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

In psychmeta: Psychometric Meta-Analysis Toolkit

Estimation of applicant and incumbent reliabilities and of true- and observed-score u ratios

Description

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:

• estimate_rxxa
  Estimate the applicant reliability of variable X from X's incumbent reliability value and X's observed-score or true-score u ratio.

• estimate_rxxa_u
  Estimate the applicant reliability of variable X from X's observed-score and true-score u ratios.

• estimate_rxxi
  Estimate the incumbent reliability of variable X from X's applicant reliability value and X's observed-score or true-score u ratio.

• estimate_rxxi_u
  Estimate the incumbent reliability of variable X from X's observed-score and true-score u ratios.

• estimate_ux
  Estimate the true-score u ratio for variable X from X's reliability coefficient and X's observed-score u ratio.

• estimate_uy
  Estimate the observed-score u ratio for variable X from X's reliability coefficient and X's true-score u ratio.

• estimate_ryya
  Estimate the applicant reliability of variable Y from Y's incumbent reliability value, Y's correlation with X, and X's u ratio.

• estimate_ryyi
  Estimate the incumbent reliability of variable Y from Y's applicant reliability value, Y's correlation with X, and X's u ratio.

• estimate_uy
  Estimate the observed-score u ratio for variable Y from Y's applicant and incumbent reliability coefficients.

• estimate_up
  Estimate the true-score u ratio for variable Y from Y's applicant and incumbent reliability coefficients.

Usage

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:

rxxa = 1 - ux^2 * (1 - rxxi)

rxxa = rxxi / (rxxi + ut^2 - rxxi * ut^2)

Formula for direct range restriction:

rxxa = rxxi / (ux^2 * (1 + rxxi * (ux^-2 - 1)))

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

Formulas for indirect range restriction:

1 - (1 - rxxa) / ux^2

rxxi = 1 - (1 - rxxa) / (rxxa * (ut^2 - (1 - 1 / rxxa)))

Formula for direct range restriction:

rxxi = (rxxa * ux^2) / (1 + rxxa * (ux^2 - 1))

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

ut = sqrt((rxxi * ux^2) / (1 + rxxi * ux^2 - ux^2))

ut = sqrt((ux^2 - (1 - rxxa)) / rxxa)

#### Formulas to estimate ux ####

ux = sqrt(ut^2 / (rxxi * (1 + ut^2 / rxxi - ut^2)))

ux = sqrt((ut^2 - (1 - 1 / rxxa)) * rxxa)

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

ryya = 1 - (1 - ryyi) / (1 - rxyi^2 * (1 - ux^-2))

#### Formula to estimate ryyi

ryyi = 1 - (1 - ryya) * (1 - rxyi^2 * (1 - ux^-2))

#### Formula to estimate uy ####

uy = sqrt((1 - ryya) / (1 - ryyi)

#### Formula to estimate up ####

up = 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

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 Aug. 26, 2022, 5:14 p.m.