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.

Usage

equate.ln(x, y, type = "linear", method = "none", w = 1, 
  internal = TRUE, 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

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

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

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

When verbose = FALSE a vector of equated scores is returned, otherwise a list is returned containing the following components:
yxform Y equivalents of the form X scores. For the random groups design, when verbose = TRUE a column of standard errors is included
coefficientsthe slope and intercept used in the linear conversion
synthstatsmeans and standard deviations for the anchor and synthetic distributions
anchortabfrequency 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 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, the nonequivalent groups with anchor test design is assumed. In this case anchor test scores must be included in x and y, so that each contains 3 columns, and the argument w is also required (see synthetic for details).

Examples

Run this code

# see the function 'equate' for more examples
x <- freqtab(ACTmath[,2],0:40,addclass=TRUE)
y <- freqtab(ACTmath[,3],0:40,addclass=TRUE)
cbind(0:40,equate.ln(x,y,type="m"),
  equate.ln(x,y,type="l"))