Power Analysis

Step 1: Generate Profiles

profiles <- cbc_profiles(
  veh_mileage        = seq(15000, 50000, 5000), #5000
  veh_price          = 15000*seq(0.8, 1.2, 0.1),
  battery_refurbish     = c('original', 'cellreplace','packreplace'),
  battery_range_year0 = seq(200, 360, 40),
  battery_degradation = seq(0.01,0.07, 0.02)
)

profiles

CBC Profiles
============
veh_mileage : Continuous (8 levels, range: 15000.00-50000.00)
veh_price   : Continuous (5 levels, range: 12000.00-18000.00)
battery_refurbish: Categorical (3 levels: original, cellreplace, packreplace)
battery_range_year0: Continuous (5 levels, range: 200.00-360.00)
battery_degradation: Continuous (4 levels, range: 0.01-0.07)

Profiles: 2400
First few rows:
  profileID veh_mileage veh_price battery_refurbish battery_range_year0
1         1       15000     12000          original                 200
2         2       20000     12000          original                 200
3         3       25000     12000          original                 200
4         4       30000     12000          original                 200
5         5       35000     12000          original                 200
6         6       40000     12000          original                 200
  battery_degradation
1                0.01
2                0.01
3                0.01
4                0.01
5                0.01
6                0.01
... and 2394 more rows

Resrictions

None

Step 2: Set up priors

Attribute	Expectation	Theory	Suggested Sign
veh_price	Lower price preferred	Standard economic theory (price disutility)	Negative (−)
veh_mileage	Lower mileage preferred	Higher mileage = older/worn vehicle	Negative (−)
battery_refurbish	Original battery > pack-based refurbishment > cell-based refurbishment	Risk aversion, resale concerns, BEV reliability	Negative (−)
battery_range_year0	More range preferred	Reduces range anxiety	Positive (+)
battery_degradation	Less degradation preferred	Reflects battery health and future value	Negative (−)

Fixed Parameters

For example, if the coefficient of battery degradation is -10, then:

- A 1% increase in degradation (from 0.01 to 0.02) reduces utility by 0.10.
- A full 7% increase in degradation (from 0.01 to 0.08) would reduce utility by -0.7.

In DCE models, utilities usually range between -2 and +2, so a utility loss of -0.7 is noticeable, but not extreme. It reflects that battery degradation is an important factor in evaluating a used EV.

priors_fixed <- cbc_priors(
  profiles = profiles,
  veh_mileage          = -0.00005,     # Each 1000 mile increase reduces utility by 0.05
  veh_price            = -0.0001,      # Each $1000 increase reduces utility by 0.1
  battery_refurbish = c(-1.0, -0.5),   # Cell refurbishment least preferred
  battery_range_year0  = 0.005,         # Each 100 mile of range adds utility by 0.5
  battery_degradation  = -10          # Each 1% of degradation increases subtracts utility by 0.05

)

priors_fixed

CBC Prior Specifications:

veh_mileage:
  Continuous variable
  Levels: 15000, 20000, 25000, 30000, 35000, 40000, 45000, 50000 
  Fixed parameter
    Coefficient: 0

veh_price:
  Continuous variable
  Levels: 12000, 13500, 15000, 16500, 18000 
  Fixed parameter
    Coefficient: 0

battery_refurbish:
  Categorical variable
  Levels: original, cellreplace, packreplace 
  Reference level: original
  Fixed parameter
    cellreplace: -1
    packreplace: -0.5

battery_range_year0:
  Continuous variable
  Levels: 200, 240, 280, 320, 360 
  Fixed parameter
    Coefficient: 0.005

battery_degradation:
  Continuous variable
  Levels: 0.01, 0.03, 0.05, 0.07 
  Fixed parameter
    Coefficient: -10

Random Parameters

priors_random_parameter <- cbc_priors(
  profiles = profiles,
  veh_mileage          = -0.00005,     # Each 1000 mile increase reduces utility by 0.05
  veh_price = -0.0001, # Assume $1,000 price increase = -0.1 utility
  battery_refurbish = rand_spec("n", c(-1.0, -0.5), c(0.1, 0.1)), # Reference = "original"
  battery_range_year0 = 0.005,   # Each 100 mile of range adds utility by 0.5
  battery_degradation = -10 # 1% increase in degradation = -0.10 utility
)

priors_random_parameter

CBC Prior Specifications:

