Interpolating between Levels

Sometimes you may want to simulate a product that has a level in between two levels you measured. This is called interpolation, and it is usually a reasonable thing to do when dealing with attributes that are quantitative in nature (price, speed, etc.). The market simulator uses a straight-line interpolation between adjacent part-worths.

Consider the following attribute:

Level #     Level Text

1           5 pages per minute

2          10 pages per minute

3          15 pages per minute

4          20 pages per minute

The simulator lets you specify a level code between two levels you measured. For instance, level 2.5 represents the point half-way between 10 and 15 pages per minute, or 12.5 pages per minute. Twelve pages per minute represents a value 40% of the way between 10 and 15 pages per minute. Therefore, level 2.4 corresponds to 12 pages per minute. But there is a much easier way to interpolate between levels. You may find it more convenient to refer to levels of quantitative attributes in the Market Simulator using values other than the original level numbers. When you click Assign Level Values, you can assign values to represent levels, such as:

Level #   Level Value      Level Text

1          5                5 pages per minute

2         10               10 pages per minute

3         15               15 pages per minute

4         20               20 pages per minute

It is much easier to specify products in the market simulator after recoding level numbers to values that match the pages per minute. To simulate a product at 12 pages per minute, we would now specify "12" for speed.

Three additional points are worth mentioning regarding recoding attribute levels for use in the simulator:

1.

Interpolation only works correctly if all values are either ascending or descending for an attribute.

2.

If you want to omit an attribute from simulations, you must omit it for all products in the simulation. You omit a level by specifying "N/A" (you type these characters) instead of a numeric code.

3.

If linear terms (coefficients) were estimated instead of part-worths for a quantitative function such as price, you should make sure not to change the level values from those that your consultant provided. For example, if the coded values for a linear price term were -2, 0 and +2 (corresponding to zero-coded values representing $2, $4, and $6), it would not be appropriate to change those to 200, 400, 600, as a utility effect 100 times the appropriate effect would be applied in simulations. The Market Simulator zero-centers (but doesn't standardize) all coded values for linear terms before multiplying by the utility coefficients. Thus, values under Assign Level Values... of 2, 4, 6 would be applied the same as 100, 102, 104 or 52, 54, 56. After zero-centering, these three different coding schemes would be applied as -2, 0, +2 in simulations.

For more information about how the Market Simulator interpolates between levels when interaction terms are involved, please see the Appendix entitled: "How the Simulator Interpolates between Levels."