Analyze and Visualize Important QOIs

We recommend working with attribute IDs rather than actual text labels because:

• Safer against special characters, languages, or typos
• Allows multiple attributes to have identical labels (e.g., “High” for both “Teaching Quality” and “Research Quality”)

Check attribute-level mappings:

out1$labels

## # A tibble: 24 × 4
##    attribute                level                        attribute_id level_id  
##    <chr>                    <chr>                        <chr>        <chr>     
##  1 Housing Cost             15% of pre-tax income        att1         att1:leve…
##  2 Housing Cost             30% of pre-tax income        att1         att1:leve…
##  3 Housing Cost             40% of pre-tax income        att1         att1:leve…
##  4 Presidential Vote (2020) 30% Democrat, 70% Republican att2         att2:leve…
##  5 Presidential Vote (2020) 50% Democrat, 50% Republican att2         att2:leve…
##  6 Presidential Vote (2020) 70% Democrat, 30% Republican att2         att2:leve…
##  7 Racial Composition       50% White, 50% Nonwhite      att3         att3:leve…
##  8 Racial Composition       75% White, 25% Nonwhite      att3         att3:leve…
##  9 Racial Composition       90% White, 10% Nonwhite      att3         att3:leve…
## 10 Racial Composition       96% White, 4% Nonwhite       att3         att3:leve…
## # ℹ 14 more rows

You can also save these labels for easier editing:

save_labels(out1, "labels.csv")

Suppose you want to estimate, within a given profile pair, the probability of choosing a profile that includes “40% of pre-tax income” (level3) for Housing Cost (att1) rather than one that includes “15% of pre-tax income” (level1) for the same attribute, averaging over all combinations of the other attributes and across respondents; then use the following code:

qoi <- set_qoi(
  .structure = "choice_level",
  .att_choose = "att1",
  .lev_choose = "level3",
  .att_notchoose = "att1",
  .lev_notchoose = "level1"
)

mm2 <- projoint(out1, qoi)
print(mm2)

## 
## Projoint results object
## -------------------------
## Estimand:  mm 
## Structure:  choice_level 
## Standard error method:  analytical 
## IRR:  Estimated 
## Tau:  0.172 
## Number of estimates:  2

summary(mm2)

## 
## Summary of Projoint Estimates
## ------------------------------
## Estimand: mm
## Structure: choice_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    0.419 0.0197    0.380     0.458 att1:level3     
## 2 mm_corrected      0.376 0.0308    0.316     0.437 att1:level3     
## # ℹ 1 more variable: att_level_notchoose <chr>

Suppose you want to quantify how the choice probability changes between the following profile pairs:

• choosing a profile that includes “40% of pre-tax income” (level3) for Housing Cost (att1) versus one that includes “15% of pre-tax income” (level1) for Housing Cost (att1); and
• [baseline] choosing a profile that includes “30% of pre-tax income” (level2) for Housing Cost (att1) versus one that includes “15% of pre-tax income” (level1) for Housing Cost (att1);

averaging over all combinations of the other attributes and across respondents. Then write the following code:

qoi <- set_qoi(
  .structure = "choice_level",
  .estimand = "amce",
  .att_choose = "att1",
  .lev_choose = "level3",
  .att_notchoose = "att1",
  .lev_notchoose = "level1",
  .att_choose_b = "att1",
  .lev_choose_b = "level2",
  .att_notchoose_b = "att1",
  .lev_notchoose_b = "level1"
)

amce2 <- projoint(out1, qoi)
print(amce2)

## 
## Projoint results object
## -------------------------
## Estimand:  amce 
## Structure:  choice_level 
## Standard error method:  analytical 
## IRR:  Estimated 
## Tau:  0.172 
## Number of estimates:  2

summary(amce2)

## 
## Summary of Projoint Estimates
## ------------------------------
## Estimand: amce
## Structure: choice_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  -0.0135 0.0269  -0.0665    0.0394 att1:level3     
## 2 amce_corrected    -0.0206 0.0412  -0.102     0.0604 att1:level3     
## # ℹ 3 more variables: att_level_notchoose <chr>,
## #   att_level_choose_baseline <chr>, att_level_notchoose_baseline <chr>

data(out1_arranged)
predicted_irr <- predict_tau(out1_arranged)

print(predicted_irr)

## Tau estimated using the extrapolation method: 0.743

summary(predicted_irr)

## # A tibble: 8 × 2
##       x predicted
##   <int>     <dbl>
## 1     0     0.743
## 2     1     0.709
## 3     2     0.675
## 4     3     0.640
## 5     4     0.606
## 6     5     0.572
## 7     6     0.537
## 8     7     0.503

plot(predicted_irr)