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What’s the difference between “profile-level” and “choice-level”conjoint analysis??

Choice-level analysis is simpler, easier, and more powerful thanprofile-level analysis.

Conjoint designs originated in market research and psychology whereeach respondent is asked to rate each of two different profiles (e.g.,two products). Each of the two ratings provided separate information,and the two are analyzed as separate observations. Researchers with thisprofile-level design find it convenient to arrange their datawith one profile per row, and thus twice as many rows asrespondents.

Unfortunately, when social scientists adopted the conjoint surveydesign, they kept the same profile-level design but changed the outcomemeasure from separate ratings to a single choice between the twoprofiles (e.g., to reflect a voter choice between two candidates). Inthis situation, respondents asked to make one choice between the twoprofiles that are exactly dependent, as choosing one necessarily meantnot choosing the other (e.g., in a two-candidate partisan election, oneobservation would be “Democrat” and the other would be “not theRepublican”). Using this profile-level design with 2*n rows but only nindependent observations requires the introduction of complicatedstatistical procedures to correct for the dependence induced solely bythe researcher’s decision to organize the data in this complicated way.

We recommend the much simpler and more powerfulchoice-leveldesign. The idea is to arrange data at the level of the respondent’schoice, so that each row in the data matrix includes information aboutone choice (and both profiles together, with n observations and n rows).OurAJPSarticle clarifies this point, shows how this choice-level analysisvastly simplifies the notation, statistical analysis procedures, andintuition, and greatly expands the substantive questions conjointanalysis be used to answer.

What if I have profile-level data?

