The "Utils" method of calculation of reach in TURF
The “Utils” method of calculating reach in TURF analysis is optimised for data that represents individual-level utilities from HB models of conjoint and MaxDiff studies.
Generally speaking, in TURF, the key performance metrics are reach and frequency:
- Reach is the percentage of the sample that is “reached” by items in the combination, and
- Frequency is the average number of times a reached respondent is reached.
When using the “Utils” method to compute reach, each respondent’s reach is the probability of them being reached using the formula:
$$ \textrm{Reach}_{iJ} = \frac{ \sum_{ij}{e^{u_{ij}}} }{ \sum_{ij}{e^{u_{ij}}} + N - n_J } $$Where:
- $$\textrm{Reach}_{iJ}$$ is the reach of respondent $$i$$ for combination $$J$$ .
- $$u_{ij}$$ is the utility in column $$j$$ for respondent $$i$$ , which is zero-centred for each respondent.
- $$N$$ is the number of total levels in the original conjoint exercise.
- $$n_J$$ is the number of items in this particular combination.
Reach for the combination $$J$$ across all respondents is the mean of the reaches for each respondent:
$$ \textrm{Reach}_{J} = \sum_{i}{\textrm{Reach}_{iJ}} $$Because the values of $$\textrm{Reach}_{iJ}$$ are between 0 and 1, there is no place to compute a discrete number of reached respondents. Hence, the frequency calculation cannot be performed when using the “Utils” method.
Individual reach by item
It is also possible to calculate individual reach by item using the formula:
$$ \textrm{Reach}_{ij} = \frac{ e^{u_{ij}} }{ e^{u_{ij}} + N - 1 } $$You can see example calculation in Excel.