estimate_artifacts | R Documentation |
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.
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)
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 |
ux_observed |
Logical vector determining whether each element of ux is an observed-score u ratio ( |
indirect_rr |
Logical vector determining whether each reliability value is associated with indirect range restriction ( |
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 |
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 |
rxx_restricted |
Logical vector determining whether each element of rxx is an incumbent reliability ( |
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. |
#### 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)
A vector of estimated artifact values.
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
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))
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