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.
rpf.1dim.fit(
spec,
params,
responses,
scores,
margin,
group = NULL,
wh.exact = TRUE
)list of item response models lifecycle::badge("deprecated")
matrix of item parameters, 1 per column lifecycle::badge("deprecated")
persons in rows and items in columns lifecycle::badge("deprecated")
model derived person scores lifecycle::badge("deprecated")
for people 1, for items 2
spec, params, data, and scores can be provided in a list instead of as arguments
whether to use the exact Wilson-Hilferty transformation
A model, or group within a model, is represented as a named list.
list of response model objects
numeric matrix of item parameters
logical matrix of indicating which parameters are free (TRUE) or fixed (FALSE)
numeric vector giving the mean of the latent distribution
numeric matrix giving the covariance of the latent distribution
data.frame containing observed item responses, and optionally, weights and frequencies
factors scores with response patterns in rows
name of the data column containing the numeric row weights (optional)
name of the data column containing the integral row frequencies (optional)
width of the quadrature expressed in Z units
number of quadrature points
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.
list of response model objects
numeric matrix of item parameters
logical matrix of indicating which parameters are free (TRUE) or fixed (FALSE)
numeric vector giving the mean of the latent distribution
numeric matrix giving the covariance of the latent distribution
data.frame containing observed item responses, and optionally, weights and frequencies
factors scores with response patterns in rows
name of the data column containing the numeric row weights (optional)
name of the data column containing the integral row frequencies (optional)
width of the quadrature expressed in Z units
number of quadrature points
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.
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.
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.
Other diagnostic:
ChenThissen1997(),
SitemFit1(),
SitemFit(),
multinomialFit(),
sumScoreEAPTest()
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)
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