| Title: | Methods for Industrial/Organizational Psychology |
|---|---|
| Description: | Collection of functions for IO Psychologists. |
| Authors: | Allen Goebl <[email protected]>, Jeff Jones <[email protected]>, Jeff Dahlke <[email protected]>, and Adam Beatty <[email protected]> |
| Maintainer: | Allen Goebl <[email protected]> |
| License: | BSD_3_clause + file LICENSE |
| Version: | 0.90.1 |
| Built: | 2024-11-05 05:06:42 UTC |
| Source: | https://github.com/allengoebl/iopsych |
Estimate adverse impact given d and sr
aiEst(d, sr, pct_minority)aiEst(d, sr, pct_minority)
d |
Subgroup difference. |
sr |
The percentage of the applicant population that is selected. |
pct_minority |
The percentage of the applicant population that is part of a given minority group. |
The adverse impact ratio.
The overall selection ratio.
The selection ratio for the majority group.
The selection ratio for the minority group.
the predictor cutoff value that corresponds to the given overall selection ratio
Jeff Jones and Allen Goebl
De Corte, W., Lievens, F.(2003). A practical procedure to estimate the quality and the adverse impact of single-stage selection decisions. International Journal of Selection and Assessment, 11(1), 87-95.
aiEst(d = -0.15, sr = 0.25, pct_minority = 0.30) aiEst(d = -0.40, sr = 0.10, pct_minority = 0.15)aiEst(d = -0.15, sr = 0.25, pct_minority = 0.30) aiEst(d = -0.40, sr = 0.10, pct_minority = 0.15)
Estimate ai and average criterion scores for majority and minority groups.
aiPux(mr, dx, dy = -1, sr, pct_minority)aiPux(mr, dx, dy = -1, sr, pct_minority)
mr |
The correlation between the predictor and criterion composites. |
dx |
A vector of d values for the predictors. These d values are expected to have been computed in the direction of Minority - Majority. |
dy |
A vector of d values for the criteria These d values are expected to have been computed in the direction of Majority - Minority. |
sr |
The percentage of the applicant population that is selected. |
pct_minority |
The percentage of the applicant population that is part of a given minority group. |
Adverse Impact
The overall selection ratio set by the user
Majority Selection Rate
Minority Selection Rate
Predicted composite criterion score relative to the majority population
Predicted composite criterion score relative to the overall population
Jeff Jones and Allen Goebl
De Corte, W., Lievens, F.(2003). A practical procedure to estimate the quality and the adverse impact of single-stage selection decisions. International Journal of Selection and Assessment., 11(1), 87-95.
aiPux(0.6, dx=-0.8, sr=0.3, pct_minority=0.25) aiPux(0.6, dx=-0.8, dy=-0.2, sr=0.3, pct_minority=0.25)aiPux(0.6, dx=-0.8, sr=0.3, pct_minority=0.25) aiPux(0.6, dx=-0.8, dy=-0.2, sr=0.3, pct_minority=0.25)
Estimate ai and average criterion scores for majority and minority groups.
aiPuxComposite(r_mat, y_col, x_col, dX, dY, wt_x, wt_y, sr, pct_minority)aiPuxComposite(r_mat, y_col, x_col, dX, dY, wt_x, wt_y, sr, pct_minority)
r_mat |
Super correlation matrix between the predictors and criteria. This argument assumes that the predictors come first in the matrix. |
y_col |
A vector of columns representing criterion variables. |
x_col |
A vector of columns representing predictor variables. |
dX |
A vector of d values for the predictors. These d values are expected to have been computed in the direction of Minority - Majority. |
dY |
A vector of d values for the criteria These d values are expected to have been computed in the direction of Minority - Majority. |
wt_x |
Weights for the predictors to form the overall composite predictor. |
wt_y |
Weights for the criteria to form the overall composite criterion. |
sr |
The percentage of the applicant population that is selected. |
pct_minority |
The percentage of the applicant population that is part of a given minority group. |
Adverse Impact
The overall selection ratio set by the user
Majority Selection Rate
Minority Selection Rate
Predicted composite criterion score relative to the majority population
Predicted composite criterion score relative to the overall population
Jeff Jones and Allen Goebl
De Corte, W., Lievens, F.(2003). A Practical procedure to estimate the quality and the adverse impact of single-stage selection decisions. International Journal of Selection and Assessment, 11(1), 87-95.
