rpf.1dim.fit: Calculate item and person Rasch fit statistics

View source: R/diagnose.R

rpf.1dim.fitR Documentation

Calculate item and person Rasch fit statistics

Description

Note: These statistics are only appropriate if all discrimination parameters are fixed equal and items are conditionally independent (see ChenThissen1997). A best effort is made to cope with missing data.

Usage

rpf.1dim.fit(
  spec,
  params,
  responses,
  scores,
  margin,
  group = NULL,
  wh.exact = TRUE
)

Arguments

spec

list of item response models \lifecycledeprecated

params

matrix of item parameters, 1 per column \lifecycledeprecated

responses

persons in rows and items in columns \lifecycledeprecated

scores

model derived person scores \lifecycledeprecated

margin

for people 1, for items 2

group

spec, params, data, and scores can be provided in a list instead of as arguments

wh.exact

whether to use the exact Wilson-Hilferty transformation

Details

Exact distributional properties of these statistics are unknown (Masters & Wright, 1997, p. 112). For details on the calculation, refer to Wright & Masters (1982, p. 100).

The Wilson-Hilferty transformation is biased for less than 25 items. Consider wh.exact=FALSE for less than 25 items.

Format of a group

A model, or group within a model, is represented as a named list.

spec

list of response model objects

param

numeric matrix of item parameters

free

logical matrix of indicating which parameters are free (TRUE) or fixed (FALSE)

mean

numeric vector giving the mean of the latent distribution

cov

numeric matrix giving the covariance of the latent distribution

data

data.frame containing observed item responses, and optionally, weights and frequencies

score

factors scores with response patterns in rows

weightColumn

name of the data column containing the numeric row weights (optional)

freqColumn

name of the data column containing the integral row frequencies (optional)

qwidth

width of the quadrature expressed in Z units

qpoints

number of quadrature points

minItemsPerScore

minimum number of non-missing items when estimating factor scores

The param matrix stores items parameters by column. If a column has more rows than are required to fully specify a model then the extra rows are ignored. The order of the items in spec and order of columns in param are assumed to match. All items should have the same number of latent dimensions. Loadings on latent dimensions are given in the first few rows and can be named by setting rownames. Item names are assigned by param colnames.

Currently only a multivariate normal distribution is available, parameterized by the mean and cov. If mean and cov are not specified then a standard normal distribution is assumed. The quadrature consists of equally spaced points. For example, qwidth=2 and qpoints=5 would produce points -2, -1, 0, 1, and 2. The quadrature specification is part of the group and not passed as extra arguments for the sake of consistency. As currently implemented, OpenMx uses EAP scores to estimate latent distribution parameters. By default, the exact same EAP scores should be produced by EAPscores.

A model, or group within a model, is represented as a named list.

spec

list of response model objects

param

numeric matrix of item parameters

free

logical matrix of indicating which parameters are free (TRUE) or fixed (FALSE)

mean

numeric vector giving the mean of the latent distribution

cov

numeric matrix giving the covariance of the latent distribution

data

data.frame containing observed item responses, and optionally, weights and frequencies

score

factors scores with response patterns in rows

weightColumn

name of the data column containing the numeric row weights (optional)

freqColumn

name of the data column containing the integral row frequencies (optional)

qwidth

width of the quadrature expressed in Z units

qpoints

number of quadrature points

minItemsPerScore

minimum number of non-missing items when estimating factor scores

The param matrix stores items parameters by column. If a column has more rows than are required to fully specify a model then the extra rows are ignored. The order of the items in spec and order of columns in param are assumed to match. All items should have the same number of latent dimensions. Loadings on latent dimensions are given in the first few rows and can be named by setting rownames. Item names are assigned by param colnames.

Currently only a multivariate normal distribution is available, parameterized by the mean and cov. If mean and cov are not specified then a standard normal distribution is assumed. The quadrature consists of equally spaced points. For example, qwidth=2 and qpoints=5 would produce points -2, -1, 0, 1, and 2. The quadrature specification is part of the group and not passed as extra arguments for the sake of consistency. As currently implemented, OpenMx uses EAP scores to estimate latent distribution parameters. By default, the exact same EAP scores should be produced by EAPscores.

References

Masters, G. N. & Wright, B. D. (1997). The Partial Credit Model. In W. van der Linden & R. K. Kambleton (Eds.), Handbook of modern item response theory (pp. 101-121). Springer.

Wilson, E. B., & Hilferty, M. M. (1931). The distribution of chi-square. Proceedings of the National Academy of Sciences of the United States of America, 17, 684-688.

Wright, B. D. & Masters, G. N. (1982). Rating Scale Analysis. Chicago: Mesa Press.

See Also

Other diagnostic: ChenThissen1997(), SitemFit1(), SitemFit(), multinomialFit(), sumScoreEAPTest()

Examples

data(kct)
responses <- kct.people[,paste("V",2:19, sep="")]
rownames(responses) <- kct.people$NAME
colnames(responses) <- kct.items$NAME
scores <- kct.people$MEASURE
params <- cbind(1, kct.items$MEASURE, logit(0), logit(1))
rownames(params) <- kct.items$NAME
items<-list()
items[1:18] <- rpf.drm()
params[,2] <- -params[,2]
rpf.1dim.fit(items, t(params), responses, scores, 2, wh.exact=TRUE)

rpf documentation built on Aug. 22, 2023, 1:06 a.m.