Guadagni Little Index

The Guadagni Little Index is a key figure developed in 1983 to measure brand loyalty . For this purpose, the brand choice of the buyer examined is determined for several subsequent purchases.

The formula for the Guadagni Little Index for a specific purchase is as follows: ${\displaystyle \rho _{t}}$ ${\displaystyle t}$

${\displaystyle \rho _{t}:=\alpha \rho _{t-1}+(1-\alpha )X_{t}}$

This equals 1 if the brand that has been bought the most so far was also used in the current act of purchase, otherwise 0. So is a Boolean variable . ${\displaystyle X_{t}}$ ${\displaystyle X_{t}}$

This index is recursively calculated using exponential smoothing : The index for the current purchase act (i.e. ) is calculated from the brand selection for the current act and from the index value for the previous purchase act (read:) . ${\displaystyle \rho _{t}}$ ${\displaystyle \rho _{t-1}}$

In a perfect marks un loyal buyers (equal distribution of the purchases of all brands) of Guadagni-Little-index reaches a value of 1 / (number of brands in the selection set), while a completely brand-loyal buyers (who always takes the same brand) its value at 1 lies.

The value is a weighting factor: the higher it is, the more past purchases are included . A suitable value for has to be selected according to the research question when using the Gaudagni Little Index . ${\displaystyle \alpha ~(\alpha \in [0;1])}$ ${\displaystyle \rho _{t}}$ ${\displaystyle \alpha }$

The Guadagni Little Index is used relatively frequently in market research. However, since it only takes into account the most frequently purchased brand, its validity is only moderate.