De Corte, W. (2003). Caiqs user's guide. http://allserv.rug.ac.be/~wdecorte/software.html
# Example taken from De Corte, W. (2003) R <- matrix(c(1.000, 0.170, 0.000, 0.100, 0.290, 0.160, 0.170, 1.000, 0.120, 0.160, 0.300, 0.260, 0.000, 0.120, 1.000, 0.470, 0.120, 0.200, 0.100, 0.160, 0.470, 1.000, 0.240, 0.250, 0.290, 0.300, 0.120, 0.240, 1.000, 0.170, 0.160, 0.260, 0.200, 0.250, 0.170, 1.000), 6, 6) wt_x <- c(.244, .270, .039, .206) wt_y <- c(6, 2) sr <- 0.25 pct_minority <- .20 dX <- c(-1, -0.09, -0.09, -0.20) dY <- c(-0.450, 0.0) aiPuxComposite(R, 5:6, 1:4, dX, dY, wt_x, wt_y, sr, pct_minority) # compare the output from predictAI with the output in the CAIQS manual on page 7 where SR = .250# Example taken from De Corte, W. (2003) R <- matrix(c(1.000, 0.170, 0.000, 0.100, 0.290, 0.160, 0.170, 1.000, 0.120, 0.160, 0.300, 0.260, 0.000, 0.120, 1.000, 0.470, 0.120, 0.200, 0.100, 0.160, 0.470, 1.000, 0.240, 0.250, 0.290, 0.300, 0.120, 0.240, 1.000, 0.170, 0.160, 0.260, 0.200, 0.250, 0.170, 1.000), 6, 6) wt_x <- c(.244, .270, .039, .206) wt_y <- c(6, 2) sr <- 0.25 pct_minority <- .20 dX <- c(-1, -0.09, -0.09, -0.20) dY <- c(-0.450, 0.0) aiPuxComposite(R, 5:6, 1:4, dX, dY, wt_x, wt_y, sr, pct_minority) # compare the output from predictAI with the output in the CAIQS manual on page 7 where SR = .250
This dataset was published in Wee, Newman, and Joseph (2014) and describes the results of a military validation study. The first four rows contain the intercorrelations of the four predictor variables. The fifth row contains the black-white score differences (d). Rows 6-12 contain the correlations between the four predictor variables and the six job performance variables.
asvabasvab
A data frame with 12 rows and 4 columns.
Wee, S., Newman, D. A., & Joseph, D. L. (2014). More than g: Selection quality and adverse impact implications of considering second-stratum cognitive abilities. Journal of Applied Psychology, 99(4).
Convert from r to d
cor2d(r, n_1 = 1, n_2 = 1)cor2d(r, n_1 = 1, n_2 = 1)
r |
A r-value or a vector of r values. |
n_1 |
The sample size of group 1. |
n_2 |
The sample size of group 2. |
A d value or a vector of d values.
Jeff Dahlke, Allen Goebl, and Jeff Jones
cor2d(.3) cor2d(.3, n_1 = 20, n_2 = 50) cor2d(((1:9)/10))cor2d(.3) cor2d(.3, n_1 = 20, n_2 = 50) cor2d(((1:9)/10))
Convert from d to r
d2cor(d, n_1 = 1, n_2 = 1)d2cor(d, n_1 = 1, n_2 = 1)
d |
A d-value or a vector of d values. |
n_1 |
The sample size of group 1. |
n_2 |
The sample size of group 2. |
A r value or a vector of r values.
Jeff Dahlke, Allen Goebl, and Jeff Jones
d2cor(.3) d2cor(.3, n_1 = 20, n_2 = 50) d2cor(((1:9)))d2cor(.3) d2cor(.3, n_1 = 20, n_2 = 50) d2cor(((1:9)))
Estimates the d of a composite.
dComposite(rxx, d_vec, wt_vec = rep(1, length(d_vec)))dComposite(rxx, d_vec, wt_vec = rep(1, length(d_vec)))
rxx |
A matrix of predictor intercorrelations. |
d_vec |
A vector containing d's for each predictor. |
wt_vec |
A vector containing the weights of each item in rxx. |
A vector of correlation coefficients.
This is essentially the same function as solveWt().
Jeff Jones and Allen Goebl
Sackett, P. R., & Ellingson, J. E. (1997). Personnel Psychology., 50(3), 707-721.
Rxx <- matrix(.3, 3, 3); diag(Rxx) <- 1 ds <- c(.2, .4, .3) dComposite(rxx = Rxx, d_vec = ds) Rxx <- matrix(c(1.0, 0.3, 0.2, 0.3, 1.0, 0.1, 0.2, 0.1, 1.0), 3, 3) ds <- c(.1, .3, .7) ws <- c(1, .5, .5) dComposite(rxx = Rxx, d_vec = ds, wt_vec = ws)Rxx <- matrix(.3, 3, 3); diag(Rxx) <- 1 ds <- c(.2, .4, .3) dComposite(rxx = Rxx, d_vec = ds) Rxx <- matrix(c(1.0, 0.3, 0.2, 0.3, 1.0, 0.1, 0.2, 0.1, 1.0), 3, 3) ds <- c(.1, .3, .7) ws <- c(1, .5, .5) dComposite(rxx = Rxx, d_vec = ds, wt_vec = ws)
This hypothetical dataset was published in De Corte, Lievens, and Sackett (2007). The first column contains black-white subgroup difference scores. Columns 2-7 contain a hypothetical predictor, job performance correlation matrix.
dls2007dls2007
A data frame with 6 rows and 7 columns.
