equate-methods {plink}R Documentation

IRT True Score and Observed Score Equating

Description

This function conducts IRT true score and observed score equating for unidimensional single-format or mixed-format item parameters for two or more groups. This function supports all item response models available in plink with the exception of the multiple-choice model.

Usage

equate(x, method="TSE", true.scores, ts.low, base.grp=1, score=1, 
  startval, weights1, weights2, syn.weights, ...) 

## S4 method for signature 'list'
equate(x, method, true.scores, ts.low, base.grp, score, startval, 
  weights1, weights2, syn.weights, ...)

## S4 method for signature 'irt.pars', 'ANY'
equate(x, method, true.scores, ts.low, base.grp, score, startval, 
  weights1, weights2, syn.weights, ...)

Arguments

x an object of class irt.pars with two or more groups or the output from plink containing rescaled item parameters.
method character vector identifying the equating method(s) to use. Values can include "TSE" and "OSE".
true.scores numeric vector of true score values to be equated
ts.low logical value. If TRUE, interpolate values for the equated true scores in the range of observed scores from one to the value below the lowest estimated true score (a rounded sum of guessing parameters)
base.grp integer identifying the group for the base scale
score if score = 1, score responses for the true-score equating method with zero for the lowest category and k-1 for the highest, k, category for each item. If score = 2, score responses with one for the lowest category and k for the highest, k, category for each item. A vector or list of scoring weights for each response category can be supplied, but this is only recommended for advanced users.
startval integer starting value for the first value of true.score
weights1 list containing information about the theta values and weights to be used in the observed score equating for population 1. See below for more details.
weights2 list containing information about the theta values and weights to be used in the observed score equating for population 2. See below for more details.
syn.weights vector of length two or a list containing vectors of length two with synthetic population weights to be used for each pair of tests for populations 1 and 2 respectively. If missing, weights of 0.5 will be used for both populations for all groups. If syn.weights is a list, there should be k-1 elements for k groups.
... further arguments passed to or from other methods. See below for details.

Details

weights1 can be a list or a list of lists. The purpose of this object is to specify the theta values for population 1 to integrate over in the observed score equating as well as any weights associated with the theta values. The function as.weight can be used to facilitate the creation of this object. If weights1 is missing, the default is to use equally spaced theta values ranging from -4 to 4 with an increment of 0.05 and normal density weights for all groups.

To better understand the elements of weights1, let us assume for a moment that x has parameters for only two groups. In this instance, weights1 would be a single list with length two. The first element should be a vector of theta values corresponding to points on the base scale. The second list element should be a vector of weights corresponding the theta values. If x contains more than two groups, a single weights1 object can be supplied, and the same set of thetas and weights will be used for all adjacent groups. However, a separate list of theta values and weights for each adjacent group in x can be supplied.

The specification of weights2 is the same as that for weights1, although the theta values and weights for this object correspond to theta values for population 2. This argument is only used when the synthetic weight associated with population 2 is greater than zero. If weights2 is missing, the same theta values and weights used for weights1 will be used for weights2.

For both equating methods, response probabilities are computed using the functions drm, grm, gpcm, and nrm for the associated models respectively. Various arguments from these functions can be passed to equate. Specifically, the argument incorrect can be passed to drm and catprob can be passed to grm. In the functions drm, grm, and gpcm there is an argument D for the value of a scaling constant. In plink, a single argument D can be passed that will be applied to all applicable models, or arguments D.drm, D.grm, and D.gpcm can be specified for each model respectively. If an argument is specified for D and, say D.drm, the values for D.grm and D.gpcm (if applicable) will be set equal to D. If only D.drm is specified, the values for D.grm and D.gpcm (if applicable) will be set to 1.

Value

Returns a matrix of equated true scores or a list of equated observed scores with associated marginal distributions or a list combining these two objects

Author(s)

Jonathan P. Weeks weeksjp@gmail.com

References

Kolen, M. J. (1981). Comparison of traditional and item response theory methods for equating tests. Journal of Educational Measurement, 18(1), 1-11.

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

Examples

# IRT true score and observed score examples from 
# Kolen & Brennan (2004, ch. 6)
pm <- as.poly.mod(36)
x <- as.irt.pars(KB04$pars, KB04$common, exclude=list(27,NA),
  cat=list(rep(2,36),rep(2,36)), poly.mod=list(pm,pm))
out <- plink(x, rescale="MS", base.grp=2, D=1.7)

# Create the quadrature points and weights
wt <- as.weight(
  theta=c(-5.2086,-4.163,-3.1175,-2.072,-1.0269,0.0184,
    1.0635,2.109,3.1546,4.2001),
  weight=c(0.000101,0.00276,0.03021,0.142,0.3149,0.3158,
    0.1542,0.03596,0.003925,0.000186))

# Conduct the equating
equate(out,method=c("TSE","OSE"),weights1=wt, synth.weights=c(1,0),D=1.7)

# Conduct true score equating for specific true scores
equate(out, true.scores=7:15, ts.low=FALSE, D=1.7)

# Observed score equating for mixed-format tests
pm1 <- as.poly.mod(55,c("drm","gpcm","nrm"),dgn$items$group1)
pm2 <- as.poly.mod(55,c("drm","gpcm","nrm"),dgn$items$group2)
x <- as.irt.pars(dgn$pars,dgn$common,dgn$cat,list(pm1,pm2))
out <- plink(x, rescale="HB") 
OSE <- equate(out, method="OSE", score=2)

# Display the equated scores
OSE[[1]]

# Multiple group equating
pars <- TK07$pars
common <- TK07$common
cat <- list(rep(2,26),rep(2,34),rep(2,37),rep(2,40),rep(2,41),rep(2,43))
pm1 <- as.poly.mod(26)
pm2 <- as.poly.mod(34)
pm3 <- as.poly.mod(37)
pm4 <- as.poly.mod(40)
pm5 <- as.poly.mod(41)
pm6 <- as.poly.mod(43)
pm <- list(pm1, pm2, pm3, pm4, pm5, pm6)
x <- as.irt.pars(pars, common, cat, pm, grp.names=paste("grade",3:8,sep=""))
out <- plink(x, rescale="SL")

# True score equating
equate(out)

# True score equating with the base group changed to 3
equate(out, base.grp=3)

# Observed score equating (These data are for non-equivalent groups, but
# this example is included to illustrate the multigroup capabilities)
OSE <- equate(out, method="OSE", base.grp=3)

# Display the equated scores for each group
OSE[[1]]


[Package plink version 1.2-2 Index]