item.fit {ltm} | R Documentation |
Item-Fit Statistics and P-values
Description
Computation of item fit statistics for ltm
, rasch
and tpm
models.
Usage
item.fit(object, G = 10, FUN = median,
simulate.p.value = FALSE, B = 100)
Arguments
object |
a model object inheriting either from class |
G |
either a number or a numeric vector. If a number, then it denotes the number of categories sample units are grouped according to their ability estimates. |
FUN |
a function to summarize the ability estimate with each group (e.g., median, mean, etc.). |
simulate.p.value |
logical; if |
B |
the number of replications in the Monte Carlo procedure. |
Details
The item-fit statistic computed by item.fit()
has the form:
where is the item,
is the interval created by grouping sample units on the basis of their ability
estimates,
is the number of sample units groupings (i.e.,
G
argument), is the number of
sample units with ability estimates falling in a given interval
,
is the observed proportion of
keyed responses on item
for interval
, and
is the expected proportion of keyed responses
on item
for interval
based on the IRT model (i.e.,
object
) evaluated at the ability estimate
within the interval, with
denoting the result of
FUN
applied to the ability estimates in
group .
If simulate.p.value = FALSE
, then the -values are computed assuming a chi-squared distribution with
degrees of freedom equal to the number of groups
G
minus the number of estimated parameters. If
simulate.p.value = TRUE
, a Monte Carlo procedure is used to approximate the distribution of the item-fit
statistic under the null hypothesis. In particular, the following steps are replicated B
times:
- Step 1:
Simulate a new data-set of dichotomous responses under the assumed IRT model, using the maximum likelihood estimates
in the original data-set, extracted from
object
.- Step 2:
Fit the model to the simulated data-set, extract the maximum likelihood estimates
and compute the ability estimates
for each response pattern.
- Step 3:
For the new data-set, and using
and
, compute the value of the item-fit statistic.
Denote by the value of the item-fit statistic for the original data-set. Then the
-value is
approximated according to the formula
where denotes the indicator function, and
denotes
the value of the item-fit statistic in the
th simulated data-set.
Value
An object of class itemFit
is a list with components,
Tobs |
a numeric vector with item-fit statistics. |
p.values |
a numeric vector with the corresponding |
G |
the value of the |
simulate.p.value |
the value of the |
B |
the value of the |
call |
a copy of the matched call of |
Author(s)
Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl
References
Reise, S. (1990) A comparison of item- and person-fit methods of assessing model-data fit in IRT. Applied Psychological Measurement, 14, 127–137.
Yen, W. (1981) Using simulation results to choose a latent trait model. Applied Psychological Measurement, 5, 245–262.
See Also
person.fit
,
margins
,
GoF.gpcm
,
GoF.rasch
Examples
# item-fit statistics for the Rasch model
# for the Abortion data-set
item.fit(rasch(Abortion))
# Yen's Q1 item-fit statistic (i.e., 10 latent ability groups; the
# mean ability in each group is used to compute fitted proportions)
# for the two-parameter logistic model for the LSAT data-set
item.fit(ltm(LSAT ~ z1), FUN = mean)