De Corte, W., Lievens, F., & Sackett, P. R. (2007). Combining predictors to achieve optimal trade-offs between selection quality and adverse impact. Journal of Applied Psychology, 92(5), 1380.
Computes the correlation between two composites of items. Composites may contain overalapping items. Items weights for each composite may be specified.
fuse(r_mat, a, b, wt_a = rep(1, length(a)), wt_b = rep(1, length(b)))fuse(r_mat, a, b, wt_a = rep(1, length(a)), wt_b = rep(1, length(b)))
r_mat |
A correlation matrix. |
a |
The items used for composite A specified as a vector of column numbers. |
b |
The items used for composite B specified as a vector of column numbers. |
wt_a |
A vector containing the weights of each item in composite A. |
wt_b |
A vector containing the weights of each item in composite B. |
A correlation coefficient.
The correlation between two composites.
The covariance between two composites.
The variance of composite A.
The variance of composite B.
This function is entended to be used for single cases. See fuse2()
for a vectorized alternative to this function.
Allen Goebl and Jeff Jones
Lord, F.M. & Novick, M.R. (1968). Statisticl theories of menal test scores.
Rxx <- matrix(c(1.00, 0.25, 0.50, 0.61, 0.25, 1.00, 0.30, 0.10, 0.50, 0.30, 1.00, -0.30, 0.61, 0.10, -0.30, 1.00), 4, 4) a <- c(1, 3) b <- c(2, 4) # Example using overlapping items and weights Rxx <- matrix(.3, 4, 4); diag(Rxx) <- 1 a <- c(1, 2, 4) b <- c(2, 3) wt_a <- c(.60, .25, .15) wt_b <- c(2, 3) fuse(r_mat = Rxx, a = a, b = b, wt_a = wt_a, wt_b = wt_b)Rxx <- matrix(c(1.00, 0.25, 0.50, 0.61, 0.25, 1.00, 0.30, 0.10, 0.50, 0.30, 1.00, -0.30, 0.61, 0.10, -0.30, 1.00), 4, 4) a <- c(1, 3) b <- c(2, 4) # Example using overlapping items and weights Rxx <- matrix(.3, 4, 4); diag(Rxx) <- 1 a <- c(1, 2, 4) b <- c(2, 3) wt_a <- c(.60, .25, .15) wt_b <- c(2, 3) fuse(r_mat = Rxx, a = a, b = b, wt_a = wt_a, wt_b = wt_b)
Computes the correlation between two composites of items. Composites may contain overalapping items. Items weights for each composite may be specified.
fuse2(r_mat, wt_a, wt_b)fuse2(r_mat, wt_a, wt_b)
r_mat |
A correlation matrix. |
wt_a |
A vector containing the weights of each item in composite A. Items which are not included in the composite should be assigned a weight of 0. |
wt_b |
A vector containing the weights of each item in composite B. Items which are not included in the composite should be assigned a weight of 0. |
A correlation coefficient.
This is an alternative version of fuse() which uses weight vectors
to specify both item selection and weight. This syntax maybe be preferable
to some users. Furthermore, this function is more powerful in that it
can return values for multiple sets of weights.
Allen Goebl and Jeff Jones
Lord, F.M. & Novick, M.R. (1968). Statisticl theories of menal test scores.
Rxx <- matrix(c(1.00, 0.25, 0.50, 0.61, 0.25, 1.00, 0.30, 0.10, 0.50, 0.30, 1.00, -0.30, 0.61, 0.10, -0.30, 1.00), 4, 4) wt_a <- c(1, 0, 1, 0) wt_b <- c(0, 1, 0, 1) # Example using overlapping items and weights Rxx <- matrix(.3, 4, 4); diag(Rxx) <- 1 wt_a <- c(.60, .25, 0, .15) wt_b <- c(0, 2, 3, 0) fuse2(r_mat = Rxx, wt_a = wt_a, wt_b = wt_b)Rxx <- matrix(c(1.00, 0.25, 0.50, 0.61, 0.25, 1.00, 0.30, 0.10, 0.50, 0.30, 1.00, -0.30, 0.61, 0.10, -0.30, 1.00), 4, 4) wt_a <- c(1, 0, 1, 0) wt_b <- c(0, 1, 0, 1) # Example using overlapping items and weights Rxx <- matrix(.3, 4, 4); diag(Rxx) <- 1 wt_a <- c(.60, .25, 0, .15) wt_b <- c(0, 2, 3, 0) fuse2(r_mat = Rxx, wt_a = wt_a, wt_b = wt_b)
The key matrix is used to specify any number of weighted item composites. A correlation matrix of these composites and the original correlation matrix is then computed and returned.
fuseMat(r_mat, wt, type = "full")fuseMat(r_mat, wt, type = "full")
r_mat |
A correlation matrix. |
wt |
A matrix with one row for each composite and one column for
each item contained in |
type |
The type of output desired. |
If type = "cxc" then a matrix of the intercorrelations between the specified
composites are returned.