veh_mileage:
  Continuous variable
  Levels: 15000, 20000, 25000, 30000, 35000, 40000, 45000, 50000 
  Fixed parameter
    Coefficient: 0

veh_price:
  Continuous variable
  Levels: 12000, 13500, 15000, 16500, 18000 
  Fixed parameter
    Coefficient: 0

battery_refurbish:
  Categorical variable
  Levels: original, cellreplace, packreplace 
  Reference level: original
  Random - Normal distribution
    cellreplace:
      Mean: -1
      SD:   0.1
    packreplace:
      Mean: -0.5
      SD:   0.1

battery_range_year0:
  Continuous variable
  Levels: 200, 240, 280, 320, 360 
  Fixed parameter
    Coefficient: 0.005

battery_degradation:
  Continuous variable
  Levels: 0.01, 0.03, 0.05, 0.07 
  Fixed parameter
    Coefficient: -10

Correlation Matrix:
                             battery_refurbishcellreplace
battery_refurbishcellreplace                            1
battery_refurbishpackreplace                            0
                             battery_refurbishpackreplace
battery_refurbishcellreplace                            0
battery_refurbishpackreplace                            1

Step 3: Generate Designs

Different designs

Random Method

random: randomly samples profiles for each respondent independently; maximum diversity but may be less statistically efficient

design_random_fixed_parameter <- cbc_design(
  profiles = profiles,
  priors = priors_fixed,
  method = "random", # randomized full-factorial design
  n_resp   = 3000, # Number of respondents
  n_alts   = 3,    # Number of alternatives per question
  n_q      = 6,    # Number of questions per respondent #6
  remove_dominant = TRUE
) 

design_random_random_parameter <- cbc_design(
  profiles = profiles,
  priors = priors_random_parameter,
  method = "random", # randomized full-factorial design
  n_resp   = 3000, # Number of respondents
  n_alts   = 3,    # Number of alternatives per question
  n_q      = 6,    # Number of questions per respondent #6
  remove_dominant = TRUE
)

Frequency-Based Methods

shortcut: balances attribute level frequencies while avoiding duplicate profiles within questions.
minoverlap: prioritizes minimizing attribute overlap within choice questions.
balanced: optimizes both frequency balance and pairwise attribute interactions.

design_shortcut <- cbc_design(
  profiles = profiles,
  method = "shortcut",
  n_resp   = 3000, # Number of respondents
  n_alts   = 3,    # Number of alternatives per question
  n_q      = 6    # Number of questions per respondent #6
  
)

Generating shortcut design for 3000 respondents using 13 cores...

Design comparisons

cbc_compare(
  "Random_fixed_parameter" = design_random_fixed_parameter,
  "Random_random_parameter" = design_random_random_parameter,
  "Shortcut" = design_shortcut
)

CBC Design Comparison
=====================
Designs compared: 3
Metrics: structure, efficiency, balance, overlap
Sorted by: d_error (ascending)

Structure
=====================
                  Design   Method respondents questions
  Random_fixed_parameter   random        3000         6
 Random_random_parameter   random        3000         6
                Shortcut shortcut        3000         6
 Alternatives Blocks    Profile Usage
            3      1 (2399/2400) 100%
            3      1 (2399/2400) 100%
            3      1 (2400/2400) 100%
 No Choice Labeled?
        No       No
        No       No
        No       No

Design Metrics
=====================
                  Design   Method D-Error (Null) D-Error (Prior) Balance
  Random_fixed_parameter   random             NA              NA   0.886
 Random_random_parameter   random             NA              NA   0.887
                Shortcut shortcut             NA              NA   0.892
 Overlap
   0.135
   0.135
   0.000

Interpretation:
- D-Error: Lower is better (design efficiency)
- Balance: Higher is better (level distribution)
- Overlap: Lower is better (attribute variation)
- Profile Usage: Higher means more profiles used

Best performers:
- Balance: Shortcut (0.892)
- Overlap: Shortcut (0.000)
- Profile Usage: Random_fixed_parameter (100.0%)

Use summary() for detailed information on any one design.

