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An expression for bias in an estimate of the change in the presence of non-ignorable nonresponse (308151)

Keywords: nonresponse bias, nonresponse rate, non-ignorable response, change, survey quality.

A well-known expression for nonresponse bias, due to Bethlehem (1988, 2009), is the ratio of the covariance between the study variable and the response probability to the mean of the response probability. We extend this expression to the nonresponse bias in an estimate of the change, that is, the difference between a total at time 1 and the total at time 2. We also discuss whether there is a ’safe area’, where the nonresponse rate has only a modest effect on bias despite non-ignorable nonresponse, thus extending Hedlin (in print) from an estimate of the level to an estimate of the change. Reference: Hedlin, D. (in print). Is there a ‘safe area’ where the nonresponse rate has only a modest effect on bias despite non-ignorable nonresponse? International Statistical Review.