Transform your data to choice-level, which is simpler and more powerful.To replicate old analyses, you can also use our profile-level tools
Profile-Level MMs (All Levels)
mm0<-projoint(out1,.structure ="profile_level",.estimand ="mm")print(mm0)
## ## Projoint results object## -------------------------## Estimand:  mm ## Structure:  profile_level ## Standard error method:  analytical ## IRR:  Estimated ## Tau:  0.172 ## Number of estimates:  48
summary(mm0)
## ## Summary of Projoint Estimates## ------------------------------## Estimand: mm## Structure: profile_level## Standard error method: analytical## SE type (lm_robust):   CR2 (clustered by id)## IRR: Estimated## Tau: 0.172
## # A tibble: 48 × 6##    estimand       estimate     se conf.low conf.high att_level_choose##    <chr>             <dbl>  <dbl>    <dbl>     <dbl> <chr>           ##  1 mm_uncorrected    0.574 0.0142    0.546     0.602 att1:level1     ##  2 mm_corrected      0.614 0.0219    0.571     0.657 att1:level1     ##  3 mm_uncorrected    0.485 0.0136    0.458     0.511 att1:level2     ##  4 mm_corrected      0.477 0.0207    0.436     0.517 att1:level2     ##  5 mm_uncorrected    0.445 0.0142    0.417     0.472 att1:level3     ##  6 mm_corrected      0.416 0.0219    0.372     0.459 att1:level3     ##  7 mm_uncorrected    0.489 0.0150    0.459     0.518 att2:level1     ##  8 mm_corrected      0.483 0.0229    0.438     0.528 att2:level1     ##  9 mm_uncorrected    0.524 0.0133    0.497     0.550 att2:level2     ## 10 mm_corrected      0.536 0.0203    0.496     0.576 att2:level2     ## # ℹ 38 more rows
Profile-Level MMs (Specific Level)
qoi_1<-set_qoi(.structure ="profile_level",.estimand ="mm",.att_choose ="att1",.lev_choose ="level1")mm1<-projoint(out1,.qoi = qoi_1)print(mm1)
## ## Projoint results object## -------------------------## Estimand:  mm ## Structure:  profile_level ## Standard error method:  analytical ## IRR:  Estimated ## Tau:  0.172 ## Number of estimates:  2
summary(mm1)
## ## Summary of Projoint Estimates## ------------------------------## Estimand: mm## Structure: profile_level## Standard error method: analytical## SE type (lm_robust):   CR2 (clustered by id)## IRR: Estimated## Tau: 0.172
## # A tibble: 2 × 7##   estimand       estimate     se conf.low conf.high att_level_choose##   <chr>             <dbl>  <dbl>    <dbl>     <dbl> <chr>           ## 1 mm_uncorrected    0.574 0.0142    0.546     0.602 att1:level1     ## 2 mm_corrected      0.614 0.0219    0.571     0.657 att1:level1     ## # ℹ 1 more variable: att_level_notchoose <chr>
Profile-Level MMs (Specific Level, Manual IRR)
mm1b<-projoint(out1,.qoi = qoi_1,.irr =0.75)print(mm1b)
## ## Projoint results object## -------------------------## Estimand:  mm ## Structure:  profile_level ## Standard error method:  analytical ## IRR:  Assumed (0.75) ## Tau:  0.146 ## Number of estimates:  2
summary(mm1b)
## ## Summary of Projoint Estimates## ------------------------------## Estimand: mm## Structure: profile_level## Standard error method: analytical## SE type (lm_robust):   CR2 (clustered by id)## IRR: Assumed (0.75)## Tau: 0.146
## # A tibble: 2 × 7##   estimand       estimate     se conf.low conf.high att_level_choose##   <chr>             <dbl>  <dbl>    <dbl>     <dbl> <chr>           ## 1 mm_uncorrected    0.574 0.0142    0.546     0.602 att1:level1     ## 2 mm_corrected      0.605 0.0201    0.566     0.645 att1:level1     ## # ℹ 1 more variable: att_level_notchoose <chr>
Profile-Level AMCEs (All Levels)
amce0<-projoint(out1,.structure ="profile_level",.estimand ="amce")
## Warning in pj_estimate(.data = .data, .structure = structure, .estimand =## estimand, : AMCE analytical SEs: CR2 produced non-PSD/NA variances; fell back## to se_type='stata' (then HC1 if needed).## Warning in pj_estimate(.data = .data, .structure = structure, .estimand =## estimand, : AMCE analytical SEs: CR2 produced non-PSD/NA variances; fell back## to se_type='stata' (then HC1 if needed).
print(amce0)
