We consider models that underlie two proposals to estimate nonparticip
ation bias. The first model posits a ''continuum of resistance,'' plac
ing people who were interviewed during the first contact on one end of
the continuum and nonparticipants on the other. The second model assu
mes that there are different classes of nonparticipants and that simil
ar classes can be found among participants; it then uses groups of par
ticipants thought to be like nonparticipants to estimate the character
istics of non-participants. We examine the justification for these mod
els of the relationship between participants and nonparticipants and c
onsider how well proposed methods based on these models describe nonpa
rticipants and the impact of nonparticipation on survey estimates. The
case we analyze is estimats of means of child support awards and paym
ents in Wisconsin. We find that neither model is successful and that t
he versions of the methods we use do not detect the true extent of non
participation error in estimates based on the unadjusted sample mean.
This failure occurs both for an external measure that is not contamina
ted with response errors and for self-reports. But response errors, wh
ich are not considered in the models we have found in the literature,
substantially worsen matters.