Market Simulation (Choice Share)

1. What Is Market Simulation?

Market simulation takes the individual-level utilities from your HB (or TasteNet) estimation and places product concepts in simulated competition. You define products with specific attribute levels, and the simulator predicts how respondents would distribute their choices among those products.

Think of it this way: imagine all your survey respondents gathered in one room, presented with a shelf of products, and each one picks their favorite. The simulator does this computationally, using each respondent’s estimated preferences to determine their choice.

This is the most practically important feature in conjoint analysis. While HB estimation tells you what people prefer in general, market simulation answers the “What if?” questions that drive business decisions:

• Product design: “What if we add a premium feature and raise the price by 20%?”
• Competitive positioning: “What happens to our share if a competitor launches a budget option?”
• Pricing strategy: “At what price does our product lose more than 10 share points?”
• Market entry: “If we introduce a new product, where does its share come from?”

2. Prerequisites

Before running a market simulation in Choicery, you need the following:

The Guide button at the top right of the Choice Share tab opens this tutorial: that is the in-app entry point for users who want to read the background while configuring a simulation.

3. Setting Up Products

The Products panel (left side of the simulator) is where you define the competitive scenario. Each product is a hypothetical offering defined by selecting one level for each attribute in your conjoint study. The same product set feeds all simulator tabs, not just Choice Share.

Adding Products

• + Add Product appends a blank product card. Then set the attribute values on that card.
• Import opens a dropdown with two groups: Saved Product Sets (sets you saved earlier, see Section 7) and Fixed Tasks (the fixed choice tasks of your experimental design). Importing a fixed task is useful when you want to simulate the exact choice task respondents saw.
• The trash icon next to Import clears all products at once.

Configuring a Product

Each product appears as a card with an editable name field, an Edit (pencil) button that expands the attribute controls, a Remove (x) button, and one control per attribute. Categorical attributes get a dropdown of their levels, linear attributes get a free numeric input. The first card carries a Focal badge, marking it as the default focal product. Reservation Price always analyses that first product (its caption reads “Calculating reservation price for <name> from the Products panel”), while the WTP and Price Elasticity tabs have their own Focal Product dropdown, and Sensitivity lets you pick up to five products to plot. For example, a car study might have:

Important Details

• Linear attributes (e.g., price coded as linear in your design): you can enter any numeric value, not just the design levels. How a value between or beyond the tested levels becomes utility depends on how the run stored the attribute. With a single linear coefficient, the utility is the coefficient times the standardized value, one straight line inside and outside the tested range. When a numeric attribute was estimated per level, the utility is interpolated linearly between the two neighbouring tested levels and, beyond the outer levels, extended along the outermost segment. Either way, values outside the range are possible but not recommended: the utility is only estimated inside the design range, and nothing in the data says whether the straight line continues beyond it. (Sawtooth's simulator behaves the same way and does not block such values either.) Simulation WTP and Sampling of Scenarios (SOS) apply the same rule and report break-even prices that fall outside the tested range as extrapolations, so you can see when a WTP figure rests on a value the survey never showed; see the Willingness to Pay guide.
• Name your products meaningfully: “Brand A SUV 45k” is far more useful than “Product 3” when interpreting results. Edit the name directly in the card header.
• Minimum products: two products are required, unless Include “None” is on and the selected run estimated a None utility. In that case a single product against the None option is a valid scenario (purchase likelihood against no purchase). Below that floor the request is rejected.
• Maximum products: 20 per simulation. Hovering the Add button shows the current count (“Add product (3/20)”); at the limit the button is disabled and its tooltip reads “Maximum 20 products reached”.

4. The Three Simulation Methods

Choicery offers three methods for computing choice shares from individual-level utilities. Choosing the right method is the most important decision in simulation setup. Each method makes different trade-offs between precision, robustness to competitive structure, and interpretability.

The method is picked with the three-way selector at the top of the Choice Share tab. The options are labelled Share of Pref., RFC and First Choice, in that order. Share of Pref. is preselected. Hovering an option shows a one-line description of the method.

4.1 Randomized First Choice (RFC)

RFC is worth considering when the product set contains very similar competing products: it addresses IIA limitations via similarity-corrected Monte Carlo. It was proposed by Bryan Orme (1998) specifically to address limitations of the other two methods.