Step 4: Inspect Design

Goal: Evaluate the quality and properties of the design. - D-error: Lower values indicate more efficient designs - Balance: Higher scores indicate better attribute level balance - Overlap: Lower scores indicate less attribute overlap within questions - Profile usage: Higher percentages indicate better use of available profiles

cbc_inspect(design_random_fixed_parameter)

DESIGN SUMMARY
=========================

STRUCTURE
================
Method: random
Created: 2025-07-15 11:28:38
Respondents: 3000
Questions per respondent: 6
Alternatives per question: 3
Total choice sets: 18000
Profile usage: 2399/2400 (100.0%)
Special features:
  • Dominance removal: total, partial

SUMMARY METRICS
=================
D-error calculation not available for random designs
Overall balance score: 0.886 (higher is better)
Overall overlap score: 0.135 (lower is better)

VARIABLE ENCODING
=================
Format: Dummy-coded (battery_refurbish)
💡 Use cbc_decode_design() to convert to categorical format

ATTRIBUTE BALANCE
=================
Overall balance score: 0.886 (higher is better)

Individual attribute level counts:

veh_mileage:

15000 20000 25000 30000 35000 40000 45000 50000 
 6471  6812  6827  6887  6998  6758  6694  6553 
  Balance score: 0.975 (higher is better)

veh_price:

12000 13500 15000 16500 18000 
10871 10607 10838 10796 10888 
  Balance score: 0.990 (higher is better)

battery_refurbishcellreplace:

    0     1 
35777 18223 
  Balance score: 0.685 (higher is better)

battery_refurbishpackreplace:

    0     1 
35925 18075 
  Balance score: 0.681 (higher is better)

battery_range_year0:

  200   240   280   320   360 
10810 10811 10987 10716 10676 
  Balance score: 0.989 (higher is better)

battery_degradation:

 0.01  0.03  0.05  0.07 
13420 13524 13485 13571 
  Balance score: 0.995 (higher is better)

ATTRIBUTE OVERLAP
=================
Overall overlap score: 0.135 (lower is better)

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

veh_mileage: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   1.5%  (268 / 18000 questions)
  2 (partial overlap):   32.9%  (5919 / 18000 questions)
  3 (partial overlap):   65.6%  (11813 / 18000 questions)
  4 (partial overlap):    0.0%  (0 / 18000 questions)
  5 (partial overlap):    0.0%  (0 / 18000 questions)
  6 (partial overlap):    0.0%  (0 / 18000 questions)
  7 (partial overlap):    0.0%  (0 / 18000 questions)
  8 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 2.64

veh_price: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   3.9%  (703 / 18000 questions)
  2 (partial overlap):   47.3%  (8520 / 18000 questions)
  3 (partial overlap):   48.8%  (8777 / 18000 questions)
  4 (partial overlap):    0.0%  (0 / 18000 questions)
  5 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 2.45

battery_refurbishcellreplace: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):  33.1%  (5957 / 18000 questions)
  2 (no overlap):        66.9%  (12043 / 18000 questions)
  Average unique levels per question: 1.67

battery_refurbishpackreplace: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):  33.1%  (5961 / 18000 questions)
  2 (no overlap):        66.9%  (12039 / 18000 questions)
  Average unique levels per question: 1.67

battery_range_year0: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   3.6%  (643 / 18000 questions)
  2 (partial overlap):   47.7%  (8592 / 18000 questions)
  3 (partial overlap):   48.7%  (8765 / 18000 questions)
  4 (partial overlap):    0.0%  (0 / 18000 questions)
  5 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 2.45

battery_degradation: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   5.9%  (1071 / 18000 questions)
  2 (partial overlap):   56.2%  (10118 / 18000 questions)
  3 (partial overlap):   37.8%  (6811 / 18000 questions)
  4 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 2.32

cbc_inspect(design_random_random_parameter)

DESIGN SUMMARY
=========================

STRUCTURE
================
Method: random
Created: 2025-07-15 11:28:48
Respondents: 3000
Questions per respondent: 6
Alternatives per question: 3
Total choice sets: 18000
Profile usage: 2399/2400 (100.0%)
Special features:
  • Dominance removal: total, partial

SUMMARY METRICS
=================
D-error calculation not available for random designs
Overall balance score: 0.887 (higher is better)
Overall overlap score: 0.135 (lower is better)

VARIABLE ENCODING
=================
Format: Dummy-coded (battery_refurbish)
💡 Use cbc_decode_design() to convert to categorical format

ATTRIBUTE BALANCE
=================
Overall balance score: 0.887 (higher is better)

Individual attribute level counts:

veh_mileage:

15000 20000 25000 30000 35000 40000 45000 50000 
 6735  6879  6781  6949  6755  6776  6610  6515 
  Balance score: 0.980 (higher is better)

veh_price:

