Indices of non-ignorable selection bias for proportions estimated from non-probability samples

Rising costs of survey data collection and declining response rates have caused researchers to turn to non-probability samples to make descriptive statements about populations. However, unlike probability samples, non-probability samples may produce severely biased descriptive estimates due to selection bias. The paper develops and evaluates a simple model-based index of the potential selection bias in estimates of population proportions due to non-ignorable selection mechanisms. The index depends on an inestimable parameter ranging from 0 to 1 that captures the amount of deviation from selection at random and is thus well suited to a sensitivity analysis. We describe modified maximum likelihood and Bayesian estimation approaches and provide new and easy-to-use R functions for their implementation. We use simulation studies to evaluate the ability of the proposed index to reflect selection bias in non-probability samples and show how the index outperforms a previously proposed index that relies on an underlying normality assumption. We demonstrate the use of the index in practice with real data from the National Survey of Family Growth.