estimate_artifacts: Estimation of applicant and incumbent reliabilities and of...
In jadahlke/psychmeta: Psychometric Meta-Analysis Toolkit
estimate_artifacts R Documentation
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:
\rho_{XX_{a}}=1-u_{X}^{2}\left(1-\rho_{XX_{i}}\right)
\rho_{XX_{a}}=\frac{\rho_{XX_{i}}}{\rho_{XX_{i}}+u_{T}^{2}-\rho_{XX_{i}}u_{T}^{2}}
Formula for direct range restriction:
\rho_{XX_{a}}=\frac{\rho_{XX_{i}}}{u_{X}^{2}\left[1+\rho_{XX_{i}}\left(\frac{1}{u_{X}^{2}}-1\right)\right]}
#### Formulas to estimate rxxi ####
Formulas for indirect range restriction:
\rho_{XX_{i}}=1-\frac{1-\rho_{XX_{a}}}{u_{X}^{2}}
\rho_{XX_{i}}=1-\frac{1-\rho_{XX_{a}}}{\rho_{XX_{a}}\left[u_{T}^{2}-\left(1-\frac{1}{\rho_{XX_{a}}}\right)\right]}
Formula for direct range restriction:
\rho_{XX_{i}}=\frac{\rho_{XX_{i}}u_{X}^{2}}{1+\rho_{XX_{i}}\left(u_{X}^{2}-1\right)}
#### Formulas to estimate ut ####
u_{T}=\sqrt{\frac{\rho_{XX_{i}}u_{X}^{2}}{1+\rho_{XX_{i}}u_{X}^{2}-u_{X}^{2}}}
u_{T}=\sqrt{\frac{u_{X}^{2}-\left(1-\rho_{XX_{a}}\right)}{\rho_{XX_{a}}}}
#### Formulas to estimate ux ####
u_{X}=\sqrt{\frac{u_{T}^{2}}{\rho_{XX_{i}}\left(1+\frac{u_{T}^{2}}{\rho_{XX_{i}}}-u_{T}^{2}\right)}}
u_{X}=\sqrt{\rho_{XX_{a}}\left[u_{T}^{2}-\left(1-\frac{1}{\rho_{XX_{a}}}\right)\right]}
#### Formula to estimate ryya ####
\rho_{YY_{a}}=1-\frac{1-\rho_{YY_{i}}}{1-\rho_{XY_{i}}^{2}\left(1-\frac{1}{u_{X}^{2}}\right)}
#### Formula to estimate ryyi
\rho_{YY_{i}}=1-\left(1-\rho_{YY_{a}}\right)\left[1-\rho_{XY_{i}}^{2}\left(1-\frac{1}{u_{X}^{2}}\right)\right]
#### Formula to estimate uy ####
u_{Y}=\sqrt{\frac{1-\rho_{YY_{a}}}{1-\rho_{YY_{i}}}}
#### Formula to estimate up ####
u_{P}=\sqrt{\frac{\frac{1-\rho_{YY_{a}}}{1-\rho_{YY_{i}}}-\left(1-\rho_{YY_{a}}\right)}{\rho_{YY_{a}}}}
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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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))
jadahlke/psychmeta documentation built on Feb. 11, 2024, 9:15 p.m.
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| estimate_artifacts | R Documentation |
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 |
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. |
Details
#### Formulas to estimate rxxa ####
Formulas for indirect range restriction:
\rho_{XX_{a}}=1-u_{X}^{2}\left(1-\rho_{XX_{i}}\right)
\rho_{XX_{a}}=\frac{\rho_{XX_{i}}}{\rho_{XX_{i}}+u_{T}^{2}-\rho_{XX_{i}}u_{T}^{2}}
Formula for direct range restriction:
\rho_{XX_{a}}=\frac{\rho_{XX_{i}}}{u_{X}^{2}\left[1+\rho_{XX_{i}}\left(\frac{1}{u_{X}^{2}}-1\right)\right]}
#### Formulas to estimate rxxi ####
Formulas for indirect range restriction:
\rho_{XX_{i}}=1-\frac{1-\rho_{XX_{a}}}{u_{X}^{2}}
\rho_{XX_{i}}=1-\frac{1-\rho_{XX_{a}}}{\rho_{XX_{a}}\left[u_{T}^{2}-\left(1-\frac{1}{\rho_{XX_{a}}}\right)\right]}
Formula for direct range restriction:
\rho_{XX_{i}}=\frac{\rho_{XX_{i}}u_{X}^{2}}{1+\rho_{XX_{i}}\left(u_{X}^{2}-1\right)}
#### Formulas to estimate ut ####
u_{T}=\sqrt{\frac{\rho_{XX_{i}}u_{X}^{2}}{1+\rho_{XX_{i}}u_{X}^{2}-u_{X}^{2}}}
u_{T}=\sqrt{\frac{u_{X}^{2}-\left(1-\rho_{XX_{a}}\right)}{\rho_{XX_{a}}}}
#### Formulas to estimate ux ####
u_{X}=\sqrt{\frac{u_{T}^{2}}{\rho_{XX_{i}}\left(1+\frac{u_{T}^{2}}{\rho_{XX_{i}}}-u_{T}^{2}\right)}}
u_{X}=\sqrt{\rho_{XX_{a}}\left[u_{T}^{2}-\left(1-\frac{1}{\rho_{XX_{a}}}\right)\right]}
#### Formula to estimate ryya ####
\rho_{YY_{a}}=1-\frac{1-\rho_{YY_{i}}}{1-\rho_{XY_{i}}^{2}\left(1-\frac{1}{u_{X}^{2}}\right)}
#### Formula to estimate ryyi
\rho_{YY_{i}}=1-\left(1-\rho_{YY_{a}}\right)\left[1-\rho_{XY_{i}}^{2}\left(1-\frac{1}{u_{X}^{2}}\right)\right]
#### Formula to estimate uy ####
u_{Y}=\sqrt{\frac{1-\rho_{YY_{a}}}{1-\rho_{YY_{i}}}}
#### Formula to estimate up ####
u_{P}=\sqrt{\frac{\frac{1-\rho_{YY_{a}}}{1-\rho_{YY_{i}}}-\left(1-\rho_{YY_{a}}\right)}{\rho_{YY_{a}}}}
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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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))
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