12000 13500 15000 16500 18000 
10684 10843 10735 10877 10861 
  Balance score: 0.992 (higher is better)

battery_refurbishcellreplace:

    0     1 
36277 17723 
  Balance score: 0.673 (higher is better)

battery_refurbishpackreplace:

    0     1 
35618 18382 
  Balance score: 0.689 (higher is better)

battery_range_year0:

  200   240   280   320   360 
10909 10738 10821 10854 10678 
  Balance score: 0.992 (higher is better)

battery_degradation:

 0.01  0.03  0.05  0.07 
13515 13469 13495 13521 
  Balance score: 0.998 (higher is better)

ATTRIBUTE OVERLAP
=================
Overall overlap score: 0.135 (lower is better)

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

veh_mileage: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   1.5%  (266 / 18000 questions)
  2 (partial overlap):   33.0%  (5931 / 18000 questions)
  3 (partial overlap):   65.6%  (11803 / 18000 questions)
  4 (partial overlap):    0.0%  (0 / 18000 questions)
  5 (partial overlap):    0.0%  (0 / 18000 questions)
  6 (partial overlap):    0.0%  (0 / 18000 questions)
  7 (partial overlap):    0.0%  (0 / 18000 questions)
  8 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 2.64

veh_price: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   3.8%  (677 / 18000 questions)
  2 (partial overlap):   46.9%  (8451 / 18000 questions)
  3 (partial overlap):   49.3%  (8872 / 18000 questions)
  4 (partial overlap):    0.0%  (0 / 18000 questions)
  5 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 2.46

battery_refurbishcellreplace: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):  33.8%  (6088 / 18000 questions)
  2 (no overlap):        66.2%  (11912 / 18000 questions)
  Average unique levels per question: 1.66

battery_refurbishpackreplace: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):  32.0%  (5756 / 18000 questions)
  2 (no overlap):        68.0%  (12244 / 18000 questions)
  Average unique levels per question: 1.68

battery_range_year0: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   3.9%  (704 / 18000 questions)
  2 (partial overlap):   47.5%  (8549 / 18000 questions)
  3 (partial overlap):   48.6%  (8747 / 18000 questions)
  4 (partial overlap):    0.0%  (0 / 18000 questions)
  5 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 2.45

battery_degradation: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   6.0%  (1081 / 18000 questions)
  2 (partial overlap):   56.2%  (10122 / 18000 questions)
  3 (partial overlap):   37.8%  (6797 / 18000 questions)
  4 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 2.32

cbc_inspect(design_shortcut)

DESIGN SUMMARY
=========================

STRUCTURE
================
Method: shortcut
Created: 2025-07-15 11:40:32
Respondents: 3000
Questions per respondent: 6
Alternatives per question: 3
Total choice sets: 18000
Profile usage: 2400/2400 (100.0%)

SUMMARY METRICS
=================
(Lower values indicate more efficient designs)

Overall balance score: 0.892 (higher is better)
Overall overlap score: 0.000 (lower is better)

VARIABLE ENCODING
=================
Format: Dummy-coded (battery_refurbish)
💡 Use cbc_decode_design() to convert to categorical format

ATTRIBUTE BALANCE
=================
Overall balance score: 0.892 (higher is better)

Individual attribute level counts:

veh_mileage:

15000 20000 25000 30000 35000 40000 45000 50000 
 6740  6721  6757  6699  6728  6779  6771  6805 
  Balance score: 0.995 (higher is better)

veh_price:

12000 13500 15000 16500 18000 
10826 10784 10821 10797 10772 
  Balance score: 0.998 (higher is better)

battery_refurbishcellreplace:

    0     1 
36000 18000 
  Balance score: 0.680 (higher is better)

battery_refurbishpackreplace:

    0     1 
36000 18000 
  Balance score: 0.680 (higher is better)

battery_range_year0:

  200   240   280   320   360 
10811 10776 10791 10806 10816 
  Balance score: 0.998 (higher is better)

battery_degradation:

 0.01  0.03  0.05  0.07 
13490 13488 13500 13522 
  Balance score: 0.999 (higher is better)

ATTRIBUTE OVERLAP
=================
Overall overlap score: 0.000 (lower is better)