If type = "full" then all the intercorrelations between both the
original items and the specified composites are returned.
Allen Goebl and Jeff Jones
Rxx <- matrix(c(1.00, 0.25, 0.50, 0.61, 0.25, 1.00, 0.30, 0.10, 0.50, 0.30, 1.00, -0.30, 0.61, 0.10, -0.30, 1.00), 4, 4); Rxx # Single composite wt <- matrix(c(1, 2, 3, -1), 1, 4); wt fuseMat(r_mat = Rxx, wt = wt) # Three composites wt <- matrix(c(1, 2, 3, -1, 2, 1, 0, -2, 1, 1, 0, 0), 3, 4, byrow = TRUE) fuseMat(Rxx, wt)Rxx <- matrix(c(1.00, 0.25, 0.50, 0.61, 0.25, 1.00, 0.30, 0.10, 0.50, 0.30, 1.00, -0.30, 0.61, 0.10, -0.30, 1.00), 4, 4); Rxx # Single composite wt <- matrix(c(1, 2, 3, -1), 1, 4); wt fuseMat(r_mat = Rxx, wt = wt) # Three composites wt <- matrix(c(1, 2, 3, -1, 2, 1, 0, -2, 1, 1, 0, 0), 3, 4, byrow = TRUE) fuseMat(Rxx, wt)
Computes the correlations between a correlation matrix and a weighted composite of items from the matrix.
fuseVec(r_mat, wt)fuseVec(r_mat, wt)
r_mat |
A correlation matrix. |
wt |
A vector containing the weights of each item in composite A or a matrix with one row per weight vector. |
A vector of correlation coefficients will be returned if wt_a
is a vector. If /codewt_b is a matrix, a matrix of correlation
coefficients with one row for each weight vector will be returned.
Allen Goebl and Jeff Jones
Lord, F.M. & Novick, M.R. (1968). Statisticl theories of mental test scores.
data(dls2007) dat <- dls2007 rxx <- dat[1:4, 2:5] wt1 <- c(1, 1, 1, 1) wt2 <- c(2, 0, 1, 0) wt <- rbind(wt1, wt2) fuseVec(r_mat=rxx, wt=wt1)data(dls2007) dat <- dls2007 rxx <- dat[1:4, 2:5] wt1 <- c(1, 1, 1, 1) wt2 <- c(2, 0, 1, 0) wt <- rbind(wt1, wt2) fuseVec(r_mat=rxx, wt=wt1)
Lawley multivariate range restriction correction.
lMvrrc(rcov, vnp, as_cor = TRUE)lMvrrc(rcov, vnp, as_cor = TRUE)
rcov |
The covariance matrix of the restricted sample. |
vnp |
The covariance matrix of predictors explicitly used for selection. This matrix should be based on the the unrestricted population. |
as_cor |
This argument can be set to FALSE to return a covariance matrix. |
The the correlation matrix or variance/covariance matrix in the unrestricted population.
The original function was written by Adam Beatty and adapted by Allen Goebl.
Lawley D. N (1943). A note on Karl Pearson's selection formulae. Proceedings of the Royal Society of Edinburgh, 62(Section A, Pt. 1), 28-30.
data(rcea1994) vstar <- rcea1994$vstar vpp <- rcea1994$vpp lMvrrc(rcov=vstar, vnp=vpp)data(rcea1994) vstar <- rcea1994$vstar vpp <- rcea1994$vpp lMvrrc(rcov=vstar, vnp=vpp)
Computes data needed for a XX Pareto plot.
paretoXX(r_mat, x_col, y_col, pts = 100)paretoXX(r_mat, x_col, y_col, pts = 100)
r_mat |
A correlation matrix. |
x_col |
A vector of columns representing predictor variables. |
y_col |
A vector of columns representing criterion variables. |
pts |
The number of points used. Determines accuracy. |
A matrix of beta weights for each criteria weight
The weight given to the first criterion
The correlation between the predictor and criterion composites
Allen Goebl and Jeff Jones
# Setup Data data(dls2007) r_mat <- dls2007[1:6, 2:7] #Run Model XX1 <- paretoXX(r_mat=r_mat, x_col=1:4, y_col=5:6) # Plot Multiple correlations plot(c(0,1), c(.3,.5), type="n", xlab="C1 Wt", ylab="mr") lines((XX1$wts)[,1], (XX1$multiple_r)[,1]) lines((XX1$wts)[,1], (XX1$multiple_r)[,2])# Setup Data data(dls2007) r_mat <- dls2007[1:6, 2:7] #Run Model XX1 <- paretoXX(r_mat=r_mat, x_col=1:4, y_col=5:6) # Plot Multiple correlations plot(c(0,1), c(.3,.5), type="n", xlab="C1 Wt", ylab="mr") lines((XX1$wts)[,1], (XX1$multiple_r)[,1]) lines((XX1$wts)[,1], (XX1$multiple_r)[,2])
Computes data needed for a XY Pareto plot.
