equate.ln {equate}R Documentation

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, and the number of examinees obtaining each score in column 2. For the nonequivalent groups design bivariate frequency tables are used, where columns 1 and 2 include all score combinations for the total and anchor test score scales, and column 3 contains the number of examinees obtaining each combination (see freqtab for details)
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 groups design
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
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

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).

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, when verbose = TRUE a column of standard errors is included
coefficients the slope and intercept used in the linear conversion
synthstats means and standard deviations for the anchor and synthetic distributions
anchortab frequency table for the anchor test

Author(s)

Anthony Albano tony.d.albano@gmail.com

See Also

equate, synthetic

Examples

# 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"))

[Package equate version 0.1-1 Index]