equate (version 0.1-0)

equate.ln: Linear Equating

Description

This function (called by equate) conducts linear equating of test scores under the random groups and nonequivalent groups with anchor test designs. Types of equating include mean and linear, and methods include Tucker and Levine (see Kolen & Brennan, 2004).

Usage

equate.ln(x, y, scale, type = "linear", method = "none", 
  xv, yv, vscale, w = 1, internal = TRUE, verbose = FALSE, ...)

Arguments

x, y

vectors of scores for forms X and Y, either as total scores (one per examinee), or total counts (one per score scale point). Total scores are required for the nonequivalent groups design

scale

the score scale, as a vector

type

the type of equating, implying the numer of coefficients used in the linear transformation, where "mean" relies on the intercept and "linear" (default) the intercept and slope

method

string specifying the equating method, where "none" (default) indicates observed score equating under the random groups design, and both "tucker" and "levine" indicate the respective methods under the nonequivalent g

xv, yv

vectors of anchor test total scores for form X and Y examinees

vscale

the score scale for the anchor test, as a vector

w

the weight applied to form X when calculating the synthetic population

internal

logical indicating whether or not the anchor item scores are included in the total scores (default is TRUE)

verbose

logical indicating whether output beyond a vector of equated scores should be supplied (TRUE) or not (FALSE, default)

...

further arguments passed to or from other methods

Value

• Returns a list including the following components when verbose = TRUE (only the first is returned when verbose = FALSE):
• yx
  form Y equivalents of the form X scores. For the random groups design, when verbose = TRUE a column of standard errors is included
• coefficients
  the slope and intercept used in the linear conversion
• synthstats
  matrix of means and standard deviations for the anchor and synthetic distributions
• anchortab
  frequency table for the anchor test

Details

As noted above, for the random groups design x and y can be supplied as either total scores, where the length of each will equal the number of examinees, or as counts, where the length of each will equal the length of the score scale, with each value indicating the total number of examinees obtaining the corresponding score. With the nonequivalent groups design, only total scores may be used. Two equating types (mean and linear) and two equating methods (Tucker and Levine) are currently supported. Varying the type and method arguments results in four possible equating scenarios. Whenever "tucker" or "levine" is specified, nonequivalent groups with anchor test design is assumed and the anchor test arguments xv, yv, vscale and w are also required (see synthetic for details).

References

Kolen, M. J., & Brennan, R. L. (2004) Test Equating, Scaling, and Linking. (2nd ed.), New York: Springer.

See Also

equate, synthetic

Examples

# see the function 'equate' for more examples
x <- ACTmath[,2]
y <- ACTmath[,3]
scale <- ACTmath[,1]
cbind(scale,equate.ln(x,y,scale,type="m")$yx,
  equate.ln(x,y,scale,type="l")$yx)