I'm seeking direction for the fit of a 5-point Likert scale attitudinal survey response to a 4-point scale that omits the center or Neutral response.
I am challenged by a very large corporate customer to assign and justify the assignment of the mid-range respondent answers to a 4-point model ranging from very satisfied to very dissatisfied. My results overall do not fit a normal distribution; rather, they skew strongly positive with the largest response frequencies being Very Satisfied (47% of total) and Satisfied (40% of total). The customer assumes that Neutral responses should be assigned to the negative, while I believe there is likely a proven approach to dividing the Neutrals between positive and negative satisfaction that mirrors the proportional split between the Very Satisfied and Satisfied versus the Dissatisfied and Very Dissatisfied.
Is there an approach that is supported by statistics and attitudinal research I should be following?