Table 3 Nonresponse bias and R-indicator formulas for reinterview and cumulative participation

Reinterview participation

Reinterview nonresponse bias_c,w

\({\overline{Y} }_{i,r,c,w}-{\overline{Y} }_{i,n,c,w}\)

(5)

Reinterview refusal bias_c,w

\({\overline{Y} }_{i,r,c,w}-{\overline{Y} }_{i,k,c,w}\)

(6)

Reinterview noncontact bias_c,w

\({\overline{Y} }_{i,k,c,w}-{\overline{Y} }_{i,n,c,w}\)

(7)

Cumulative participation

Cumulative nonresponse bias_c,w

\({\overline{Y} }_{i,r,c,w}-{\overline{Y} }_{i,n,c,1}\)

(8)

Reinterview participation

Absolute relative reinterview nonresponse bias_c,w

\(\left|\frac{{\overline{Y} }_{i,r,c,w}-{\overline{Y} }_{i,n,c,w}}{{\overline{Y} }_{i,n,c,w}}\right|\)

(9)

Absolute relative reinterview refusal bias_c,w

\(\left|\frac{{\overline{Y} }_{i,r,c,w}-{\overline{Y} }_{i,k,c,w}}{{\overline{Y} }_{i,k,c,w}}\right|\)

(10)

Absolute relative reinterview noncontact bias_c,w

\(\left|\frac{{\overline{Y} }_{i,k,c,w}-{\overline{Y} }_{i,n,c,w}}{{\overline{Y} }_{i,n,c,w}}\right|\)

(11)

Cumulative participation

Absolute relative cumulative nonresponse bias_c,w

\(\left|\frac{{\overline{Y} }_{i,r,c,w}-{\overline{Y} }_{i,n,c,1}}{{\overline{Y} }_{i,n,c,1}}\right|\)

(12)

Reinterview participation

Average absolute relative reinterview nonresponse bias_c,w

\(\frac{{\sum }_{i=1}^{V}\left|\frac{{\overline{Y} }_{i,r,c,w}-{\overline{Y} }_{i,n,c,w}}{{\overline{Y} }_{i,n,c,w}}\right|}{V}\)

(13)

Average absolute relative reinterview refusal bias_c,w

\(\frac{{\sum }_{i=1}^{V}\left|\frac{{\overline{Y} }_{i,r,c,w}-{\overline{Y} }_{i,k,c,w}}{{\overline{Y} }_{i,k,c,w}}\right|}{V}\)

(14)

Average absolute relative reinterview noncontact bias_c,w

\(\frac{{\sum }_{i=1}^{V}\left|\frac{{\overline{Y} }_{i,k,c,w}-{\overline{Y} }_{i,n,c,w}}{{\overline{Y} }_{i,n,c,w}}\right|}{V}\)

(15)

Cumulative participation

Average absolute relative cumulative nonresponse bias_c,w

\(\frac{{\sum }_{i=1}^{V}\left|\frac{{\overline{Y} }_{i,r,c,w}-{\overline{Y} }_{i,n,c,1}}{{\overline{Y} }_{i,n,c,1}}\right|}{V}\)

(16)

Reinterview and cumulative participation

Sample-based R-indicator \(R\left(\rho \right)\) (Schouten et al. 2009)

\(1-2\sqrt{\frac{1}{n-1}\sum_{j=1}^{n}{({\rho }_{j}-\overline{\rho })}^{2}}\)

(17)