How it works

For each respondent, the simulator runs many simulated “shopping trips” (default: 1,000 iterations). In each trip:

1. Zero-mean Normal noise is added at the attribute level; optional independent product noise uses a centered Gumbel distribution.
2. Products that share attribute levels receive correlated noise (the same random shock for the shared level). This is the “similarity correction.”
3. The respondent “picks” the product with the highest noisy utility.

The product’s share for that respondent is the fraction of shopping trips in which it was chosen. Shares are then averaged across all respondents.

Controls

Selecting RFC reveals an Advanced Settings toggle below the method selector. Expanding it shows five fields:

• Iterations (starting value: 1,000; accepted range 100 to 10,000): the number of Monte Carlo shopping trips per respondent. Higher means more stable results but slower computation; required precision depends on sample size, product count, and the smallest share differences that matter.
• Attribute variability (default 1.3; range 0 to 5): the Normal error budget applied at the attribute level. 1.3 is a rounded, variance-matched starting value, not a calibrated one: π/√6 ≈ 1.28 is the standard deviation of a single unit-scale Gumbel error. The difference of two independent such errors is logistic, with variance π²/3 and standard deviation π/√3 ≈ 1.81. Two independent Normal errors with SD π/√6 have the same difference variance. That brings RFC close to Share of Preference for products with no shared levels, but not equal to it, because a Normal difference is not logistically distributed. For two fully dissimilar products with a utility gap of 1, RFC at 1.3 gives the better product about 70.7% while Share of Preference gives 73.1%, a gap of 2.4 points with no level overlap involved. Sawtooth describes the variability as something to calibrate for the scenario at hand rather than a universal constant, so treat 1.3 as the starting point of that calibration. The budget is split by variance over the k attributes that take part in the error model (the attributes whose levels differ between the products, every attribute when the None option is included because the products carry the draw and None does not, and an uncorrelated price attribute whenever there is more than one product) (each attribute draw has a standard deviation of variability / √k). With categorical level errors this gives each product the configured total SD. A single-coefficient linear attribute instead contributes a draw multiplied by its standardized value z, so its contribution to variance depends on z²; the None alternative receives one draw with the full budget. In the Sensitivity tab the swept attribute always counts towards k, so the split does not change at the base level. Calibrate it against holdouts where possible.
• Product variability (starting value: 0; range 0 to 5): optional independent product-level Gumbel error. 0 means off.
• Random seed (starting value: 1): the same seed always gives identical results. Clear the field to let the server pick a seed; the seed actually used is reported with the results either way.
• Price correlation (a Correlate toggle, off by default): normally left off, because a shared price error can create artificial kinks in demand curves.

Strengths and weaknesses

• Handles similar/clone products correctly (IIA correction)
• Balances precision with robustness
• The CSV export carries each product’s standard deviation across simulations (column Std (%)), a measure of Monte Carlo variability
• Stochastic: results vary by seed; the effective seed is recorded so a run can be reproduced exactly

4.2 Share of Preference (Logit / MNL Rule)

Share of Preference computes each respondent’s choice probability via the softmax function (the multinomial logit rule):

Each respondent “splits” their vote probabilistically across all products. A respondent with utilities of 5.0, 3.0, and 2.0 for three products doesn’t just vote for product 1: they give it a high probability (about 73%) while still allocating some probability to the other products.

Strengths and weaknesses

• Completely deterministic: no random variation, same result every time you run it
• More precise per respondent: extracts more information than 0/1 voting since each respondent distributes a full probability vector
• Susceptible to IIA (Independence of Irrelevant Alternatives): adding a near-clone product steals share from all products proportionally, not just from its close substitute (see Section 13)
• With HB individual-level utilities, IIA is “greatly reduced” but not eliminated (Orme, 2020)

4.3 First Choice (Maximum Utility Rule)

First Choice is the simplest method: each respondent votes for the single product with the highest total utility. No probabilities, no noise, just a straight vote.

Strengths and weaknesses

• Simplest to understand and explain: “Each person picks their favorite” is intuitive for management audiences
• Nearly eliminates IIA: each respondent makes a discrete choice, so clones only split one person’s vote at most
• Less precise: each respondent contributes 0 or 1 (not a probability), so larger samples are needed for stable shares
• Shares can be too extreme: a product that is slightly better for most respondents can capture a disproportionately high share
• Scale-invariant: multiplying all utilities by a constant does not change the winner

4.4 Which Method Should I Use?

The following table summarizes when each method is most appropriate:

5. The None Option

The Include “None” toggle, next to the method selector, adds a no-purchase alternative to the simulation. This represents respondents who would not buy any of the defined products. It is on by default.

