Estimation efficiency of RP/SP models considering SP design and error structures

SP attribute values are sometimes set X times or 1/X times the RP attribute values in the direction that changes respondents' RP behaviour. In estimating RP/SP models, assumptions on error structures are required: (a) RP and SP have both a common error component and independent error components (general model); (b) RP and SP have a common error component and SP only has an independent error component (SP-off-RP model); (c) RP and SP have independent error components only (independent model); and (d) RP and SP have a common error component only (double-bound model). This study simulates and examines the estimation efficiency of RP/SP models based on the D-error considering both error structures and attribute differences. Insights obtained are the following. (1) The general model offers better estimation efficiency in the neighbourhood of X=1.0. (2) For the SP-off-RP model and the independent model, the larger the variance in the error components of the SP model relative to the RP model, the larger the value of X that is required to minimise the D-error. The authors propose a method for designing an SP experiment in which the level-of-service of the SP differs from that of the RP by only a single attribute value.