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

veh_mileage: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   0.0%  (0 / 18000 questions)
  2 (partial overlap):    0.0%  (0 / 18000 questions)
  3 (partial overlap):  100.0%  (18000 / 18000 questions)
  4 (partial overlap):    0.0%  (0 / 18000 questions)
  5 (partial overlap):    0.0%  (0 / 18000 questions)
  6 (partial overlap):    0.0%  (0 / 18000 questions)
  7 (partial overlap):    0.0%  (0 / 18000 questions)
  8 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 3.00

veh_price: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   0.0%  (0 / 18000 questions)
  2 (partial overlap):    0.0%  (0 / 18000 questions)
  3 (partial overlap):  100.0%  (18000 / 18000 questions)
  4 (partial overlap):    0.0%  (0 / 18000 questions)
  5 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 3.00

battery_refurbishcellreplace: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   0.0%  (0 / 18000 questions)
  2 (no overlap):       100.0%  (18000 / 18000 questions)
  Average unique levels per question: 2.00

battery_refurbishpackreplace: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   0.0%  (0 / 18000 questions)
  2 (no overlap):       100.0%  (18000 / 18000 questions)
  Average unique levels per question: 2.00

battery_range_year0: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   0.0%  (0 / 18000 questions)
  2 (partial overlap):    0.0%  (0 / 18000 questions)
  3 (partial overlap):  100.0%  (18000 / 18000 questions)
  4 (partial overlap):    0.0%  (0 / 18000 questions)
  5 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 3.00

battery_degradation: Continuous variable
  Questions by # unique levels:
  1 (complete overlap):   0.0%  (0 / 18000 questions)
  2 (partial overlap):    0.0%  (0 / 18000 questions)
  3 (partial overlap):  100.0%  (18000 / 18000 questions)
  4 (no overlap):         0.0%  (0 / 18000 questions)
  Average unique levels per question: 3.00

Step 5: Simulate Choices

choices_random_fixed_parameter <- cbc_choices(design_random_fixed_parameter, priors = priors_fixed)
choices_random_random_parameter <- cbc_choices(design_random_random_parameter, priors = priors_random_parameter)

choices_shortcut <- cbc_choices(design_shortcut)

random_fixed_parameter

choices_cat <- cbc_decode(choices_random_fixed_parameter)

# Filter for the chosen rows only
choices_cat <- choices_cat[which(choices_cat$choice == 1), ]

# Counts of choices made for each attribute level
table(choices_cat$veh_mileage)


15000 20000 25000 30000 35000 40000 45000 50000 
 3164  2999  2745  2387  2184  1756  1482  1283

table(choices_cat$veh_price)


12000 13500 15000 16500 18000 
 4154  3767  3581  3372  3126

table(choices_cat$battery_refurbish)


   original cellreplace packreplace 
       7269        4709        6022

table(choices_cat$battery_range_year0)


 200  240  280  320  360 
2907 3263 3699 3894 4237

table(choices_cat$battery_degradation)


0.01 0.03 0.05 0.07 
5091 4674 4302 3933

random_random_parameter

choices_cat <- cbc_decode(choices_random_random_parameter)

# Filter for the chosen rows only
choices_cat <- choices_cat[which(choices_cat$choice == 1), ]

# Counts of choices made for each attribute level
table(choices_cat$veh_mileage)


15000 20000 25000 30000 35000 40000 45000 50000 
 3290  2974  2707  2483  2056  1799  1439  1252

table(choices_cat$veh_price)


12000 13500 15000 16500 18000 
 4060  3789  3542  3450  3159

table(choices_cat$battery_refurbish)


   original cellreplace packreplace 
       7482        4450        6068

table(choices_cat$battery_range_year0)


 200  240  280  320  360 
3038 3210 3590 3996 4166

table(choices_cat$battery_degradation)


0.01 0.03 0.05 0.07 
5151 4707 4283 3859

shortcut

choices_cat <- cbc_decode(choices_shortcut)

# Filter for the chosen rows only
choices_cat <- choices_cat[which(choices_cat$choice == 1), ]

# Counts of choices made for each attribute level
table(choices_cat$veh_mileage)


15000 20000 25000 30000 35000 40000 45000 50000 
 2249  2259  2277  2197  2262  2253  2217  2286

table(choices_cat$veh_price)


12000 13500 15000 16500 18000 
 3563  3546  3629  3593  3669

table(choices_cat$battery_refurbish)


   original cellreplace packreplace 
       5925        5998        6077

table(choices_cat$battery_range_year0)


 200  240  280  320  360 
3594 3659 3556 3675 3516

table(choices_cat$battery_degradation)


