estimate_artifacts: Estimation of applicant and incumbent reliabilities and of...

Description Usage Arguments Details Value References Examples

Description

\loadmathjax

Functions to estimate the values of artifacts from other artifacts. These functions allow for reliability estimates to be corrected/attenuated for range restriction and allow u ratios to be converted between observed-score and true-score metrics. Some functions also allow for the extrapolation of an artifact from other available information.

Available functions include:

Usage

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estimate_rxxa(
  rxxi,
  ux,
  ux_observed = TRUE,
  indirect_rr = TRUE,
  rxxi_type = "alpha"
)

estimate_rxxi(
  rxxa,
  ux,
  ux_observed = TRUE,
  indirect_rr = TRUE,
  rxxa_type = "alpha"
)

estimate_ut(ux, rxx, rxx_restricted = TRUE)

estimate_ux(ut, rxx, rxx_restricted = TRUE)

estimate_ryya(ryyi, rxyi, ux)

estimate_ryyi(ryya, rxyi, ux)

estimate_uy(ryyi, ryya, indirect_rr = TRUE, ryy_type = "alpha")

estimate_up(ryyi, ryya)

estimate_rxxa_u(ux, ut)

estimate_rxxi_u(ux, ut)

Arguments

rxxi

Vector of incumbent reliability estimates for X.

ux

Vector of observed-score u ratios for X (if used in the context of estimating a reliability value, a true-score u ratio may be supplied by setting ux_observed to FALSE).

ux_observed

Logical vector determining whether each element of ux is an observed-score u ratio (TRUE) or a true-score u ratio (FALSE).

indirect_rr

Logical vector determining whether each reliability value is associated with indirect range restriction (TRUE) or direct range restriction (FALSE).

rxxi_type, rxxa_type, ryy_type

String vector identifying the types of reliability estimates supplied (e.g., "alpha", "retest", "interrater_r", "splithalf"). See the documentation for ma_r for a full list of acceptable reliability types.

rxxa

Vector of applicant reliability estimates for X.

rxx

Vector of reliability estimates for X (used in the context of estimating ux and ut - specify that reliability is an incumbent value by setting rxx_restricted to FALSE).

rxx_restricted

Logical vector determining whether each element of rxx is an incumbent reliability (TRUE) or an applicant reliability (FALSE).

ut

Vector of true-score u ratios for X.

ryyi

Vector of incumbent reliability estimates for Y.

rxyi

Vector of observed-score incumbent correlations between X and Y.

ryya

Vector of applicant reliability estimates for Y.

Details

#### Formulas to estimate rxxa ####

Formulas for indirect range restriction: \mjdeqn\rho_XX_a=1-u_X^2\left(1-\rho_XX_i\right)rxxa = 1 - ux^2 * (1 - rxxi) \mjdeqn\rho_XX_a=\frac\rho_XX_i\rho_XX_i+u_T^2-\rho_XX_iu_T^2rxxa = rxxi / (rxxi + ut^2 - rxxi * ut^2)

Formula for direct range restriction: \mjdeqn\rho_XX_a=\frac\rho_XX_iu_X^2\left[1+\rho_XX_i\left(\frac1u_X^2-1\right)\right]rxxa = rxxi / (ux^2 * (1 + rxxi * (ux^-2 - 1)))

#### Formulas to estimate rxxi ####

Formulas for indirect range restriction: \mjdeqn\rho_XX_i=1-\frac1-\rho_XX_au_X^21 - (1 - rxxa) / ux^2 \mjdeqn\rho_XX_i=1-\frac1-\rho_XX_a\rho_XX_a\left[u_T^2-\left(1-\frac1\rho_XX_a\right)\right]rxxi = 1 - (1 - rxxa) / (rxxa * (ut^2 - (1 - 1 / rxxa)))

Formula for direct range restriction: \mjdeqn\rho_XX_i=\frac\rho_XX_iu_X^21+\rho_XX_i\left(u_X^2-1\right)rxxi = (rxxa * ux^2) / (1 + rxxa * (ux^2 - 1))