paretoXY(r_mat, x_col, y_col, d_vec = NULL, gen = 100, pop = 100, pred_lower = rep(-2, length(x_col)), pred_upper = rep(2, length(x_col)), ...)paretoXY(r_mat, x_col, y_col, d_vec = NULL, gen = 100, pop = 100, pred_lower = rep(-2, length(x_col)), pred_upper = rep(2, length(x_col)), ...)
r_mat |
A correlation matrix. |
x_col |
A vector of columns representing predictor variables. |
y_col |
A vector of columns representing criterion variables. |
d_vec |
A vector of d scores. |
gen |
The number of iterations used by the algorithim. |
pop |
The population or number of cases used by the algorithim. |
pred_lower |
The minimum weight allowed for each predictor. |
pred_upper |
The maximum weight allowed for each predictor. |
A matrix of beta weights for each criteria weight
A matrix of multiple correlations or d values corresponding to each row of beta weights.
A vector indicating whether each value is pareto optimal
Allen Goebl Jeff Jones
data(dls2007) dat <- dls2007 r_mat <- dat[1:6, 2:7] x_col <- 1:4 y_col <- 5:6 d_vec <- -dat[1:4, 1] paretoXY(r_mat=r_mat, x_col=1:4, y_col=5, d_vec=d_vec, pred_lower=c(0,0,0,0)) paretoXY(r_mat=r_mat, x_col=1:4, y_col=c(5,6))data(dls2007) dat <- dls2007 r_mat <- dat[1:6, 2:7] x_col <- 1:4 y_col <- 5:6 d_vec <- -dat[1:4, 1] paretoXY(r_mat=r_mat, x_col=1:4, y_col=5, d_vec=d_vec, pred_lower=c(0,0,0,0)) paretoXY(r_mat=r_mat, x_col=1:4, y_col=c(5,6))
This example data was published in Ree, Carretta, Earles, and Albert (1994). The data set contains two matrices stored as a list, which can be used to demonstrate multivariate range restriction corrections. The vstar matrix is the variance-covariance matrix of the unrestricted sample. The vpp matrix is the variance covariance matrix of the restricted sample. The vpp matrix represents the subset of variables which were explicitly used for selection, which are also found in the upper left corner of the vstar matrix.
rcea1994rcea1994
A list containing a 4x4 matrix and a 2x2 matrix as elements.
Ree, M. J., Carretta, T. R., Earles, J. A., & Albert, W. (1994). Sign changes when correcting for range restriction: A note on Pearson's and Lawley's selection formulas. Journal of Applied Psychology, 72(2), 298.
Disattenuate a correlation matrix using an estimate of the component reliabilities
reliabate(r_mat, rel_vec)reliabate(r_mat, rel_vec)
r_mat |
A correlation matrix |
rel_vec |
A vector or reliabilities. |
A reliabated (disattenauted) correlation matrix.
Allen Goebl and Jeff Jones
r_mat <- matrix(c(1.00, 0.25, 0.30, 0.25, 1.00, 0.50, 0.30, 0.50, 1.00), 3, 3) rel <- c(.70, .64, .81) reliabate(r_mat = r_mat, rel_vec = rel)r_mat <- matrix(c(1.00, 0.25, 0.30, 0.25, 1.00, 0.50, 0.30, 0.50, 1.00), 3, 3) rel <- c(.70, .64, .81) reliabate(r_mat = r_mat, rel_vec = rel)
Function to implement Johnson's (2000) relative weight computation.
relWt(r_mat, y_col, x_col)relWt(r_mat, y_col, x_col)
r_mat |
A correlation matrix. |
y_col |
A vector of columns representing criterion variables. |
x_col |
A vector of columns representing predictor variables. |
A list containing the objects eps, beta_star, and lambda_star. The object eps contains
the vector of relative weights of the predictors whose sum is equivalent to the model
(see Johnson, 2000, ps 8 - 9). The object beta_star contains the regression weights from
regressing the criterion on Z, the 'best fitting orthogonal approximation' of the predictor
variables (see Johnson, 2000, p. 5). The object lambda_star contains the regression coefficients
from regressing Z on the predictor variables (see Johnson, 2000, p. 8).
Jeff Jones and Allen Goebl
Johnson, J. (2000). A heuristic method for estimating the relative weight of predictor variables in multiple regression. Multivariate Behavioral Research, 35, 1–19.
