Variable Encoding

This article demonstrates how to convert between different encoding schemes for categorical variables in choice-based conjoint designs using the cbc_encode() function.

Overview

Choice-based conjoint data can use different encoding schemes for categorical variables:

The cbc_encode() function allows you to convert between these encodings and customize reference levels.

Basic Encoding Conversion

Creating a Design

Let’s start by creating a simple design:

library(cbcTools)

# Create profiles
profiles <- cbc_profiles(
  price = c(1, 1.5, 2, 2.5, 3),
  type = c("Fuji", "Gala", "Honeycrisp"),
  freshness = c("Poor", "Average", "Excellent")
)

# Create design (uses standard encoding by default)
design <- cbc_design(
  profiles = profiles,
  n_alts = 3,
  n_q = 6,
  n_resp = 100,
  method = "random"
)

head(design)
#> Design method: random
#> Encoding: standard
#> Structure: 100 respondents × 6 questions × 3 alternatives
#> Profile usage: 45/45 (100.0%)
#> 
#> 💡 Use cbc_inspect() for a more detailed summary
#> 
#> First few rows of design:
#>   profileID respID qID altID obsID price type freshness
#> 1         5      1   1     1     1   3.0 Fuji      Poor
#> 2         4      1   1     2     1   2.5 Fuji      Poor
#> 3        34      1   1     3     1   2.5 Fuji Excellent
#> 4        38      1   2     1     2   2.0 Gala Excellent
#> 5         5      1   2     2     2   3.0 Fuji      Poor
#> 6        24      1   2     3     2   2.5 Gala   Average

By default, designs are created with standard encoding where categorical variables remain as factors.

Converting to Dummy Coding

Convert to dummy coding for model estimation:

design_dummy <- cbc_encode(design, coding = "dummy")
head(design_dummy)
#> Design method: random
#> Encoding: dummy
#> Structure: 100 respondents × 6 questions × 3 alternatives
#> Profile usage: 45/45 (100.0%)
#> 
#> 💡 Use cbc_inspect() for a more detailed summary
#> 💡 Use cbc_encode(design, 'standard') to view categorical format
#> 
#> First few rows of design:
#>   profileID respID qID altID obsID price typeGala typeHoneycrisp
#> 1         5      1   1     1     1   3.0        0              0
#> 2         4      1   1     2     1   2.5        0              0
#> 3        34      1   1     3     1   2.5        0              0
#> 4        38      1   2     1     2   2.0        1              0
#> 5         5      1   2     2     2   3.0        0              0
#> 6        24      1   2     3     2   2.5        1              0
#>   freshnessAverage freshnessExcellent
#> 1                0                  0
#> 2                0                  0
#> 3                0                  1
#> 4                0                  1
#> 5                0                  0
#> 6                1                  0

Notice that: - The type variable is replaced with typeGala and typeHoneycrisp - The freshness variable is replaced with freshnessAverage and freshnessExcellent - Fuji and Poor are the reference levels (represented when dummy variables = 0) - Continuous variables like price remain unchanged

Converting to Effects Coding

Effects coding uses -1 for the reference level:

design_effects <- cbc_encode(design, coding = "effects")
head(design_effects)
#> Design method: random
#> Encoding: effects
#> Structure: 100 respondents × 6 questions × 3 alternatives
#> Profile usage: 45/45 (100.0%)
#> 
#> 💡 Use cbc_inspect() for a more detailed summary
#> 💡 Use cbc_encode(design, 'standard') to view categorical format
#> 
#> First few rows of design:
#>   profileID respID qID altID obsID price typeGala typeHoneycrisp
#> 1         5      1   1     1     1   3.0       -1             -1
#> 2         4      1   1     2     1   2.5       -1             -1
#> 3        34      1   1     3     1   2.5       -1             -1
#> 4        38      1   2     1     2   2.0        1              0
#> 5         5      1   2     2     2   3.0       -1             -1
#> 6        24      1   2     3     2   2.5        1              0
#>   freshnessAverage freshnessExcellent
#> 1               -1                 -1
#> 2               -1                 -1
#> 3                0                  1
#> 4                0                  1
#> 5               -1                 -1
#> 6                1                  0

