Share of Preference Options

These options do not assume that the respondent always chooses the product with highest utility. Instead, they estimate probability of choosing the simulated product, arriving at a "share of preference" for the product.

This is done in two steps:

1.   Subject the respondent's total utilities for the product to the exponential transformation (also known as the antilog): s = exp(utility).

2.   Rescale the resulting numbers so they sum to 100.

Suppose two products, A and B, have total utilities 1.0 and 2.0. Then their shares of preference would be computed as follows:

product                 share of

utility   exp(utility)  preference

A         1.0       2.72          26.9

B         2.0       7.39          73.1

(For the Share of Preference with Correction for Product Similarity, shares of preference are modified by further computations.)

Unlike the First Choice option, the scaling of utilities can make a big difference with the Share of Preference Options. Consider what happens if we multiply the utilities by constants of 0.1 or 10.0:

For multiplier of 0.1

product                 share of

utility   exp(utility)  preference

A         1.0       1.105         47.5

B         2.0       1.221         52.5

For multiplier of 10.

product                 share of

utility   exp(utility)  preference

A         10.0      22026        100.005

B         20.0      4.85E08       99.995

If we multiply the utilities by a small enough constant, the shares of preference can be made nearly equal. If the utilities are made small enough, every product receives an identical share of preference, irrespective of the data.

If we multiply the utilities by a large enough constant, the shares of preference can be made equivalent to the First Choice model.

It is apparent that scaling of the utilities can make a big difference with the Share of Preference Models. Most of Sawtooth Software's utility estimation methods result in utilities appropriate for use with Share of Preference models. We strongly suggest you include holdout (fixed) choice tasks in your conjoint questionnaires to use for calibration, or check the simulation predictions against actual market share.

The Market Simulator lets you scale the utilities within the Share of Preference option at the time the simulation is done. This is accomplished by a parameter called the "exponent" that you can set when preparing for simulations. The default value of the exponent is 1. It has the same effect as the multiplier illustrated immediately above. The exponent can be used to adjust the sensitivity of the simulation results so that it more accurately reflects holdout choices, or actual market behavior.

A smaller exponent causes small shares to become larger, and large shares to become smaller — it has a "flattening" effect. In the limit, with a very small exponent every product receives the same share of preference.

A large exponent causes large shares to become larger, and small shares to become smaller — it has a "sharpening" effect. In the limit, a very large exponent produces results like those of the First Choice option.

If you have solid external information (such as existing market share data) and have reason to expect that conjoint shares should resemble market shares, you may want to tune the exponent within simulations. If you do not have solid external information, you probably should not change the exponent from the default value of 1.

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Share of Preference Model with Correction for Product Similarity

Share of preference models that do not consider similarities among products have a serious problem: if an identical product is entered into the simulation twice, it can receive up to twice as much total share of preference as it would when entered only once. Although no researcher would make the mistake of entering the same product twice, the principle is still troublesome. Products differ in similarity to one another, and "plain" share of preference models tend to give too little share to relatively unique products.

The third choice model in the Market Simulator includes a correction to prevent the preference shares of similar products from being overstated. The correction is based on each product's total similarity with other products. The basic idea behind this correction was suggested by Richard D. Smallwood of Applied Decision Analysis, although we are responsible for the details of
its implementation.

The procedure is:

1.

For the n products in a simulation, an n x n similarity matrix is computed, with 1's indicating complete similarity, 0's indicating total lack of similarity, and fractional values for differing degrees of similarity:

First a "dissimilarity" matrix is computed. Consider a scale for each attribute where its levels are coded 10, 20, 30, and so on. The dissimilarity of a pair of products on an attribute is taken as the absolute difference between their codes, but with a maximum of 10. (This allows "continuous" and "categorical" attributes to be treated in the same way.) The total dissimilarity between two products is the sum of their dissimilarities over all attributes. Two products differing by an entire level on each attribute are maximally dissimilar.

Next, total dissimilarities are rescaled by a constant so the maximum possible is 3.0, rather than 10 times the number of attributes.

Dissimilarities are then converted to similarities by a negative exponential transformation. At this point the minimum possible similarity is exp(-3) ~ .05, achieved if two products have completely different levels on every attribute, and the maximum possible similarity is exp(0) = 1, achieved only if they have identical levels on all attributes.

Finally, the similarities are subjected to a further rescaling that sets the minimum to 0 and the maximum to 1.

2.

Column totals of the similarity matrix are calculated to get a vector of "total similarities." The smallest possible value is 1.0, which is found if a product is maximally dissimilar to all others and similar only to itself. If two products are identical but maximally dissimilar to all others, those products each have values of 2.0.

3.

For each respondent, shares of preference are divided by corresponding "total similarities," and then renormalized to have sum of unity. This has the effect of reducing shares for products that are relatively similar to others, and increasing shares for products that are relatively unique. In the limit, where two or more products are identical and totally unlike any others, they divide among themselves the share that each product would have if the others were not present.