Rs <- matrix(c(1.0, 0.2, 0.3, 0.4, -0.4, 0.2, 1.0, 0.5, 0.1, 0.1, 0.3, 0.5, 1.0, 0.2, -0.3, 0.4, 0.1, 0.2, 1.0, 0.4, -0.4, 0.1, -0.3, 0.4, 1.0), 5, 5) ys <- 5 xs <- 1:4 relWt(Rs, ys, xs)Rs <- matrix(c(1.0, 0.2, 0.3, 0.4, -0.4, 0.2, 1.0, 0.5, 0.1, 0.1, 0.3, 0.5, 1.0, 0.2, -0.3, 0.4, 0.1, 0.2, 1.0, 0.4, -0.4, 0.1, -0.3, 0.4, 1.0), 5, 5) ys <- 5 xs <- 1:4 relWt(Rs, ys, xs)
Regression
rmatReg(r_mat, y_col, x_col, N = NULL, alpha = 0.05)rmatReg(r_mat, y_col, x_col, N = NULL, alpha = 0.05)
r_mat |
A correlation matrix. |
y_col |
The column representing the criterion variable. |
x_col |
A vector of columns representing predictor variables. |
N |
Number of observations |
alpha |
alpha value for (1 - alpha)% Confidence Interval |
Regression beta weights and . If N is supplied, the standard error of
the beta weights as well as the confidence intervals are returned as well.
If N is non-null the function will compute corrected standard errors for the standardized regression coefficients using the delta method. For additional details on the calculation of the corrected standard errors see Yuan and Chan (2011) and Jones and Waller (2015).
Allen Goebl and Jeff Jones
Jones, J. A. & Waller, N. G. (2015). The normal-theory and asymptotic distribution-free covariance matrix of standardized regression coefficients: Theoretical extensions and finite sample behavior. Psychometrika, 80, 365-378.
Yuan, K. and Chan, W. (2011). Biases and standard errors of standardized regression coefficients. Psychometrika, 76, 670-690.
Rs <- matrix(c(1.0, 0.2, 0.3, 0.4, -0.4, 0.2, 1.0, 0.5, 0.1, 0.1, 0.3, 0.5, 1.0, 0.2, -0.3, 0.4, 0.1, 0.2, 1.0, 0.4, -0.4, 0.1, -0.3, 0.4, 1.0), 5, 5) ys <- 5 xs <- 1:4 rmatReg(Rs, ys, xs) # Example with standard errors rmatReg(Rs, ys, xs, N = 100)Rs <- matrix(c(1.0, 0.2, 0.3, 0.4, -0.4, 0.2, 1.0, 0.5, 0.1, 0.1, 0.3, 0.5, 1.0, 0.2, -0.3, 0.4, 0.1, 0.2, 1.0, 0.4, -0.4, 0.1, -0.3, 0.4, 1.0), 5, 5) ys <- 5 xs <- 1:4 rmatReg(Rs, ys, xs) # Example with standard errors rmatReg(Rs, ys, xs, N = 100)
Find given arbitrary predictor weights
rmatWtR2(r_mat, y_col, x_col, wt)rmatWtR2(r_mat, y_col, x_col, wt)
r_mat |
A correlation matrix. |
y_col |
A vector of columns representing criterion variables. |
x_col |
A vector of columns representing predictor variables. |
wt |
A vector of predictor weights or a list of multiple vectors. |
Regression R2.
This is a wrapper for solveWt().
Allen Goebl and Jeff Jones
library(iopsych) #Get Data data(dls2007) r_mat <- dls2007[1:6, 2:7] #Get weights unit_wt <- c(1,1,1,1) other_wt <- c(1,2,1,.5) wt_mat <- rbind(unit_wt, other_wt) #Solve rmatWtR2(r_mat=r_mat, y_col=6, x_col=1:4, wt=unit_wt) rmatWtR2(r_mat=r_mat, y_col=6, x_col=1:4, wt=other_wt) rmatWtR2(r_mat=r_mat, y_col=6, x_col=1:4, wt=wt_mat)library(iopsych) #Get Data data(dls2007) r_mat <- dls2007[1:6, 2:7] #Get weights unit_wt <- c(1,1,1,1) other_wt <- c(1,2,1,.5) wt_mat <- rbind(unit_wt, other_wt) #Solve rmatWtR2(r_mat=r_mat, y_col=6, x_col=1:4, wt=unit_wt) rmatWtR2(r_mat=r_mat, y_col=6, x_col=1:4, wt=other_wt) rmatWtR2(r_mat=r_mat, y_col=6, x_col=1:4, wt=wt_mat)
Find beta weights
solveBeta(rxx, rxy)solveBeta(rxx, rxy)
rxx |
A matrix of predictor intercorrelations. |
rxy |
A vector of predictor criterion intercorrelations, or a matrix with one row per criterion. |
A vector or matrix of regression weights.
