equate (version 0.1-0)

equate.eq: Equipercentile Equating

Description

This function (called by equate) conducts equipercentile equating of test scores under the random groups and nonequivalent groups with anchor test designs (see Kolen & Brennan, 2004). Methods for presmoothing scores are supported.

Usage

equate.eq(x, y, scale, method = "none", Ky = max(scale), 
  xv, yv, vscale, w, smooth = "none",  jmin, xscorefun, 
  yscorefun, 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

method

string specifying the equating method, where "none" (default) indicates observed score equating under the random groups design, and "frequency" indicates frequency estimation with nonequivalent groups and requires additional anch

Ky

integer, typically indicating the number of items on form Y, or the maximum possible score on Y. This value is used in equating the extremes of the scale (see below for more details)

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

value between 0 and 1 specifying the weight applied to form X scores (and implicitly specifying the form Y weight as 1 - w)

smooth

string indicating one of four smoothing methods: "none" (default), "bump", "average", and "loglin" (see below for details)

jmin

smoothing parameter required for methods "bump" and "average"

xscorefun, yscorefun

matrices, required by smoothing method "loglin", which specify the score functions for forms X and Y (see below for details)

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, and when verbose = TRUE, a column of standard errors is included
• smoothmethod
  smoothing method
• smoothout
  output corresponding to the particular smoothing method (see smoothing functions for details)
• synthstats
  matrix of means and standard deviations for the anchor and synthetic distributions
• synthtab
  frequency table for the synthetic distribution
• 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 methods are currently supported: observed score equipercentile equating, which assumes a random groups equating design, and frequency estimation equipercentile equating, which assumes a nonequivalent groups with anchor test design. Smoothing via equate.eq is only possible for the random groups design, where the additional argument jmin is required for methods "bump" and "average" (see freqbump and freqavg). Loglinear smoothing requires additional parameters (see loglinear). If smoothed distributions are desired for the frequency estimation method they must be supplied. The frequency estimation method also requires the additional arguments xv, yv, vscale, and w, which are passed to synthetic. The parameter Ky is used to obtain form Y equivalents of form X scores with percentile ranks of 100. Typically Ky is set to be the number of score points in the form Y scale, which assumes that scores are integers ranging from 1 (or 0) to the total number of items, and that each item is scored correct/incorrect. Scores on other scales (such as scales which include negative values, or which exclude zero) may also be used. In such cases Ky be set to the highest possible score on form Y, or alternatively the highest observed score on Y. For optimal results, scales should be monotonically increasing integer sequences. As another alternative, Ky = "i" will leave all form X scores with percentiles of 0 and 100 in raw form (i.e., unequated).

References

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

See Also

equate, synthetic, freqbump, freqavg, loglinear

Examples

# see the function 'equate' for more examples
x <- KBneat$x
y <- KBneat$y
scale <- 0:36
equate.eq(x[,1],y[,1],scale,method="f",
  xv=x[,2],yv=y[,2],w=.5,vscale=0:12)