## ## Projoint results object## -------------------------## Estimand:  amce ## Structure:  profile_level ## Standard error method:  analytical ## IRR:  Estimated ## Tau:  0.172 ## Number of estimates:  34
summary(amce0)
## ## Summary of Projoint Estimates## ------------------------------## Estimand: amce## Structure: profile_level## Standard error method: analytical## SE type (lm_robust):   CR2 (clustered by id)## IRR: Estimated## Tau: 0.172
## # A tibble: 34 × 7##    estimand         estimate     se conf.low conf.high att_level_choose##    <chr>               <dbl>  <dbl>    <dbl>     <dbl> <chr>           ##  1 amce_uncorrected -0.0899  0.0236  -0.136    -0.0435 att1:level2     ##  2 amce_corrected   -0.137   0.0360  -0.208    -0.0662 att1:level2     ##  3 amce_uncorrected -0.130   0.0250  -0.179    -0.0808 att1:level3     ##  4 amce_corrected   -0.198   0.0386  -0.274    -0.122  att1:level3     ##  5 amce_uncorrected  0.0348  0.0244  -0.0132    0.0828 att2:level2     ##  6 amce_corrected    0.0530  0.0372  -0.0202    0.126  att2:level2     ##  7 amce_uncorrected -0.00177 0.0263  -0.0536    0.0500 att2:level3     ##  8 amce_corrected   -0.00270 0.0402  -0.0817    0.0763 att2:level3     ##  9 amce_uncorrected  0.0240  0.0233  -0.0218    0.0699 att3:level2     ## 10 amce_corrected    0.0366  0.0357  -0.0336    0.107  att3:level2     ## # ℹ 24 more rows## # ℹ 1 more variable: att_level_choose_baseline <chr>
Profile-Level AMCEs (Specific Level)
qoi_3<-set_qoi(.structure ="profile_level",.estimand ="amce",.att_choose ="att1",.lev_choose ="level3",.att_choose_b ="att1",.lev_choose_b ="level1")amce1<-projoint(out1,.qoi = qoi_3)print(amce1)
## ## Projoint results object## -------------------------## Estimand:  amce ## Structure:  profile_level ## Standard error method:  analytical ## IRR:  Estimated ## Tau:  0.172 ## Number of estimates:  2
summary(amce1)
## ## Summary of Projoint Estimates## ------------------------------## Estimand: amce## Structure: profile_level## Standard error method: analytical## SE type (lm_robust):   CR2 (clustered by id)## IRR: Estimated## Tau: 0.172
## # A tibble: 2 × 9##   estimand         estimate     se conf.low conf.high att_level_choose##   <chr>               <dbl>  <dbl>    <dbl>     <dbl> <chr>           ## 1 amce_uncorrected   -0.130 0.0250   -0.179   -0.0808 att1:level3     ## 2 amce_corrected     -0.198 0.0386   -0.274   -0.122  att1:level3     ## # ℹ 3 more variables: att_level_notchoose <chr>,## #   att_level_choose_baseline <chr>, att_level_notchoose_baseline <chr>
Profile-Level AMCEs (Specific Level, Manual IRR)
amce1b<-projoint(out1,.qoi = qoi_3,.irr =0.75)print(amce1b)
## ## Projoint results object## -------------------------## Estimand:  amce ## Structure:  profile_level ## Standard error method:  analytical ## IRR:  Assumed (0.75) ## Tau:  0.146 ## Number of estimates:  2
summary(amce1b)
## ## Summary of Projoint Estimates## ------------------------------## Estimand: amce## Structure: profile_level## Standard error method: analytical## SE type (lm_robust):   CR2 (clustered by id)## IRR: Assumed (0.75)## Tau: 0.146
## # A tibble: 2 × 9##   estimand         estimate     se conf.low conf.high att_level_choose##   <chr>               <dbl>  <dbl>    <dbl>     <dbl> <chr>           ## 1 amce_uncorrected   -0.130 0.0250   -0.179   -0.0808 att1:level3     ## 2 amce_corrected     -0.184 0.0353   -0.253   -0.114  att1:level3     ## # ℹ 3 more variables: att_level_notchoose <chr>,## #   att_level_choose_baseline <chr>, att_level_notchoose_baseline <chr>
💡 Tip: When to Use.by_var