0.01 0.03 0.05 0.07 
4563 4462 4410 4565

Step 6: Assess Power

Statistical power is the probability of correctly detecting an effect when it truly exists, which depends on effect size, sample size, design efficiency, and model complexity.
Power analysis focuses on prevision (standard errors)

random_fixed_parameter

power_random_fixed_parameter <- cbc_power(
  data=choices_random_fixed_parameter,
  outcome = "choice",
  obsID = "obsID",
  n_q = 6,
  n_breaks = 10
  )

Auto-detected parameters: veh_mileage, veh_price, battery_refurbishcellreplace, battery_refurbishpackreplace, battery_range_year0, battery_degradation

Using 'respID' as panelID for panel data estimation.

Estimating models using 10 cores...

Model estimation complete!

plot(power_random_fixed_parameter, type = "power", power_threshold = 0.9)

plot(power_random_fixed_parameter, type = "se")

summary(power_random_fixed_parameter, power_threshold = 0.9)

CBC Power Analysis Summary
===========================

Sample size requirements for 90% power:

veh_mileage    : n >= 300 (achieves 100.0% power, SE = 0.0000)
veh_price      : n >= 300 (achieves 100.0% power, SE = 0.0000)
battery_refurbishcellreplace: n >= 300 (achieves 100.0% power, SE = 0.0801)
battery_refurbishpackreplace: n >= 300 (achieves 100.0% power, SE = 0.0758)
battery_range_year0: n >= 300 (achieves 100.0% power, SE = 0.0006)
battery_degradation: n >= 300 (achieves 100.0% power, SE = 1.4100)

random_random_parameter

power_random_random_parameter <- cbc_power(
  data=choices_random_random_parameter,
  outcome = "choice",
  obsID = "obsID",
  n_q = 6,
  n_breaks = 10)

Auto-detected parameters: veh_mileage, veh_price, battery_refurbishcellreplace, battery_refurbishpackreplace, battery_range_year0, battery_degradation

Using 'respID' as panelID for panel data estimation.

Estimating models using 10 cores...

Model estimation complete!

plot(power_random_random_parameter, type = "power", power_threshold = 0.9)

plot(power_random_random_parameter, type = "se")

summary(power_random_random_parameter, power_threshold = 0.9)

CBC Power Analysis Summary
===========================

Sample size requirements for 90% power:

veh_mileage    : n >= 300 (achieves 100.0% power, SE = 0.0000)
veh_price      : n >= 300 (achieves 99.9% power, SE = 0.0000)
battery_refurbishcellreplace: n >= 300 (achieves 100.0% power, SE = 0.0828)
battery_refurbishpackreplace: n >= 300 (achieves 100.0% power, SE = 0.0759)
battery_range_year0: n >= 300 (achieves 100.0% power, SE = 0.0006)
battery_degradation: n >= 300 (achieves 100.0% power, SE = 1.4504)

shortcut

power_shortcut <- cbc_power(
  data=choices_shortcut,
  outcome = "choice",
  obsID = "obsID",
  n_q = 6,
  n_breaks = 10)

Auto-detected parameters: veh_mileage, veh_price, battery_refurbishcellreplace, battery_refurbishpackreplace, battery_range_year0, battery_degradation

Using 'respID' as panelID for panel data estimation.

Estimating models using 10 cores...

Model estimation complete!

plot(power_shortcut, type = "power", power_threshold = 0.9)

plot(power_shortcut, type = "se", power_threshold = 0.9)

summary(power_shortcut, power_threshold = 0.9)

CBC Power Analysis Summary
===========================

Sample size requirements for 90% power:

veh_mileage    : Threshold not reached (max 42.6% power at n = 3000)
veh_price      : Threshold not reached (max 54.1% power at n = 3000)
battery_refurbishcellreplace: Threshold not reached (max 73.9% power at n = 3000)
battery_refurbishpackreplace: Threshold not reached (max 49.0% power at n = 3000)
battery_range_year0: Threshold not reached (max 21.7% power at n = 3000)
battery_degradation: Threshold not reached (max 62.0% power at n = 3000)

comparison

plot_compare_power(
  random_fixed_parameter = power_random_fixed_parameter,
  random_random_parameter = power_random_random_parameter,
  shortcut = power_shortcut,
  type = "power"
)

plot_compare_power(
  random_fixed_parameter = power_random_fixed_parameter,
  random_random_parameter = power_random_random_parameter,
  shortcut = power_shortcut,
  type = "se"
)