estimate_var_tsa {psychmeta}

Taylor Series Approximation of effect-size variances corrected for psychometric artifacts

Description

Functions to estimate the variances corrected for psychometric artifacts. These functions use Taylor series approximations (i.e., the delta method) to estimate the corrected variance of an effect-size distribution.

The available Taylor-series functions include:

• estimate_var_tsa_meas: Variance of \rho corrected for measurement error only

• estimate_var_tsa_uvdrr: Variance of \rho corrected for univariate direct range restriction (i.e., Case II) and measurement error

• estimate_var_tsa_bvdrr: Variance of \rho corrected for bivariate direct range restriction and measurement error

• estimate_var_tsa_uvirr: Variance of \rho corrected for univariate indirect range restriction (i.e., Case IV) and measurement error

• estimate_var_tsa_bvirr: Variance of \rho corrected for bivariate indirect range restriction (i.e., Case V) and measurement error

• estimate_var_tsa_rb1: Variance of \rho corrected using Raju and Burke's TSA1 correction for direct range restriction and measurement error

• estimate_var_tsa_rb2: Variance of \rho corrected using Raju and Burke's TSA2 correction for direct range restriction and measurement error. Note that a typographical error in Raju and Burke's article has been corrected in this function so as to compute appropriate partial derivatives.

Usage

estimate_var_tsa_meas(mean_rtp, var = 0, mean_qx = 1, mean_qy = 1, ...)

estimate_var_tsa_uvdrr(
  mean_rtpa,
  var = 0,
  mean_ux = 1,
  mean_qxa = 1,
  mean_qyi = 1,
  ...
)

estimate_var_tsa_bvdrr(
  mean_rtpa,
  var = 0,
  mean_ux = 1,
  mean_uy = 1,
  mean_qxa = 1,
  mean_qya = 1,
  ...
)

estimate_var_tsa_uvirr(
  mean_rtpa,
  var = 0,
  mean_ut = 1,
  mean_qxa = 1,
  mean_qyi = 1,
  ...
)

estimate_var_tsa_bvirr(
  mean_rtpa,
  var = 0,
  mean_ux = 1,
  mean_uy = 1,
  mean_qxa = 1,
  mean_qya = 1,
  sign_rxz = 1,
  sign_ryz = 1,
  ...
)

estimate_var_tsa_rb1(
  mean_rtpa,
  var = 0,
  mean_ux = 1,
  mean_rxx = 1,
  mean_ryy = 1,
  ...
)

estimate_var_tsa_rb2(
  mean_rtpa,
  var = 0,
  mean_ux = 1,
  mean_qx = 1,
  mean_qy = 1,
  ...
)

Arguments

mean_rtp

Mean corrected correlation.

var

Variance to be corrected for artifacts.

mean_qx

Mean square root of reliability for X.

mean_qy

Mean square root of reliability for Y.

...

Additional arguments.

mean_rtpa

Mean corrected correlation.

mean_ux

Mean observed-score u ratio for X.

mean_qxa

Mean square root of unrestricted reliability for X.

mean_qyi

Mean square root of restricted reliability for Y.

mean_uy

Mean observed-score u ratio for Y.

mean_qya

Mean square root of unrestricted reliability for Y.

mean_ut

Mean true-score u ratio for X.

sign_rxz

Sign of the relationship between X and the selection mechanism.

sign_ryz

Sign of the relationship between Y and the selection mechanism.

mean_rxx

Mean reliability for X.

mean_ryy

Mean reliability for Y.

Value

Vector of variances corrected for mean artifacts via Taylor series approximation.

Notes

A typographical error in Raju and Burke's article has been corrected in estimate_var_tsa_rb2() so as to compute appropriate partial derivatives.

References

Dahlke, J. A., & Wiernik, B. M. (2020). Not restricted to selection research: Accounting for indirect range restriction in organizational research. Organizational Research Methods, 23(4), 717–749. doi:10.1177/1094428119859398

Hunter, J. E., Schmidt, F. L., & Le, H. (2006). Implications of direct and indirect range restriction for meta-analysis methods and findings. Journal of Applied Psychology, 91(3), 594–612. doi:10.1037/0021-9010.91.3.594

Raju, N. S., & Burke, M. J. (1983). Two new procedures for studying validity generalization. Journal of Applied Psychology, 68(3), 382–395. doi:10.1037/0021-9010.68.3.382

Examples

estimate_var_tsa_meas(mean_rtp = .5, var = .02,
                 mean_qx = .8,
                 mean_qy = .8)
estimate_var_tsa_uvdrr(mean_rtpa = .5, var = .02,
                  mean_ux = .8,
                  mean_qxa = .8,
                  mean_qyi = .8)
estimate_var_tsa_bvdrr(mean_rtpa = .5, var = .02,
                  mean_ux = .8,
                  mean_uy = .8,
                  mean_qxa = .8,
                  mean_qya = .8)
estimate_var_tsa_uvirr(mean_rtpa = .5, var = .02,
                  mean_ut = .8,
                  mean_qxa = .8,
                  mean_qyi = .8)
estimate_var_tsa_bvirr(mean_rtpa = .5, var = .02,
                  mean_ux = .8,
                  mean_uy = .8,
                  mean_qxa = .8,
                  mean_qya = .8,
                  sign_rxz = 1, sign_ryz = 1)
estimate_var_tsa_rb1(mean_rtpa = .5, var = .02,
                mean_ux = .8,
                mean_rxx = .8,
                mean_ryy = .8)
estimate_var_tsa_rb2(mean_rtpa = .5, var = .02,
                mean_ux = .8,
                mean_qx = .8,
                mean_qy = .8)