Requirements

The None option is only available if the estimation behind the selected run included a None option (i.e., the conjoint design had a “none of these” alternative and a None utility was estimated). If it was not, the control area shows the note “None not available in active run”.

With vs. without None

When to include None

• Market size estimation: The None share indicates what fraction of the market is not served by the current product offerings.
• Purchase likelihood: A high None share suggests that the products in the scenario are unattractive to many respondents.
• Price sensitivity: As you raise prices, the None share increases, indicating respondents opting out rather than paying more.

6. Running and Interpreting Results

6.1 Running the Simulation

Click Run Simulation after defining your products and selecting a method. Results appear immediately for Share of Preference and First Choice, or after a moment for RFC with many iterations.

6.2 Share Cards and Bars

Each alternative gets a share card with its choice share as a percentage. The cards follow the order of the Products panel as it was when the simulation ran, with None last. The product with the highest share among the products carries a Winner tag; None never does, and no tag is shown when two products tie at one decimal place. Below the cards, a horizontal bar list shows the same shares sorted from largest to smallest, and a line above the cards states the None share in words when it is included.

A meta line under the bars records how the numbers were produced: the method, and for RFC the iteration count, the variability settings and the seed actually used, plus +None when the None option was included and the segment sample size when a filter is active. Quote that line whenever you report a share, because RFC numbers are only reproducible together with their seed.

6.3 Confidence Intervals

The CI button above the results computes 95% percentile confidence intervals for the shares by resampling respondents with replacement (200 bootstrap draws, seed 1). The interval is then printed on each share card and drawn as a marker on the bar, the meta line adds “95% CI B=200”, and the CI method, level, number of bootstrap draws and bootstrap seed are added to the CSV export. Use it before claiming that one product beats another: if the intervals overlap heavily, the ranking is not established by your sample.

6.4 Downloading Results

Two export buttons sit in the results header, next to CI, and a third below the result block:

• CSV writes choice_share.csv: a header block with the method and its parameters, the aggregate shares (with standard deviations and confidence intervals where available), and the per-respondent rows.
• PNG exports the cards and bars as an image for slides.
• Download Individual Data, below the result block, writes individual_data.csv with one row per respondent. For First Choice it contains the chosen product and the utility of every product; for Share of Preference and RFC it contains each respondent’s probability per product.

The individual file is useful for identifying respondent clusters, linking choices to survey demographics, or spotting unusual preference patterns. It is a download only: there is no inline per-respondent table in the tab.

6.5 Segmented Results

When filters are active (see Section 7), a second block appears below the main results with one sub-block per segment, each with its own share cards, bars, respondent count (n=...) and its own CSV / PNG buttons; the CI button appears once the segment result is stored and the segment has at least two respondents. The heading reads Choice Share (Segment: <name>) when exactly one filter is active, and Choice Share (Segments) when there are several. This answers: “Do different demographic or attitudinal groups prefer different products?”

6.6 The PDF Report

The PDF button at the right of the simulator tab bar exports the currently open tab. From Choice Share it produces the Choice Share Simulation report, containing the settings used, the active filters, the aggregate shares and, when present, the per-segment results. The export uses the results currently on screen, so run the simulation before requesting the PDF.

7. Product Sets, Filters & Price Setup

7.1 Saved Product Sets

A product set is the current product configuration stored under a name. This is how you keep “what-if” configurations side by side:

• Type a name into the Product set name field at the top of the Products panel and click Save Products.
• Reload a set later from Import → Saved Product Sets. Loading a set replaces the products currently in the panel and restores the name into the name field.
• Example workflow: save “Current Market” with the existing products, then add your proposed product, save it as “New Launch”, and switch between the two to compare shares.

7.2 Filters

The Filters button above the Products panel restricts the simulation to a subgroup of respondents based on their survey responses. The modal has a Categorical and a Numeric tab, and the variables offered are the survey variables of the active run sample (for AI-Driven Profile Analysis runs the Categorical tab offers the run’s profile groups instead):

• Categorical: pick one value per variable, for example Gender = Female or Region = North.
• Numeric: pick one condition per variable, using <, ≤, >, ≥ or =, for example Age ≥ 30. The condition is prefilled with ≤ the median of the variable.