Use.by_varonly when comparingprofile-level MMs between two groups (e.g., Democratsvs. Republicans).

For AMCEs or choice-level quantities,.by_var is notcurrently supported.

📈 Profile-Level MMs and AMCEs

Estimate
data("out1_arranged")mm<-projoint(out1_arranged,.structure ="profile_level")amce<-projoint(out1_arranged,.structure ="profile_level",.estimand ="amce")
## Warning in pj_estimate(.data = .data, .structure = structure, .estimand =## estimand, : AMCE analytical SEs: CR2 produced non-PSD/NA variances; fell back## to se_type='stata' (then HC1 if needed).## Warning in pj_estimate(.data = .data, .structure = structure, .estimand =## estimand, : AMCE analytical SEs: CR2 produced non-PSD/NA variances; fell back## to se_type='stata' (then HC1 if needed).
Visualize
  • Marginal Means
plot(mm)

  • AMCEs
plot(amce)

Profile-Level Subgroup Comparison: White vs. Non-WhiteRespondents
outcomes<-c(paste0("choice",1:8),"choice1_repeated_flipped")df<- exampleData1|>mutate(white =ifelse(race=="White",1,0))df_0<- df|>filter(white==0)|>reshape_projoint(outcomes)df_1<- df|>filter(white==1)|>reshape_projoint(outcomes)df_d<- df|>reshape_projoint(outcomes,.covariates ="white")data_file<-system.file("extdata","labels_arranged.csv",package ="projoint")if (data_file=="")stop("File not found!")df_0<-read_labels(df_0, data_file)df_1<-read_labels(df_1, data_file)df_d<-read_labels(df_d, data_file)out_0<-projoint(df_0,.structure ="profile_level")out_1<-projoint(df_1,.structure ="profile_level")out_d<-projoint(df_d,.structure ="profile_level",.by_var ="white")plot_0<-plot(out_0)plot_1<-plot(out_1)plot_d<-plot(out_d,.by_var =TRUE)plot_0+coord_cartesian(xlim =c(0.2,0.8))+labs(title ="Non-white",x ="AMCE")+theme(plot.title =element_text(hjust =0.5))+plot_1+coord_cartesian(xlim =c(0.2,0.8))+labs(title ="White",x ="AMCE")+theme(axis.text.y =element_blank(),plot.title =element_text(hjust =0.5))+plot_d+coord_cartesian(xlim =c(-0.4,0.4))+labs(title ="Difference",x ="Difference")+theme(axis.text.y =element_blank(),plot.title =element_text(hjust =0.5))

Is there other conjoint software??

See Anton Strezhnev’sConjoint Survey Design Tool(Link:conjointSDT)

1. Generate a JavaScript or PHP randomizer

Anton Strezhnev’sConjoint Survey Design Tool (Link:conjointSDT)produces a JavaScript or PHP randomizer.

JavaScript

The JavaScript randomizer can be inserted into the first screen ofyour Qualtrics survey usingEdit Question JavaScript.Example screenshot:

  • Example #"https://raw.githubusercontent.com/yhoriuchi/projoint/master/data-raw/example.js">Downloadhere

The JavaScript runs internally within Qualtrics and generatesembedded fields for each conjoint task.
For example:

  • "K-1-1-7" = value for the 7th attribute, first profile,first task
  • "K-5-2-5" = value for the 5th attribute, secondprofile, fifth task

PHP

Alternatively, the PHP randomizer must be hosted externally.

Example hosted on our server:
https://www.horiuchi.org/php/ACHR_Modified_2.php
(PHP filehere)

This method was used in:
Agadjanian,Carey, Horiuchi, and Ryan (2023)

2. Modify your JavaScript or PHP randomizer

You may want to add constraints — for example,preventties between profiles.
To do this, you can manually modify your JavaScript or PHP.

In the future,projoint will offer easier ways toadd constraints!
Until then, resources likeOpenAI’sGPT-4 can help you edit scripts.

Example PHP snippet ensuring racial balance between profiles:

$treat_profile_one="B-".(string)$p."-1-".(string)$treat_number;$treat_profile_two="B-".(string)$p."-2-".(string)$treat_number;$cond1=$returnarray[$treat_profile_one]=="White"&&$returnarray[$treat_profile_two]==$type;$cond2=$returnarray[$treat_profile_two]=="White"&&$returnarray[$treat_profile_one]==$type;if ($cond1or$cond2) {$complete=True;}

If you have good examples of manual constraints, please emailYusaku Horiuchi!

3. Add conjoint tables with embedded fields in Qualtrics

After generating the randomizer, you must createHTMLtables displaying embedded fields for each task.

Example of the first task:

Each conjoint study typically includes5-10tasks.

The embedded fields update across tasks:
e.g.,"K-1..." for Task 1,"K-2..." for Task2, and so on.

Adding a repeated task (recommended!)

It’s easy to create arepeated task forintra-respondent reliability (IRR) estimation:

  • Copy the HTML for Task 1 later into the survey (e.g., after Task5)
  • Flip Profile 1 and Profile 2 (swap the embeddedfield digits)

Example repeated task:

4. Sample Qualtrics survey template

We provide a fullQualtrics QSF file ready touse!


This file recreates a standard conjoint survey setup based on Mummoloand Nall (2017).

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