Allen Goebl and Jeff Jones
library(iopsych) data(dls2007) dat <- dls2007[1:6, 2:7] rxx <- dat[1:4, 1:4] rxy <- dat[1:4, 5] solveBeta(rxx=rxx, rxy=rxy)library(iopsych) data(dls2007) dat <- dls2007[1:6, 2:7] rxx <- dat[1:4, 1:4] rxy <- dat[1:4, 5] solveBeta(rxx=rxx, rxy=rxy)
Find R2
solveR2(rxx, rxy)solveR2(rxx, rxy)
rxx |
A matrix of predictor intercorrelations. |
rxy |
rxy A vector of predictor criterion intercorrelations, or a matrix with one row per criterion. |
R2 and Regression weights
Allen Goebl and Jeff Jones
print("example needed")print("example needed")
Find beta weights and R2
solveReg(rxx, rxy)solveReg(rxx, rxy)
rxx |
A matrix of predictor intercorrelations. |
rxy |
A vector of predictor criterion intercorrelations, or a matrix with one row per criterion. |
R2 and Regression weights
Allen Goebl and Jeff Jones
print("example needed")print("example needed")
Correlation between weighted criterion composite and predictors.
solveWtCrit(ryy, rxy, wt)solveWtCrit(ryy, rxy, wt)
ryy |
A matrix of criterion intercorrelations. |
rxy |
A vector of predictor criterion intercorrelations, or a matrix with one row per criterion. |
wt |
A vector of criterion weights, or a matrix with one set of criterion weights per row. |
A matrix of correlation coefficent with one row per weight vector and one column per predictor.
Allen Goebl Jeff Jones
library(iopsych) data(dls2007) dat <- dls2007[1:6, 2:7] ryy <- dat[5:6, 5:6] rxy <- dat[5:6, 1:4] wt1 <- c(.25, .75) wt2 <- c(.75, .25) wt_mat <- rbind(wt1, wt2) solveWtCrit(ryy=ryy, rxy=rxy, wt=wt_mat)library(iopsych) data(dls2007) dat <- dls2007[1:6, 2:7] ryy <- dat[5:6, 5:6] rxy <- dat[5:6, 1:4] wt1 <- c(.25, .75) wt2 <- c(.75, .25) wt_mat <- rbind(wt1, wt2) solveWtCrit(ryy=ryy, rxy=rxy, wt=wt_mat)
Correlation between weighted predictor composite and criterion.
solveWtPred(rxx, rxy, wt)solveWtPred(rxx, rxy, wt)
rxx |
A matrix of predictor intercorrelations. |
rxy |
A vector of predictor criterion intercorrelations, or a matrix with one row per criterion. |
wt |
A vector of predictor weights, or a matrix with one set of predictor weights per row. |
A matrix of correlation coefficent with one row per weight vector and one column per rxy vector.
Allen Goebl Jeff Jones
library(iopsych) data(dls2007) dat <- dls2007[1:6, 2:7] rxx <- dat[1:4, 1:4] rxy <- dat[5:6, 1:4] wt1 <- c(1,1,1,1) wt2 <- c(1,2,3,4) wt_mat <- rbind(wt1, wt2) solveWtPred(rxx=rxx, rxy=rxy, wt=wt_mat)library(iopsych) data(dls2007) dat <- dls2007[1:6, 2:7] rxx <- dat[1:4, 1:4] rxy <- dat[5:6, 1:4] wt1 <- c(1,1,1,1) wt2 <- c(1,2,3,4) wt_mat <- rbind(wt1, wt2) solveWtPred(rxx=rxx, rxy=rxy, wt=wt_mat)
Computes the Taylor Russel ratio
trModel(rxy, sr, br)trModel(rxy, sr, br)
rxy |
The correaltion between the predictor composite and the criterion. |
sr |
The selection ratio. |
br |
The base rate of the criterion. The cutoff point indicating success or failure. |
The success ratio.
Allen Goebl and Jeff Jones
Taylor, H. C., & Russell, J. T. (1939). The relationship of validity coefficients to the practical effectiveness of tests in selection: Discussion and tables. Journal of Applied Psychology, 25(5), 565.
trModel(rxy=.5, sr=.5, br=.6)trModel(rxy=.5, sr=.5, br=.6)
This utility model extends the BCG model with additional financial variables.
utilityB(n = 1, sdy, rxy = NULL, uxs = NULL, sr = NULL, pux = NULL, cost = 0, period = 1, v = 0, tax = 0, i = 0)utilityB(n = 1, sdy, rxy = NULL, uxs = NULL, sr = NULL, pux = NULL, cost = 0, period = 1, v = 0, tax = 0, i = 0)
n |
The size of the applicant pool |
sdy |
The standard deviation of performance in monetary units. |
rxy |
the correlation between the predictor composite and the criterion. |
uxs |
The average predicter score of those selected. If the uxs is unknown, the sr argument can used instead. |
sr |
A selection ratio or a vector of selection ratios. |
pux |
The expected average criterion score of selected applicants. |
cost |
The cost per applicant of a selection system. |
period |
The anticipated tenure of selected employees. |
v |
The proportion of new costs to new revenue (i.e. sc/sv). |
tax |
The marginal tax rate. |
i |
Discount rate. |
Estimated gain in utility.