Selected filters are listed in the modal; Apply activates them, Clear Filters removes them. When filters are active, the simulation is computed both for the full sample and for each filtered subgroup, so the overall result and the segment results stay comparable.

Filters work on the same people as the overall result: everyone in the selected estimation run. The answers come from the current data, so a value corrected in the Data Editor counts in its new group. A response moved to the bin after the run is still part of the run and therefore still counts in its segment; to leave it out of both, estimate the model again. Responses collected after the run are not part of it and appear in no segment.

7.3 Price Setup

Price Setup in the top bar opens the Global Price Setup dialog. It tells every market analysis method which attribute represents price, and for categorical price attributes what each level is worth numerically. Click Apply globally to store the choice. It is required for:

• WTP (Willingness to Pay): how much extra a respondent would pay for a feature improvement
• Reservation Price: the maximum price at which a respondent would still buy
• Price Elasticity: how share changes as price moves up or down

For categorical price attributes, you enter a numeric value per level (e.g., “Budget” = 19.99, “Standard” = 29.99, “Premium” = 49.99). For linear price, no mapping is needed since the levels are already numeric. If your study has no price attribute at all (a treatment or feature study), select the “(None - no price attribute)” entry and the price-based methods stay disabled.

The money amounts are shown in the currency selected in the top bar next to Price Setup; the selector also controls whether the symbol is printed before or after the number.

7.4 Analysis Settings

Analysis Settings, next to Price Setup, holds three shared toggles for the price-based tabs: Include unusual price responses in price analyses (keep respondents with a positive or near-zero price response), Exclude outliers (drop outliers before aggregation), and Allow negative prices. They apply to WTP, Reservation Price, Price Elasticity and the Sensitivity tab when it sweeps price. Choice Share always uses all respondents.

8. Best Practices & Common Pitfalls

Do

• Define realistic competitor products that reflect the actual market. Use real brands, real price points, and real feature sets.
• Start with Share of Preference (the UI default). It is recommended for HB-estimated data because it is fully deterministic (no Monte Carlo variance). Switch to RFC when the product set contains very similar competing products, and to First Choice when you want the strictest max-utility rule.
• Include the None option when estimating market size or purchase likelihood.
• Save a product set before making changes. You can always load the previous configuration back.
• Compare results across methods. If RFC, Share of Preference, and First Choice all agree on the ranking, your shares are robust.
• Use filters to understand how preferences differ across customer groups.
• Compute confidence intervals with the CI button before you claim that one product beats another.
• Name products clearly: “Brand A SUV 45k” tells you more at a glance than “Product 3.”

Don’t

• Don’t interpret simulated shares as actual market shares. They are “shares of preference” that do not account for distribution, awareness, brand equity beyond the conjoint attributes, or competitive advertising.
• Don’t add near-identical products and use Share of Preference. Use RFC or First Choice instead to avoid the IIA problem.
• Don’t run RFC at the low end of the iteration range. The field accepts 100, but results will be noisy; the starting value of 1,000 is a reasonable working minimum.
• Don’t report an RFC share without its seed. The meta line under the results carries the seed actually used, and it is the only way to reproduce the number.
• Don’t forget Price Setup before using the WTP or Price Elasticity tabs.
• Don’t compare shares across different product sets. Shares are relative to the products in the scenario. A product’s 40% share in a 3-product scenario means something different from its 25% share in a 5-product scenario.

9. Key Definitions

10. Share of Preference, The Logit Rule

10.1 Formula

The Share of Preference method applies the multinomial logit (softmax) function to each respondent’s utilities:

The aggregate share for product j is the average across all N respondents:

Where V_ij is the total utility of product j for respondent i, computed as the sum of part-worth utilities for the product’s attribute levels.

10.2 Properties

• Probabilistic: each respondent distributes a full probability vector across products, not a single vote.
• Deterministic: given the same utilities, the result is always identical (no random component).
• Scale-sensitive: the magnitude of utilities matters. Multiplying all utilities by 2 changes the shares (they become more extreme).

