price** | Continuous | -0.1
**Type**  | Fuji | 0
          | Gala | N(0.1, 0.5)
          | Honeycrisp  | N(0.2, 1)
**Freshness**  | Average | 0
               | Excellent | 0.1
               | Poor  | -0.2

]

---

## .center[Simulate choices according to a prior]

```r
data <- cbc_choices(
  design = design,
  obsID = "obsID",
  priors = list( 
    price     = -0.1, 
    type      = c(0.1, 0.2), 
    freshness = c(0.1, -0.2),
*   "price*type" = c(0.1, 0.5)
  ) 
)
```

]

]

---

---

# .center[Conduct a power analysis]

```r
power <- cbc_power(
    nbreaks = 10,
    n_q     = 6,
    data    = data,
    obsID   = "obsID",
    outcome = "choice",
    pars    = c("price", "type", "freshness")
)
```

```r
head(power)
```

```
#>   sampleSize               coef         est         se
#> 1         30              price -0.18969925 0.09519838
#> 2         30           typeGala -0.03074145 0.19389450
#> 3         30     typeHoneycrisp  0.19956629 0.18165533
#> 4         30   freshnessAverage  0.46713033 0.23479744
#> 5         30 freshnessExcellent  0.47712173 0.22886577
#> 6         60              price -0.13185249 0.06576991
```

]

```r
tail(power)
```

```
#>    sampleSize               coef         est         se
#> 45        270 freshnessExcellent -0.14791440 0.07498391
#> 46        300              price -0.11983143 0.02896963
#> 47        300           typeGala  0.08577075 0.05984688
#> 48        300     typeHoneycrisp  0.22142284 0.05810356
#> 49        300   freshnessAverage  0.17092085 0.07083180
#> 50        300 freshnessExcellent -0.11784026 0.07093520
```

]

---

# .center[Conduct a power analysis]

```r
plot(power)
```

---

# .center[Conduct a power analysis]

```r
power_int <- cbc_power(
    nbreaks = 10,
    n_q     = 6,
    data    = data,
    pars    = c(
      "price", 
      "type", 
      "freshness", 
*     "price*type"
    ), 
    outcome = "choice",
    obsID   = "obsID"
)
```

]

```r
plot(power_int)
```

]

---

---

---

background-color: #fff
background-image: url("images/cbcTools-sawtooth.png")
background-position: center
background-size: contain

---

# Your turn

- Be sure to have downloaded and unzipped the [practice code](https://jhelvy.github.io/2023-qux-conf-conjoint/practice/2023-qux-conf-conjoint.zip).
- Open the `2023-qux-conf-conjoint.Rproj` file to open RStudio.
- In RStudio, open the `designing-surveys.R` file.
- Experiment with different design options, then examine the power:
    - What if you modify the quesitons per respondent?
    - What if you use a labeled design? 
    - What if you include a "no choice" option?
    - What if you use a Bayesian D-efficient design?
    
---

<br>

## .center[Back to workshop website:<br><br> https://jhelvy.github.io/2023-qux-conf-conjoint/]

@JohnHelveston <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg><br>
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