# composite: Composite Linking and Equating In equate: Observed-Score Linking and Equating

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```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`”. `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. `...` further arguments passed to or from other functions.

## 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.

## Value

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.

## 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.

## Author(s)

Anthony Albano [email protected]

## 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.

`equate`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# 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) ```