estimate_var_tsa: Taylor Series Approximation of effect-size variances...

In psychmeta/psychmeta: Psychometric Meta-Analysis Toolkit

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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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)

psychmeta/psychmeta documentation built on Feb. 12, 2024, 1:21 a.m.