factor.scores {ltm} | R Documentation |
Computation of factor scores for grm
, ltm
and rasch
models.
factor.scores(object, ...) ## S3 method for class 'grm': factor.scores(object, resp.patterns = NULL, method = c("EB", "MI"), B = 5, ...) ## S3 method for class 'ltm': factor.scores(object, resp.patterns = NULL, method = c("EB", "MI", "Component"), B = 5, robust.se = FALSE, ...) ## S3 method for class 'rasch': factor.scores(object, resp.patterns = NULL, method = c("EB", "MI"), B = 5, robust.se = FALSE, ...)
object |
an object inheriting either from class grm , class ltm or class rasch . |
resp.patterns |
a matrix or a data.frame of response patterns with columns denoting the items; if NULL
the factor scores are computed for the observed response patterns. |
method |
a character supplying the scoring method. For ltm objects available methods are:
Component scores, Empirical Bayes and Multiple Imputation.
For grm and rasch objects available methods are: Empirical Bayes and Multiple Imputation.
See Details section for more info. |
B |
the number of multiple imputations to be used if method = "MI" . |
robust.se |
logical; if TRUE the sandwich estimator is used for the estimation of the covariance
matrix of the MLEs. See Details section for more info. |
... |
additional argument; currently none is used. |
Factor scores are summary measures of the posterior distribution p(z|x), where z denotes the vector of latent variables and x the vector of manifest variables.
Usually as factor scores we assign the modes of the above posterior distribution evaluated at the MLEs. These
Empirical Bayes estimates (use method = "EB"
) and their associated variance are good measures of the
posterior distribution while p -> infinity, where p is the number of items.
This is based on the result
p(z|x)=p(z|x; hat{theta})(1+O(1/p)),
where hat{theta} are the MLEs. However, in cases where p and/or n (the sample size) is small
we ignore the variability of plugging-in estimates but not the true parameter values. A solution to this
problem can be given using Multiple Imputation (MI; use method = "MI"
). In particular, MI is used the
other way around, i.e.,
robust.se = TRUE
,
C(hat{theta}) is based on the sandwich estimator).B
times and combine the estimates using the known formulas of MI.
This scheme explicitly acknowledges the ignorance of the true parameter values by drawing from their large sample
posterior distribution while taking into account the sampling error. The modes of the posterior distribution
p(z|x; theta) are numerically approximated using the BFGS algorithm in optim()
.
The Component scores (use method = "Component"
) proposed by Bartholomew (1984) is an alternative method
to scale the sample units in the latent dimensions identified by the model that avoids the calculation of the
posterior mode. However, this method is not valid in the general case where nonlinear latent terms are assumed.
An object of class fscores
is a list with components,
score.dat |
the data.frame of observed response patterns including, observed and expected
frequencies as well as the factor scores. |
method |
a character giving the scoring method used. |
B |
the number of multiple imputations used; relevant only if method = "MI" . |
call |
a copy of the matched call of object . |
Dimitris Rizopoulos dimitris.rizopoulos@med.kuleuven.be
Bartholomew, D. (1984) Scaling binary data using a factor model. Journal of the Royal Statistical Society, Series B, 46, 120–123.
Bartholomew, D. and Knott, M. (1999) Latent Variable Models and Factor Analysis, 2nd ed. London: Arnold.
Bartholomew, D., Steel, F., Moustaki, I. and Galbraith, J. (2002) The Analysis and Interpretation of Multivariate Data for Social Scientists. London: Chapman and Hall.
Rizopoulos, D. and Moustaki, I. (2006) Generalized latent variable models with nonlinear terms. submitted for publication.
## Factor Scores for the Rasch model m <- rasch(Lsat) factor.scores(m) # Empirical Bayes ## Factor Scores for the two-parameter logistic model m <- ltm(Abortion ~ z1) factor.scores(m, method = "MI", B = 20) # Multiple Imputation ## Factor Scores for the graded response model m <- grm(Science[c(1,3,4,7)]) factor.scores(m, resp.patterns = rbind(1:4))