estimate_var_rho_int {psychmeta}

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

Description

Functions to estimate the variance of \rho 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 \rho corrected for measurement error only

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

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

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

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

• estimate_var_rho_int_rb
  Variance of \rho 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