10.3 The Scale Factor Issue

CBC utilities estimated by HB tend to be too large in magnitude compared to real-world choice behavior. This produces simulated shares that are too extreme: the best product gets a share of, say, 85% when its real market share might be 35%.

A scale factor λ < 1 can be applied to flatten shares toward reality. Louviere (1988) suggests values around 0.3 to 0.5 depending on the study. With λ = 1.0, the raw HB utilities are used as-is.

10.4 The IIA Problem

The logit model has a well-known structural limitation: the Independence of Irrelevant Alternatives (IIA). This is covered in full detail in Section 13, but the key implication for Share of Preference is this: adding a product that is nearly identical to an existing one will draw share from all products proportionally, not just from the similar one. This can produce seriously misleading results when the competitive set includes similar products.

11. First Choice Rule

11.1 Formula

Each respondent votes for the single product with the highest total utility:

The standard error of each share estimate follows the binomial proportion formula:

This is the textbook standard error of a proportion. Choicery does not print it; the CI button uses a respondent bootstrap for all three methods (Section 6.3).

11.2 Properties

• Discrete votes: each respondent contributes exactly one vote. The share is the fraction of respondents who chose each product.
• Scale-invariant: multiplying all utilities by any positive constant does not change the argmax. The winner is the winner regardless of utility scale.
• Nearly IIA-free: since each respondent makes a single choice, adding a clone of Product A can at most change one respondent’s vote (the one who was choosing A but now slightly prefers the clone). This is a single discrete switch, not a proportional reallocation.

11.3 Limitations

• Less precise: With N respondents, the share estimate is based on N binary observations. Share of Preference, by contrast, uses N continuous probability values. This makes First Choice noisier for small samples.
• Extreme shares: A product that is slightly preferred by a slim majority can capture a very high share, because “slightly better” is treated the same as “overwhelmingly better.”
• No tuning: First Choice has no parameter at all, so there is nothing to calibrate against observed market shares. In Choicery, RFC is the only method of the three with tunable settings.

12. Randomized First Choice (RFC)

12.1 Origin

RFC was proposed by Bryan Orme in 1998 to combine the strengths of First Choice (IIA resistance) with those of Share of Preference (precision), while adding a similarity correction mechanism. It is widely used in conjoint analysis when product sets contain near-substitute alternatives.

12.2 The Algorithm

RFC is a Monte Carlo method. For each respondent, the algorithm runs M simulated “shopping trips” (Choicery starts at M = 1,000):

The critical detail is in how noise is applied: for an attribute using similarity correction, the random shock is drawn once per attribute level, not once per product. Every product that shares that level receives the exact same shock. Price is uncorrelated by default because correlated price error can create artificial kinks in demand curves; it can be enabled explicitly for a justified design.

12.3 Why This Fixes IIA

The key insight is that products sharing many attribute levels have highly correlated noise. If two products share 4 out of 5 attributes, 80% of their random shocks are identical. When one gets a positive shock, the other does too. This means:

• In trips where both get positive shocks, they compete intensely with each other for the top spot.
• A dissimilar product benefits only when the shared attribute levels happen to get negative shocks.
• The net effect: near-identical products primarily cannibalize each other, not dissimilar products, exactly the realistic substitution pattern that IIA-afflicted logit models miss.

12.4 Special Cases

RFC generalizes both other methods as limiting cases:

12.5 Choicery Implementation

In Choicery, the RFC defaults are:

• Iterations (M): 1,000 shopping trips per respondent. With modern hardware, this runs in seconds even for large samples.
• Attribute variability: 1.3 as the total Normal error budget per product, a variance-matched starting value (π/√6) that brings RFC close to Share of Preference for dissimilar products without reproducing it exactly (see Section 4.1). It is a configuration default in the server limits, not a value fitted to your holdout data; Sawtooth treats the variability as something to calibrate per scenario. The None alternative receives its own Normal draw with the same total standard deviation, so it is not systematically disadvantaged against the noisy products.
• Product variability: 0. Optional product-level Gumbel error is disabled unless explicitly configured.
• Price correlation: off. Price perturbations are independent by product unless explicitly enabled.
• Random seed: the field starts at 1, so an unchanged setup reproduces itself. Clearing the field makes the server draw a seed; either way the seed used is recorded with the result for exact reruns.

