Why is there no frequency value when using the "Utils" method of reach?
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. The frequency values will not be displayed when using the “Utils” method.
In TURF, the key performance metrics are reach and frequency. Generally speaking:
- 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:
$$ \textrm{Reach}_{iJ} = \frac{ \sum_{ij}{e^{u_{ij}}} }{ \sum_{ij}{e^{u_{ij}}} + (\textrm{Number of alternatives}) - 1 } $$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.
- $$e$$ is the base of the natural logarithm.
- $$\textrm{Number of alternatives}$$ is the number of alternatives in the original conjoint exercise.
Reach for the full combination $$J$$ 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.
Individual reach by item
It is also possible to calculate individual reach by item using the formula:
$$ \textrm{Reach}_{ij} = \frac{ e^{u_{ij}} }{ e^{u_{ij}} + (\textrm{Number of alternatives}) - 1 } $$You can see example calculation in Excel.