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

Description

Functions to estimate the variance of 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 corrected for measurement error only
estimate_var_rho_int_uvdrr
Variance of corrected for univariate direct range restriction (i.e., Case II) and measurement error
estimate_var_rho_int_bvdrr
Variance of corrected for bivariate direct range restriction and measurement error
estimate_var_rho_int_uvirr
Variance of corrected for univariate indirect range restriction (i.e., Case IV) and measurement error
estimate_var_rho_int_bvirr
Variance of corrected for bivariate indirect range restriction (i.e., Case V) and measurement error
estimate_var_rho_int_rb
Variance of 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
)

Value

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

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.

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. tools:::Rd_expr_doi("10.1037/0021-9010.79.3.425")