#### Formulas to estimate ut ####

\mjdeqn

u_T=\sqrt\frac\rho_XX_iu_X^21+\rho_XX_iu_X^2-u_X^2ut = sqrt((rxxi * ux^2) / (1 + rxxi * ux^2 - ux^2)) \mjdeqnu_T=\sqrt\fracu_X^2-\left(1-\rho_XX_a\right)\rho_XX_aut = sqrt((ux^2 - (1 - rxxa)) / rxxa)

#### Formulas to estimate ux #### \mjdeqnu_X=\sqrt\fracu_T^2\rho_XX_i\left(1+\fracu_T^2\rho_XX_i-u_T^2\right)ux = sqrt(ut^2 / (rxxi * (1 + ut^2 / rxxi - ut^2))) \mjdeqnu_X=\sqrt\rho_XX_a\left[u_T^2-\left(1-\frac1\rho_XX_a\right)\right]ux = sqrt((ut^2 - (1 - 1 / rxxa)) * rxxa)

#### Formula to estimate ryya ####

\mjdeqn\rho

_YY_a=1-\frac1-\rho_YY_i1-\rho_XY_i^2\left(1-\frac1u_X^2\right)ryya = 1 - (1 - ryyi) / (1 - rxyi^2 * (1 - ux^-2))

#### Formula to estimate ryyi \mjdeqn\rho_YY_i=1-\left(1-\rho_YY_a\right)\left[1-\rho_XY_i^2\left(1-\frac1u_X^2\right)\right]ryyi = 1 - (1 - ryya) * (1 - rxyi^2 * (1 - ux^-2))

#### Formula to estimate uy #### \mjdeqnu_Y=\sqrt\frac1-\rho_YY_a1-\rho_YY_iuy = sqrt((1 - ryya) / (1 - ryyi)

#### Formula to estimate up #### \mjdeqnu_P=\sqrt\frac\frac1-\rho_YY_a1-\rho_YY_i-\left(1-\rho_YY_a\right)\rho_YY_aup = sqrt(((1 - ryya) / (1 - ryyi) - (1 - ryya)) / ryya)

Value

A vector of estimated artifact values.

References

Schmidt, F. L., & Hunter, J. E. (2015). Methods of meta-analysis: Correcting error and bias in research findings (3rd ed.). Sage. doi: 10.4135/9781483398105 p. 127.

Le, H., & Schmidt, F. L. (2006). Correcting for indirect range restriction in meta-analysis: Testing a new meta-analytic procedure. Psychological Methods, 11(4), 416–438. doi: 10.1037/1082-989X.11.4.416

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

Le, H., Oh, I.-S., Schmidt, F. L., & Wooldridge, C. D. (2016). Correction for range restriction in meta-analysis revisited: Improvements and implications for organizational research. Personnel Psychology, 69(4), 975–1008. doi: 10.1111/peps.12122

Examples

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estimate_rxxa(rxxi = .8, ux = .8, ux_observed = TRUE)
estimate_rxxi(rxxa = .8, ux = .8, ux_observed = TRUE)
estimate_ut(ux = .8, rxx = .8, rxx_restricted = TRUE)
estimate_ux(ut = .8, rxx = .8, rxx_restricted = TRUE)
estimate_ryya(ryyi = .8, rxyi = .3, ux = .8)
estimate_ryyi(ryya = .8, rxyi = .3, ux = .8)
estimate_uy(ryyi = c(.5, .7), ryya = c(.7, .8))
estimate_up(ryyi = c(.5, .7), ryya = c(.7, .8))
estimate_rxxa_u(ux = c(.7, .8), ut = c(.65, .75))
estimate_rxxi_u(ux = c(.7, .8), ut = c(.65, .75))

psychmeta documentation built on Jan. 3, 2022, 5:07 p.m.