Relative importance of a conjoint attribute as its share of the total part-worth range

Takes the range of an attribute's part-worths, the difference between its most and least preferred levels over the levels in the study, and divides it by the sum of the ranges of all attributes. Written here for three attributes; with K attributes the denominator has K ranges. The share depends on the levels chosen, so it describes the study's design as much as the respondent.

Signature

RI_1 = r_1 / (r_1 + r_2 + r_3)
Inputs
InputsDefinitionUnit
r_1Largest minus smallest part-worth of attribute 1, the reference level counting as 0rating points or utility
r_2Largest minus smallest part-worth of attribute 2rating points or utility
r_3Largest minus smallest part-worth of attribute 3rating points or utility
Output
RI_1Share of the total part-worth range taken by attribute 1proportion

Function

Decomposition of whole-profile ratings into attribute part-worths in conjoint analysis

Maps a respondent's ratings of profiles, each described by levels of several attributes, to a part-worth for each level under an additive model, so that a profile's value is the intercept plus the part-worths of its levels. One level of each attribute is the reference, with a part-worth of zero. Relative importance and trade-offs between attributes follow from the part-worths. The notation follows the Conjoint Analysis article, whose outpatient clinic example is used throughout.

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Implementations

  • Excel

    Relative importance from named attribute ranges

    With the ranges in RangeOne, RangeTwo and RangeThree, the formula returns the first attribute's importance, held in ImportanceOne; ImportanceTwo and ImportanceThree follow by swapping the numerator. A dummy-coded attribute's range is =MAX(0,LevelWorths)-MIN(0,LevelWorths) over its non-reference part-worths.

    =RangeOne/(RangeOne+RangeTwo+RangeThree)

Assumptions

  • Ranges computed over the levels included in the conjoint study

    Each range covers only the levels shown, so a wider range of waits would raise waiting time's share without any change in preferences.

  • All attribute ranges on the same part-worth scale

    The ranges come from one model for one respondent or one pooled sample, so they share a scale.

Worked examples

  • Waiting time importance in the outpatient clinic example

    Ranges of 3.00 for waiting time, 1.50 for location and 1.00 for clinic lead give waiting time a share of 3.00 / 5.50, about 0.5455 (54.5 per cent in the article).

    r_1 = 3; r_2 = 1.5; r_3 = 1; RI_1 = 0.5455

  • Clinic lead importance in the outpatient clinic example

    Putting clinic lead first, 1.00 / 5.50 gives about 0.1818, the 18.2 per cent in the article; location takes 27.3 per cent.

    r_1 = 1; r_2 = 3; r_3 = 1.5; RI_1 = 0.1818

  • Waiting time importance with a 26-week maximum wait

    If value fell linearly by 0.375 a week, a range of waits from 4 to 26 weeks would give a waiting time range of 8.25 and a share of about 0.7674, against 0.5455 with a 12-week maximum (computed here for illustration).

    r_1 = 8.25; r_2 = 1.5; r_3 = 1; RI_1 = 0.7674

Common errors

  • Adding intermediate levels changes importance

    Relative importance rises with the number of levels defining an attribute even with the minimum and maximum fixed; in one study price's importance rose by seven percentage points when two intermediate levels were added to three.

  • Using signed part-worths in place of ranges

    Dividing minus 3.00 by the sum of the signed part-worths, minus 2.50, gives 1.2, a share above 1; ranges are differences between the best and worst levels and cannot be negative.

  • Comparing importances across studies with different level ranges

    An importance holds only over the levels in its own study; a 26-week maximum wait gives waiting time 0.77 instead of 0.55 with the same per-week preference.

Sources

  • Relative importance as the difference between the best and worst level weights

    Hauber AB, González JM, Groothuis-Oudshoorn CGM, Prior T, Marshall DA, Cunningham C, IJzerman MJ, Bridges JFP. Statistical methods for the analysis of discrete choice experiments: a report of the ISPOR Conjoint Analysis Good Research Practices Task Force. Value in Health. 2016;19(4):300-315. doi:10.1016/j.jval.2016.04.004. Section Interpreting the Results of the Conditional Logit Model: the difference in preference weights between the best or most preferred level of an attribute and the worst or least preferred level provides an estimate of the relative importance of that attribute over the range of levels included in the experiment, and the report compares attributes by the ratio of these differences (a severe to mild side effect change yields about 1.2 times the utility of the efficacy change); dividing each range by the total, as here, is a presentation of the same differences.

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  • Relative importance rises with the number of levels of an attribute

    Green PE, Srinivasan V. Conjoint analysis in marketing: new developments with implications for research and practice. Journal of Marketing. 1990;54(4):3-19. doi:10.1177/002224299005400402. Section Stimulus Set Construction: the relative importance of an attribute increases as the number of levels on which it is defined increases, even though its minimum and maximum are held fixed; for instance, the relative importance of price went up by seven percentage points when two more intermediate levels were added to the three levels used for price.

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Canonical Identity

Persistent URI
https://healtheconomics.wiki/formula/relative-importance-of-a-conjoint-attribute-as-its-share-of-the-total-part-worth-range

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