composite function

Composite Linking and Equating

This function creates a composite linking or equating as a combination of two or more other linking or equating functions.

composite(x, ...)

## Default S3 method:
composite(x, wc, ...)

## S3 method for class 'equate.list'
composite(x, wc, name, symmetric = FALSE, p = 1, verbose = TRUE, ...)

## S3 method for class 'list'
composite(x, wc, name, symmetric = FALSE, p = 1, verbose = TRUE, ...)

Arguments

• x: for the default method, x is a matrix of equating functions, with one function per column. Otherwise, x is a list of equatings, where each element is an object of class ‘equate’ .

• ...: further arguments passed to or from other functions.

• wc: vector of weights for creating the composite. length(wc)

  should match either ncol(x) for the default method or length(x).

• name: an optional name, used to label the output. If missing, a name will be created using x.

• symmetric: logical, with default FALSE, indicating whether or not weights wc should be modified to create symmetric weights. Only supported for composites of linear functions.

• p: integer specifying the type of circle used to define symmetry.

• verbose: logical, with default TRUE, indicating whether or not full output should be returned. When FALSE, only the equated scores are returned.

Returns

For the default method, and when verbose = FALSE, a vector of composite equated scores is returned. Otherwise, a list of equating output is returned, including output for the composite and each function being combined.

Details

Composite linking and equating create a single linking or equating function as a weighted combination of two or more other linking or equating functions. See Holland and Strawderman (2011) for details.

Methods (by class)

• default: Default method for a matrix of equating functions, one per column.
• equate.list: Create composite across functions in ‘equate.list’ object.
• list: Create composite across functions in ‘list’ object.

Examples

# See vignette("equatevignette") for additional examples

# Example from the equate help file, without the bootstrapping
# Random groups equating for (1) identity, (2) mean, 
# (3) linear, (4) equipercentile with loglinear
# smoothing, and (5) a composite of mean and identity
rx <- as.freqtab(ACTmath[, 1:2])
ry <- as.freqtab(ACTmath[, c(1, 3)])
set.seed(2007)

req1 <- equate(rx, ry, type = "i")
req2 <- equate(rx, ry, type = "m")
req3 <- equate(rx, ry, type = "l")
req4 <- equate(rx, ry, type = "e", smooth = "loglin",
  degrees = 3)
req5 <- composite(list(req1, req2), wc = .5, symmetric = TRUE)

# Compare equating functions
plot(req1, req2, req3, req4, req5[[1]], addident = FALSE)

References

Holland, P. W., and Strawderman, W. E. (2011). How to average equating functions, if you must. In A. A. von Davier (Ed.), Statistical models for test equating, scaling, and linking (pp. 89-107). New York, NY: Springer.

See Also

equate

Author(s)

Anthony Albano tony.d.albano@gmail.com