equate (version 0.1-1)

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. Methods for presmoothing scores are supported.

Usage

equate.eq(x, y, method = "none", Ky = max(y[,1]), w = 1, smooth = "none", 
  jmin, xscorefun, yscorefun, verbose = FALSE, ...)

Arguments

x, y

score distributions of class freqtab for forms X and Y. Under the random groups design (i.e., no anchor test) x and y will each contain the score scale in column 1

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)

w

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

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

• When verbose = FALSE a vector of equated scores is returned, otherwise a list is returned containing the following components:
• 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
  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

For the random groups design x and y are separate frequency tables where each row contains 1) a score scale point and 2) the total number of examinees obtaining that score. For the nonequivalent groups design each row contains 1) a score scale point on x or y, 2) a score scale point on the anchor test, and 3) the total number of examinees obtaining that score combination (see freqtab for more details). 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. For the random groups design, all three smoothing options are available: "bump" and "average" (see freqbump and freqavg) require the additional argument jmin and loglinear smoothing ("loglin") requires the score functions xscorefun and yscorefun (see loglinear). For frequency estimation and the nonequivalent groups design, only smoothing methods "freqbump" and "loglin" are supported. For frequency estimation a synthetic distribution of scores is used to equate X to Y. These procedures are carried out by 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 can 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. Specifying Ky = "i" will leave all form X scores with percentiles of 0 and 100 in raw form (i.e., unequated).

See Also

equate, synthetic, freqbump, freqavg, loglinear

Examples

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