estimate_var_rho_int: Non-linear estimate of variance of rho corrected for...

In psychmeta: Psychometric Meta-Analysis Toolkit

Non-linear estimate of variance of ρ corrected for psychometric artifacts using numeric integration

Description

Functions to estimate the variance of ρ corrected for psychometric artifacts. These functions integrate over the residual distribution of correlations from an interactive artifact-distribution meta-analysis to non-linearly estimate the variance of rho.

Available functions include:

• estimate_var_rho_int_meas
  Variance of ρ corrected for measurement error only

• estimate_var_rho_int_uvdrr
  Variance of ρ corrected for univariate direct range restriction (i.e., Case II) and measurement error

• estimate_var_rho_int_bvdrr
  Variance of ρ corrected for bivariate direct range restriction and measurement error

• estimate_var_rho_int_uvirr
  Variance of ρ corrected for univariate indirect range restriction (i.e., Case IV) and measurement error

• estimate_var_rho_int_bvirr
  Variance of ρ corrected for bivariate indirect range restriction (i.e., Case V) and measurement error

• estimate_var_rho_int_rb
  Variance of ρ corrected using Raju and Burke's correction for direct range restriction and measurement error

Usage

estimate_var_rho_int_meas(mean_qx, mean_qy, var_res)

estimate_var_rho_int_uvdrr(
  mean_rxyi,
  mean_rtpa,
  mean_qxa,
  mean_qyi,
  mean_ux,
  var_res
)

estimate_var_rho_int_uvirr(
  mean_rxyi,
  mean_rtpa,
  mean_qxi,
  mean_qyi,
  mean_ut,
  var_res
)

estimate_var_rho_int_bvirr(mean_qxa, mean_qya, mean_ux, mean_uy, var_res)

estimate_var_rho_int_bvdrr(
  mean_rxyi,
  mean_rtpa,
  mean_qxa,
  mean_qya,
  mean_ux,
  mean_uy,
  var_res
)

estimate_var_rho_int_rb(
  mean_rxyi,
  mean_rtpa,
  mean_qx,
  mean_qy,
  mean_ux,
  var_res
)

Arguments

mean_qx	Mean square root of reliability for X.
mean_qy	Mean square root of reliability for Y.
var_res	Residual variance from an interative artifact distribution (i.e., variance of observed correlations minus predicted error variance and predicted artifact variance).
mean_rxyi	Mean observed correlation.
mean_rtpa	Mean corrected correlation.
mean_qxa	Mean square root of unrestricted reliability for X.
mean_qyi	Mean square root of restricted reliability for Y.
mean_ux	Mean observed-score u ratio for X.
mean_qxi	Mean square root of restricted reliability for X.
mean_ut	Mean true-score u ratio for X.
mean_qya	Mean square root of unrestricted reliability for Y.
mean_uy	Mean observed-score u ratio for Y.

Value

A vector of non-linear estimates of the variance of rho.

Notes

estimate_var_rho_int_meas and estimate_var_rho_int_bvirr do not make use of numeric integration because they are linear functions.

References

Law, K. S., Schmidt, F. L., & Hunter, J. E. (1994). Nonlinearity of range corrections in meta-analysis: Test of an improved procedure. Journal of Applied Psychology, 79(3), 425–438. doi: 10.1037/0021-9010.79.3.425

psychmeta documentation built on Aug. 26, 2022, 5:14 p.m.