Sensitivity Analysis

1. What Is Sensitivity Analysis?

Sensitivity analysis systematically varies one attribute level-by-level while holding everything else constant. For each level of the chosen attribute, Choicery runs a full market simulation with the focal product set to that level and records that product's resulting share. In Own-Price mode this sweep is repeated separately for every plotted product; in Joint Pricing mode a single simulation per level moves all plotted products together. The result is a clear picture of how each attribute level shift affects competitive outcomes.

The central question it answers:

Sensitivity analysis is superior to raw attribute importance scores because it accounts for competitive context. Importance scores tell you which attributes matter most in general, but sensitivity shows you the concrete share impact of a specific change given the products actually in the market. The results are on a ratio scale: a product with 40% share genuinely captures twice the preference of one with 20% share.

2. Prerequisites

Before running sensitivity analysis, ensure the following are in place:

3. Running Sensitivity Analysis

3.1 Controls & Options

The Sensitivity tab provides the following controls:

• Vary Attribute: A dropdown listing every attribute of the run. Each level of the selected attribute is tested one at a time. If an attribute whose name contains "price" (or "preis") exists, it is preselected.
• Simulation Method: A three-way pill toggle: Share of Pref. (default, logit-based share), RFC (Randomized First Choice) and First Choice (winner takes all).
• Focal Products to Plot (select up to 5): Click a product pill to include or exclude it. The first two products are preselected. The hint below reads "Click products to include or exclude them", and switches to "Select up to 5 products for this analysis." once more than five products exist. Only the selected products get curves; every product in the Products panel still competes in the simulation.
• Include "None": A toggle switch that controls whether the "None" (no-purchase) option participates in the simulation. On by default, and available for all three simulation methods. It only takes effect when the selected run was estimated with a None option; otherwise the simulation runs without a None alternative.

The Sensitivity tab reads the products from the Products panel and uses at most the first 10 of them. If you have more, a note above the configuration says how many products you have, that only the first 10 are shown, and that you can select up to 5. With six to ten products the note only states the five-product cap.

Respondent filters are set outside the tab, through the Filters button above the Products panel. Any filter you apply there is sent along with the run and produces an extra result per filter group next to the full sample.

When the varied attribute is the price attribute from Price Setup, respondents who prefer higher prices or barely react to price are left out, as in WTP, Reservation Price and Price Elasticity: their share rises with price and would make the curves climb again at high prices. Include unusual price responses in price analyses in Analysis Settings keeps them. Other attributes always use all respondents, like Choice Share.

3.2 Starting the Calculation

Click Calculate. Choicery iterates through every level of the chosen attribute, swaps it into each focal product one at a time, runs the simulation, and collects the share results. The button shows "Analyzing..." while the run is in progress. The chart, the crossover list and the data table appear once all levels have been evaluated.

If no attribute is selected, or no product pill is active, Choicery refuses to start and says so. The size of a request is the number of plotted products times the number of tested levels times the number of filter groups (at least 1). Above 500 combinations the run is rejected with "Sensitivity combinations is above the synchronous safety threshold (N requested, maximum 500). Reduce the request size."; reduce the number of levels, products or filter groups in that case. RFC runs are also rejected when the requested number of draws exceeds the synchronous cap.

4. Interpreting Results

4.1 The Chart

The primary output is a line chart with attribute levels on the X-axis and the simulated preference share (%) on the Y-axis (axis title "Simulated Preference Share (%)"). Each focal product is shown in its own color and every point carries its share as a label. Reading left to right, you can see exactly how share rises or falls as the attribute level changes.

Whether the points are connected depends on how the attribute was estimated. A linear-coded attribute (typically a numeric price) gets a connected, slightly smoothed line, because the values lie on a continuum. A categorical attribute gets markers only, with the share label beside each marker: its level utilities are estimated independently, and a connecting line would suggest a continuum that does not exist.

The results header carries a pricing mode toggle with two buttons. Switching it re-runs the analysis immediately.

• Own-Price: the default. Each curve is a separate simulation in which only that product moves through the levels; every other product stays at the configuration you set in the Products panel. This is the ceteris paribus interpretation: "what happens to each product's share if only that product changes?" Because the curves come from different simulated markets, shares at the same X value do not sum to 100%.
• Joint Pricing: all selected products move to the same level together, in a single simulation per level. Products that are not selected keep competing at their configured settings, they are just not plotted. This is useful for category-wide pricing scenarios, for example an entire brand line repositioning to a different price point. If every configured product is selected and the None option is off, relative prices never change, all curves come out flat, and Choicery shows a note explaining why.

Above the chart a Show: row appears with filter pills, one group for samples (Overall plus each active filter group) and one group for products, whenever there is more than one of them. These pills only show or hide curves, they do not change the simulation.

4.2 Crossover Points

A crossover point is where two products' share curves intersect, the level at which the competitive ranking reverses. Choicery detects these automatically for every pair of plotted products and lists them in a Crossover Points block below the chart. The block is hidden when no crossing was found.

Each entry reads "Product A & Product B cross at <level> (share: XX.X%)". When each of the two adjacent levels has a stored value in the run, or its label contains exactly one unambiguous number (for example "25000", "EUR 25000.50" or "0,325 €", but not "25,000" or "1.500", which could be a decimal or a thousands separator), the crossing level is linearly interpolated and printed with a tilde, for example ~27500. Otherwise the entry names the two levels the crossing falls between. A note in the same block states that crossover points are linearly interpolated between tested levels.