In effects coding: - Non-reference levels are coded as 0 or 1 (same as dummy) - Reference level rows have -1 for all level indicators - This ensures coefficients sum to zero

Converting Back to Standard

Convert back to categorical variables:

design_standard <- cbc_encode(design_dummy, coding = "standard")
head(design_standard)
#> Design method: random
#> Encoding: standard
#> Structure: 100 respondents × 6 questions × 3 alternatives
#> Profile usage: 45/45 (100.0%)
#> 
#> 💡 Use cbc_inspect() for a more detailed summary
#> 
#> First few rows of design:
#>   profileID respID qID altID obsID price type freshness
#> 1         5      1   1     1     1   3.0 Fuji      Poor
#> 2         4      1   1     2     1   2.5 Fuji      Poor
#> 3        34      1   1     3     1   2.5 Fuji Excellent
#> 4        38      1   2     1     2   2.0 Gala Excellent
#> 5         5      1   2     2     2   3.0 Fuji      Poor
#> 6        24      1   2     3     2   2.5 Gala   Average

Customizing Reference Levels

By default, the first level of each categorical variable is used as the reference. You can specify different reference levels using the ref_levels argument.

Setting Custom References

# Use "Honeycrisp" as reference for type, "Excellent" for freshness
design_custom <- cbc_encode(
  design,
  coding = "dummy",
  ref_levels = list(
    type = "Honeycrisp",
    freshness = "Excellent"
  )
)

head(design_custom)
#> Design method: random
#> Encoding: dummy
#> Structure: 100 respondents × 6 questions × 3 alternatives
#> Profile usage: 45/45 (100.0%)
#> 
#> 💡 Use cbc_inspect() for a more detailed summary
#> 💡 Use cbc_encode(design, 'standard') to view categorical format
#> 
#> First few rows of design:
#>   profileID respID qID altID obsID price typeFuji typeGala freshnessPoor
#> 1         5      1   1     1     1   3.0        1        0             1
#> 2         4      1   1     2     1   2.5        1        0             1
#> 3        34      1   1     3     1   2.5        1        0             0
#> 4        38      1   2     1     2   2.0        0        1             0
#> 5         5      1   2     2     2   3.0        1        0             1
#> 6        24      1   2     3     2   2.5        0        1             0
#>   freshnessAverage
#> 1                0
#> 2                0
#> 3                0
#> 4                0
#> 5                0
#> 6                1

Now Honeycrisp and Excellent are the reference categories.

Updating References Without Changing Encoding

You can update reference levels while keeping the current encoding:

# Start with dummy coding
design_dummy <- cbc_encode(design, coding = "dummy")

# Update reference levels only (keeps dummy coding)
design_updated <- cbc_encode(
  design_dummy,
  ref_levels = list(type = "Gala")
)

head(design_updated)
#> Design method: random
#> Encoding: dummy
#> Structure: 100 respondents × 6 questions × 3 alternatives
#> Profile usage: 45/45 (100.0%)
#> 
#> 💡 Use cbc_inspect() for a more detailed summary
#> 💡 Use cbc_encode(design, 'standard') to view categorical format
#> 
#> First few rows of design:
#>   profileID respID qID altID obsID price typeFuji typeHoneycrisp
#> 1         5      1   1     1     1   3.0        1              0
#> 2         4      1   1     2     1   2.5        1              0
#> 3        34      1   1     3     1   2.5        1              0
#> 4        38      1   2     1     2   2.0        0              0
#> 5         5      1   2     2     2   3.0        1              0
#> 6        24      1   2     3     2   2.5        0              0
#>   freshnessAverage freshnessExcellent
#> 1                0                  0
#> 2                0                  0
#> 3                0                  1
#> 4                0                  1
#> 5                0                  0
#> 6                1                  0

Working with No-Choice Options

When using designs with no-choice options, you should convert to dummy coding before power analysis or model estimation:

# Create profiles
profiles_nc <- cbc_profiles(
  price = c(1, 2, 3),
  quality = c("Low", "High")
)

# Create priors including no-choice
priors_nc <- cbc_priors(
  profiles = profiles_nc,
  price = -0.1,
  quality = c("High" = 0.5),
  no_choice = -1.5
)