This functions can except either (1) pux, (2) uxs and rxy, or (3) sr and rxy.
Allen Goebl and Jeff Jones
Boudreau, J.W. (1983). Economic considerations in estimating the utility of human resource productivity improvement programs. Personnel Psychology, 36, 551-576.
utilityB(sdy=10000, rxy=.50, sr=.30, period=4, v=.5, tax=.1, i=.02)utilityB(sdy=10000, rxy=.50, sr=.30, period=4, v=.5, tax=.1, i=.02)
Estimates the utility of an employee selection system.
utilityBcg(n = 1, sdy, rxy = NULL, uxs = NULL, sr = NULL, pux = NULL, cost = 0, period = 1)utilityBcg(n = 1, sdy, rxy = NULL, uxs = NULL, sr = NULL, pux = NULL, cost = 0, period = 1)
n |
The size of the applicant pool |
sdy |
The standard deviation of performance in monetary units. |
rxy |
The correlation between the predictor composite and the criterion. |
uxs |
The average predicter score of those selected. If the uxs is unknown, the sr argument can used instead. |
sr |
A selection ratio or a vector of selection ratios. |
pux |
The expected average criterion score of selected applicants |
cost |
The cost per applicant of a selection system. |
period |
The anticipated tenure of selected employees. |
Estimated gain in utility.
This functions can except either (1) pux, (2) uxs and rxy, or (3) sr and rxy.
Allen Goebl and Jeff Jones
Cronbach, L. J., & Gleser, G. C. (1965). Psychological tests and personnel decisions.
utilityBcg(sdy=10000, rxy=.50, sr=.30)utilityBcg(sdy=10000, rxy=.50, sr=.30)
This utility model uses SD of job performance ratings rather than the SD of job performance in monetary units.
utilityRbn(n = 1, sdr, a, rxy, uxs = NULL, sr = NULL, pux = NULL, cost = 0, period = 1)utilityRbn(n = 1, sdr, a, rxy, uxs = NULL, sr = NULL, pux = NULL, cost = 0, period = 1)
n |
The size of the applicant pool. |
sdr |
The standard deviation of ratings of job performance. |
a |
The average total compensation. |
rxy |
The correlation between the predictor composite and the criterion. |
uxs |
The average predicter score of those selected. If the uxs is unknown, the sr argument can used instead. |
sr |
A selection ratio or a vector of selection ratios. |
pux |
The expected average criterion score of selected applicants. |
cost |
The cost per applicant of a selection system. |
period |
The anticipated tenure of selected employees. |
Estimated gain in utility.
This functions can except either (1) pux, (2) uxs and rxy, or (3) sr and rxy.
Allen Goebl and Jeff Jones
Raju, N.S., Burke, M.J. and Normand, J. (1990). A new approach for utility analysis. Journal of Applied Psychology, 75, 3-12.
utilityRbn(sdr=10000, a=90000, rxy=.50, sr=.30)utilityRbn(sdr=10000, a=90000, rxy=.50, sr=.30)
This model calculates the utility of an intervention accepting d rather than rxy as an argument.
utilityShp(n = 1, sdy, d, cost = 0, period = 1)utilityShp(n = 1, sdy, d, cost = 0, period = 1)
n |
The number of employees involved in the intervention. |
sdy |
The standard deviation of performance in monetary units. |
d |
The difference in job performance between the group recieving a treatment and the group not recieving a treatment, expressed in standard deviation units. |
cost |
The cost of the intervention per participant. |
period |
The anticipate duration of the training effect. |
Estimated gain in utility.
Allen Goebl and Jeff Jones
Schmidt, F. L., Hunter, J. E., & Pearlman, K. (1982). Assessing the economic impact of personnel programs on workforce productivity. Personnel Psychology, 35(2), 333-347.
utilityShp(sdy=10000, d=.50, period=4)utilityShp(sdy=10000, d=.50, period=4)
When scores on the predictor composite are assumed to be normally distributed, the average score of selected applicants can be computed for an arbitrary selection ratio using the ordinate of the normal curve.
ux(sr)ux(sr)
sr |
A selection ratio or a vector of selection ratios. |
ux: The average score of those selected on a predicter composite.
Allen Goebl and Jeff Jones
Naylor, J. C., & Shine, L. C. (1965). A table for determining the increase in mean criterion score obtained by using a selection device. Journal of Industrial Psychology, 78-109.
ux(.6)ux(.6)