4.3 Segment Comparison

If you applied respondent filters through the Filters button, an extra block appears under the chart, titled Sensitivity: Overall vs followed by the name of the active group (or "Segments" when several are active). It is a compact table with one row per product and these columns:

• Product, the plotted product's name.
• Share range: Overall, the difference between the highest and the lowest simulated share across the tested levels, in percentage points, for the full sample.
• Share range: <group> (n=...), the same figure computed inside each filter group. The count is the number of respondents the shares were computed on; when the price attribute is varied this excludes unusual price responses and can be smaller than the group.
• Difference, shown only when exactly one group is active: group minus Overall. A positive value means the group reacts more strongly to the tested attribute.

Groups that produced no result are listed underneath as errors, for example when no respondent matches the filter. Without active filters this block stays hidden.

4.4 Data Table

The full numeric results are presented in a table below the chart. The first column is named after the varied attribute, and each plotted product contributes two columns, its share and its delta versus base:

Shares and deltas are printed with two decimals. The base badge sits directly below the share of the level that the product is currently configured to in the Products panel; that share is the reference for the deltas, which are expressed in percentage points (pp). In Joint Pricing mode the first tested level serves as the base instead. Positive and negative deltas are colored.

When filters are active the table is split into labeled blocks: first "Overall (full sample)", then one block per filter group with its respondent count.

4.5 Downloads

Two buttons sit in the results header, next to the pricing-mode toggle:

• CSV writes the plotted curves to a file named sensitivity_<mode>_<attribute>.csv, for example sensitivity_own_price_price.csv. Its columns are Sample, the attribute, and one share column per plotted product. Filter groups are appended as additional rows in the Sample column.
• PNG saves the chart as a high-resolution image, named sensitivity_<mode>_<attribute>.png.

The PDF button in the tab bar produces a "Sensitivity Analysis" report from the currently displayed result.

5. Demand Curves (Price Sensitivity)

When you select the price attribute as the varied attribute, the resulting chart is a demand curve: price on the X-axis, market share on the Y-axis. This is one of the most valuable outputs of conjoint-based market simulation. Keep in mind that the X-axis carries the price levels of your design, in design order, and that the points are connected into a line only if price was estimated as a linear attribute.

An important subtlety: even when using a main-effects HB model (no explicit interaction terms), the simulation reveals brand-by-price interactions implicitly. This happens because each respondent has individual-level utilities, and the logit share calculation is nonlinear. As Orme (2020, Ch. 17) notes, this is one of the key advantages of individual-level HB estimation over aggregate models.

6. Best Practices & Common Pitfalls

Do

• Compare multiple products simultaneously. Sensitivity analysis is most powerful when you see how share redistributes across competitors, not just how one product changes in isolation.
• Use crossover points for pricing decisions. The exact price at which you lose competitive advantage is directly actionable intelligence.
• Test the price attribute for demand curves. This is the single most common and most useful application of sensitivity analysis.
• Use the Filters button for group-specific sensitivity. If you have respondent variables or Latent Class memberships available, apply them as filters before calculating. Choicery then reports the full sample and each group side by side, so you can see whether the pattern holds universally or differs across groups.

Don't

• Assume competitors react. Sensitivity analysis holds all non-focal products constant. In reality, competitors adjust their offerings. The results show what would happen under current competitive conditions, not what will happen after competitive response.
• Extrapolate beyond the design range. The utilities are estimated only for the levels included in the conjoint design. Drawing conclusions about levels outside that range (e.g., prices never tested) is unreliable.
• Ignore that one-at-a-time (OAT) misses interaction effects between simultaneous changes. Sensitivity varies one attribute at a time. If you plan to change two attributes simultaneously (e.g., upgrade features and raise price), the combined effect may differ from the sum of individual effects. Use the base market simulator for multi-attribute what-if scenarios.

7. Key Definitions

8. The Algorithm

8.1 Step-by-Step Procedure

The sensitivity analysis algorithm proceeds as follows:

Step 3 is where the two pricing modes differ. In Own-Price mode the loop runs once per focal product, so product j's curve comes from simulations in which only product j moved. In Joint Pricing mode there is a single loop over levels in which all focal products are set to level l simultaneously, so one simulation per level feeds all curves at once. Non-focal products keep their base configuration in both modes.

The per-product summary statistic Choicery reports is the share range, the plain difference between the highest and the lowest simulated share across the tested levels:

8.2 Worked Example

9. Crossover Points

9.1 Linear Interpolation

When two products' share curves cross between adjacent tested levels, Choicery estimates the exact crossover using linear interpolation:

This formula finds the point where the share difference between Product A and Product B passes through zero, assuming a linear relationship between the two tested levels.

9.2 Numeric vs. Categorical Attributes

10. Why Sensitivity Beats Raw Importance

Attribute importance scores (derived from the range of part-worth utilities) are a useful summary of how much each attribute could matter. But they have significant limitations that sensitivity analysis overcomes:

The key insight is that importance scores are context-free while sensitivity results are context-dependent. The same attribute may have high importance but low sensitivity if all products in the market already offer similar levels. Conversely, a low-importance attribute can produce large share swings if it is the key differentiator between two closely matched products.