Iterations, attribute variability and product variability are also bounded server-side: iterations must stay within the accepted range, and both variability parameters within 0 to 5.

13. The IIA Problem

The Independence of Irrelevant Alternatives (IIA) is the single most important theoretical issue in market simulation. Understanding it is essential for choosing the right simulation method and interpreting results correctly.

13.1 Formal Definition

A choice model satisfies IIA if, for any two alternatives A and B:

This is a direct consequence of the logit model’s mathematical structure (McFadden, 1974). In the softmax function, each product’s probability depends only on its own utility relative to the sum of all utilities: there is no notion of “similarity” between products.

13.2 The Red Bus / Blue Bus Problem

This is the classic illustration of IIA, originally described by McFadden (1974):

13.3 The Coke / Pepsi / Milk Example

A more practical illustration relevant to conjoint research:

13.4 Why HB Helps

With aggregate-level (pooled) utilities, every respondent has the same preferences, and IIA is at its worst. HB (Hierarchical Bayes) individual-level utilities substantially reduce the IIA problem (Orme, 2020).

Here is why: different respondents have different preference patterns. Some are brand-loyal (Coke lovers who would never drink Pepsi), others are price-sensitive (switching at any price difference), and others have unique idiosyncratic preferences. When you average across these heterogeneous individual choices, the aggregate substitution patterns become more realistic.

However, HB does not fully eliminate IIA. Within each respondent’s logit model, the IIA property still holds. The correction comes from aggregating across heterogeneous respondents, not from fixing the model at the individual level.

13.5 Why RFC Goes Further

RFC adds an additional layer of IIA correction on top of HB’s individual-level heterogeneity. The attribute-level correlated shocks create explicit similarity-based substitution:

• Products sharing many attribute levels get highly correlated noise, so they substitute heavily from each other.
• Products sharing few attribute levels get nearly independent noise, so adding one barely affects the other.
• This similarity correction operates at the individual respondent level within each Monte Carlo trip, providing IIA resistance even for a single respondent.

The combination of HB heterogeneity + RFC similarity correction provides the strongest defense against IIA in practical conjoint simulation.

14. Practical Considerations

14.1 Shares of Preference vs. Actual Market Shares

Simulated choice shares should never be equated with actual market shares. They represent preference shares, the share of stated preferences among the defined products, given the attributes measured in the conjoint study.

To convert preference shares to approximate market share predictions, you would need to account for many factors not captured in the conjoint model:

• Distribution: a product not available in a respondent’s region cannot be purchased regardless of preference.
• Awareness: respondents may not know a product exists in the real market.
• Brand equity: aspects of the brand not captured by conjoint attributes (heritage, emotional attachment, social signaling).
• Loyalty and habit: inertia keeps people buying what they know.
• Competitive activity: advertising, promotions, and shelf placement are not modeled.

14.2 Source of Volume Analysis

One of the most actionable analyses you can perform is a Source of Volume (or “switchback”) analysis:

1. Run a simulation without Product X (the product you are considering launching).
2. Run the same simulation with Product X.
3. Compare: the share that each competitor lost is Product X’s source of volume.

14.3 Sensitivity Analysis

Systematically varying one attribute level while holding all others constant produces a demand curve (or “sensitivity plot”) for that attribute. For price, this is a classic price-response curve:

• Set up a baseline scenario with realistic competitor products.
• Vary the price of your product across a range (e.g., from the lowest to highest design level).
• Record the share at each price point.
• Plot price vs. share to see the demand curve and identify optimal pricing.

The same approach works for any attribute: vary the feature level and observe how share responds. This reveals which attribute improvements have the greatest impact on market position.

You do not have to do this by hand. The simulator carries a Sensitivity tab that sweeps an attribute automatically against the products you defined, and a Price Elasticity tab that produces the price-response curve and the elasticity for a focal product. Both have their own methodology guides, reachable from the Guide button on those tabs.

14.4 Comparing Methods as a Robustness Check

Running the same scenario with all three methods serves as a robustness check:

• If all three methods produce similar rankings and similar magnitudes, the results are robust and not sensitive to modeling assumptions.
• If Share of Preference and RFC disagree significantly, IIA may be distorting the Share of Preference results. Trust RFC.
• If First Choice and Share of Preference agree but RFC differs, the similarity correction is having a large effect: check whether products in the scenario share many attribute levels.