How Much is Too Much? Using Non-linear Modeling to Identify Saturation Effects and Optimal Zones of Intervention

Jan Müller, Tatiana Mochalova, Gabriele Eckstein
Ipsos Loyalty Hamburg
Presented at the 13th Frontiers in Service conference, Taipei, Taiwan

Traditional  methods  of  customer  satisfaction  research  like  regression  analysis  build  on linear modeling to identify key drivers of customer satisfaction. Strong drivers with a low level of satisfaction are taken as the primary targets of intervention in order to optimize overall  satisfaction.  These  methods  assume  a  linear  relationship  between  performance and  satisfaction.  Such  an  assumption  is  often  justified.  There  are,  however,  important exceptions.  Linear  models  fall  short  when  it  comes  to  the  identification  of  saturation effects  or  zones  where  changes  of  performance  yield  a  maximum effect.  Real-life market-research  examples  are  the  maximum  tolerable waiting  time  on  telephone hotlines or the relationship between satisfaction and the opening hours of shops.

We  present  a  methodology  that  builds  on  non-linear  modeling  to  identify  saturation effects. Our approach is based on least-squares estimation and bootstrapping. If adequate, a non-linear modeling of customer satisfaction does not only improve model fit but yields additional  qualitative  insights  when  the  shape  of  the  curve  of  the  fitted  function  is  taken into  consideration.  We  therefore  put  special  emphasis  on  the  choice  of  the  non-linear function and the interpretability of its shape. While the choice of the function depends on
the  circumstances,  we  found  that  fitting  an  S-shaped  logistic  function  is  especially well-suited  to  customer  satisfaction  research.  Its  mathematical  properties  provide  a heuristic to identify saturation zones and optimal zones of intervention.

Using  real-life  data,  we  demonstrate  how  a  multivariate  analysis  of  non-linear  effects  is conducted  by  integrating  the  approach  into  structural  equation  modeling.  Saturation effects  are  visualized  by  an  improved  action  portfolio  chart  that  takes  non-linear  effects into account.