How to Manually Calculate Partworth Utilities
This guide describes how to manually calculate partworth utilities. This replicates the calculation of standard Conjoint.ly outputs for an example Generic Conjoint regarding different mobile plan options.
To replicate the calculation in your report, firstly export the raw data from your survey. Navigate to the Individual preferences tab. Within this tab you will see individual preferences for each level tested.
Relative importance by attribute (Attribute partworths)
To calculate the attribute partworths:
Step 1: Calculate the range of preference within each attribute for each individual. This is defined as the maximum preference value within each attribute, minus the minimum for each individual.
Step 2: Calculate the importance ratio of each attribute for each individual. This is the range of preference for each attribute, divided by the total sum of all range of preferences for the individual.
Step 3: Calculate the average importance across respondents, through averaging the importance ratios across all respondents.
Relative value by level (Level partworths)
To calculate level partworths:
Step 1: Calculate the average preference across individuals for each level, through averaging the utility across each column.
Step 2: Within each attribute, scale the partworth utility to set 0 as average. This is performed through subtracting the value for each level from the sum across the corresponding attribute.
Step 3: Scale the partworth utility across each attribute. This is done through dividing the level utility by the overall utility range for all attributes which is the sum of range utility of each level’s average utility across respondents for each attribute.
Distribution of preferences for levels
To calculate the distribution of preferences for each level:
Step 1: Scale the level utility with exponential function.
Step 2: Calculate the ratio of level utility within each attribute for each respondent, by dividing the level utility by the overall utility for this attribute.
Step 3: Average the ratio of level utility across respondents.
Distribution of most preferred levels
To calculate the distribution of preferred levels:
Step 1: Identify the most preferred level within each attribute.
Step 2: Calculate the percentage of the level is most preferred across respondents (with the average most preferred value across respondents)