# Analyze and Visualize Important QOIs

## 🎯 Estimate Corrected MMs or AMCEs

In conjoint analysis, default MMs and AMCEs can be biased due to measurement error from intra-respondent variability.

projoint corrects for this bias automatically.

The following instructions apply to choice-level data. What if you have profile-level data?ⓘ Our FAQ Page has instructions to estimate and visualize profile-level QOIs.

## 📦 Prepare Example Data

> Outcome naming & order (important)

> - List `.outcomes` in the order questions were asked.
> - If you have a repeated task, its outcome must be the last element.
> - For base tasks (all but last), the function reads the digits in each name as the task id (e.g., `"choice4"`, `"Q4"`, `"task04"` → task 4).
> - The repeated base task is inferred from the first base outcome’s digits. The repeated outcome itself need not contain digits—only its position (last) matters.
> - Outcome strings should end with your choice labels; by default we parse the last character and expect `"A"`/`"B"`. If your survey uses `"1"`/`"2"` (or other endings), set `.choice_labels` accordingly.

Examples

    # Standard order; repeated = task 1
    data("exampleData1")
    outcomes <- c(paste0("choice", 1:8), "choice1_repeated_flipped")
    out1 <- reshape_projoint(exampleData1, outcomes)

## 🛠️ Why Use IDs (e.g., `att1`, `level1`)?

Before estimating quantities, it’s important to understand how attribute and level IDs work inside projoint.

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")

## 📈 Estimate Marginal Means (MMs)

Choice-Level MMs (Specific Level)

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>

## 📉 Estimate AMCEs

Choice-Level AMCEs (Specific Level)

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>

## 🔎 Predict Intra-Respondent Reliability (IRR)

If your design does not include a repeated task, you can predict IRR using predict_tau(), based on observed respondent behavior.

Predict IRR Using `predict_tau()`

    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)

## 🎨 Visualize MMs or AMCEs

The projoint package provides ready-to-publish plotting tools for conjoint analysis results.

Note: The current version of projoint supports plotting choice-level MMs only.
Support for choice-level AMCEs will be available in future updates!

### ⚖️ Choice-Level Analysis

Estimate

- Specify your quantity of interest:

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

- Estimate

    choice_mm <- projoint(
      .data = out1_arranged,
      .qoi = qoi_mm,
      .ignore_position = TRUE
    )

Visualize (Levels)

    plot(choice_mm)

Visualize (Differences)

    plot(choice_mm, .type = "pointrange")

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