# Create design with no-choice
design_nc <- cbc_design(
  profiles = profiles_nc,
  priors = priors_nc,
  n_alts = 2,
  n_q = 4,
  n_resp = 50,
  no_choice = TRUE,
  method = "random"
)

# Simulate choices
choices_nc <- cbc_choices(design_nc, priors_nc)

head(choices_nc)
#> CBC Choice Data
#> ===============
#> Encoding: dummy
#> Observations: 2 choice tasks
#> Alternatives per task: 3
#> Total choices made: 2
#> 
#> Simulation method: utility_based
#> Priors: Used for utility-based simulation
#> Simulated at: 2025-10-20 15:22:21
#> 
#> Choice rates by alternative:
#>   Alt 1: 0.0% (0 choices)
#>   Alt 2: 50.0% (1 choices)
#>   Alt 3: 50.0% (1 choices)
#> 
#> No-choice rate: 50.0%
#> 
#> 💡 Use cbc_encode(choices, 'standard') to view categorical format
#> 
#> First few rows:
#>   profileID respID qID altID obsID price no_choice qualityHigh choice
#> 1         5      1   1     1     1     2         0           1      0
#> 2         2      1   1     2     1     2         0           0      0
#> 3         0      1   1     3     1     0         1           0      1
#> 4         1      1   2     1     2     1         0           0      0
#> 5         2      1   2     2     2     2         0           0      1
#> 6         0      1   2     3     2     0         1           0      0

For modeling or power analysis with no-choice data, convert to dummy or effects coding:

# Convert to dummy coding for power analysis
choices_dummy <- cbc_encode(choices_nc, coding = "dummy")

# Run power analysis
power_result <- cbc_power(
  data = choices_dummy,
  n_breaks = 5
)

power_result

Use Cases

For Model Estimation

While it is not required for the logitr package, encoding the data into dummy or effects coding can be helpful when estimating models for easier interpretation or simply greater control over which levels are included in the model:

library(logitr)

# Convert to dummy coding
choices_dummy <- cbc_encode(choices, coding = "dummy")

# Estimate model
model <- logitr(
  data = choices_dummy,
  outcome = "choice",
  obsID = "obsID",
  pars = c("price", "typeGala", "typeHoneycrisp",
           "freshnessAverage", "freshnessExcellent")
)

For Data Inspection

It is generally easier to inspect your data when using standard encoding:

# Work with categorical variables
choices_standard <- design

# Filter for chosen alternatives
chosen <- choices_standard[sample(1:nrow(choices_standard), 100), ]

# Examine choice frequencies by category
table(chosen$type)
#> 
#>       Fuji       Gala Honeycrisp 
#>         27         31         42
table(chosen$freshness)
#> 
#>      Poor   Average Excellent 
#>        23        35        42

# Use cbc_inspect
cbc_inspect(choices_standard, sections = 'balance')
#> DESIGN SUMMARY
#> =========================
#> 
#> ATTRIBUTE BALANCE
#> =================
#> Overall balance score: 0.967 (higher is better)
#> 
#> Individual attribute level counts:
#> 
#> price:
#> 
#>   1 1.5   2 2.5   3 
#> 377 340 377 358 348 
#>   Balance score: 0.955 (higher is better)
#> 
#> type:
#> 
#>       Fuji       Gala Honeycrisp 
#>        610        614        576 
#>   Balance score: 0.966 (higher is better)
#> 
#> freshness:
#> 
#>      Poor   Average Excellent 
#>       589       596       615 
#>   Balance score: 0.978 (higher is better)

For Power Analysis

You can use either encoding, but results differ:

# Dummy coding: estimates for each level
power_dummy <- cbc_power(
  cbc_encode(choices, coding = "dummy"),
  n_breaks = 5
)

# Standard coding: estimates categorical effect
power_standard <- cbc_power(
  cbc_encode(choices, coding = "standard"),
  pars = c("price", "type", "freshness"),
  n_breaks = 5
)