# fungibleExtrema: Locate Extrema of Fungible Regression Weights In fungible: Psychometric Functions from the Waller Lab

 fungibleExtrema R Documentation

## Locate Extrema of Fungible Regression Weights

### Description

Locate extrema of fungible regression weights.

### Usage

``````fungibleExtrema(
R.X,
rxy,
r.yhata.yhatb,
Nstarts = 100,
MaxMin = "Max",
Seed = NULL,
PrintLevel = 1
)
``````

### Arguments

 `R.X` p x p Predictor variable correlation matrix. `rxy` p x 1 Vector of predictor-criterion correlations. `r.yhata.yhatb` Correlation between least squares (yhatb) and alternate-weight (yhata) composites. `Nstarts` Maximum number of (max) minimizations from random starting configurations. `MaxMin` Character: "Max" = maximize cos(a,b); "Min" = minimize cos(a,b). `Seed` Starting seed for the random number generator. If Seed = NULL then the program will sample a random integer in the (0, 100,000) interval. Default (Seed = NULL). `maxGrad` The optimization routine will end when the maximimum of the (absolute value of the ) function gradient falls below the value specified in maxGrad. Default (maxGrad = 1E-05). `PrintLevel` (integer). If PrintLevel = 1 then the program will print additional output during function convergence. Default (PrintLevel = 1).

### Value

 `cos.ab` cosine between OLS and alternate weights. `a` extrema of fungible weights. `k` k weights. `z` z weights: a normalized random vector. `b` OLS weights. `u` p x 1 vector of u weights. `r.yhata.yhatb` Correlation between yhata and yhatb. `r.y.yhatb` Correlation between y and yhatb. `gradient` Gradient of converged solution.

### Author(s)

Niels Waller and Jeff Jones

### References

Koopman, R. F. (1988). On the sensitivity of a composite to its weights. Psychometrika, 53(4), 547–552.

Waller, N. & Jones, J. (2009). Locating the extrema of fungible regression weights in multiple regression. Psychometrika, 74, 589–602.

### Examples

``````## Not run:
## Example
## This is Koopman's Table 2 Example

R.X <- matrix(c(1.00,  .69,  .49,  .39,
.69, 1.00,  .38,  .19,
.49,  .38, 1.00,  .27,
.39,  .19,  .27, 1.00),4,4)

b <- c(.39, .22, .02, .43)
rxy <- R.X %*% b

OLSRSQ <- t(b) %*% R.X %*% b

theta <- .02
r.yhata.yhatb <- sqrt( 1 - (theta)/OLSRSQ)

Converged = FALSE
SEED = 1234
MaxTries = 100
iter = 1

while( iter <= MaxTries){
SEED <- SEED + 1

cat("\nCurrent Seed = ", SEED, "\n")
output <- fungibleExtrema(R.X, rxy,
r.yhata.yhatb,
Nstarts = 5,
MaxMin = "Min",
Seed = SEED,
PrintLevel = 1)

Converged <- output\$converged
if(Converged) break
iter = iter + 1
}

print( output )

## Scale to replicate Koopman
a <- output\$a
a.old <- a
aRa <- t(a) %*% R.X %*% a

## Scale a such that a' R a = .68659
## vc = variance of composite
vc <- aRa
## sf = scale factor
sf <- .68659/vc
a <- as.numeric(sqrt(sf)) * a
cat("\nKoopman Scaling\n")
print(round(a,2))

## End(Not run)
``````

fungible documentation built on March 31, 2023, 5:47 p.m.