IRT {exametrika} | R Documentation |
Estimating Item parameters using EM algorithm
Description
A function for estimating item parameters using the EM algorithm.
Usage
IRT(U, model = 2, na = NULL, Z = NULL, w = NULL, verbose = TRUE)
Arguments
U |
U is either a data class of exametrika, or raw data. When raw data is given,
it is converted to the exametrika class with the |
model |
This argument takes the number of item parameters to be estimated in the logistic model. It is limited to values 2, 3, or 4. |
na |
na argument specifies the numbers or characters to be treated as missing values. |
Z |
Z is a missing indicator matrix of the type matrix or data.frame |
w |
w is item weight vector |
verbose |
logical; if TRUE, shows progress of iterations (default: TRUE) |
Details
Apply the 2, 3, and 4 parameter logistic models to estimate the item and subject populations. The 4PL model can be described as follows.
P(\theta,a_j,b_j,c_j,d_j)= c_j + \frac{d_j -c_j}{1+exp\{-a_j(\theta - b_j)\}}
a_j, b_j, c_j
, and d_j
are parameters related to item j, and are parameters that
adjust the logistic curve.
a_j
is called the slope parameter, b_j
is the location, c_j
is the lower asymptote,
and d_j
is the upper asymptote parameter.
The model includes lower models, and among the 4PL models, the case where d=1
is the 3PL model,
and among the 3PL models, the case where c=0
is the 2PL model.
Value
- model
number of item parameters you set.
- testlength
Length of the test. The number of items included in the test.
- nobs
Sample size. The number of rows in the dataset.
- params
Matrix containing the estimated item parameters
- Q3mat
Q3-matrix developed by Yen(1984)
- itemPSD
Posterior standard deviation of the item parameters
- ability
Estimated parameters of students ability
- ItemFitIndices
Fit index for each item.See also
ItemFit
- TestFitIndices
Overall fit index for the test.See also
TestFit
References
Yen, W. M. (1984) Applied Psychological Measurement, 8, 125-145.
Examples
# Fit a 3-parameter IRT model to the sample dataset
result.IRT <- IRT(J15S500, model = 3)
# Display the first few rows of estimated student abilities
head(result.IRT$ability)
# Plot Item Characteristic Curves (ICC) for items 1-6 in a 2x3 grid
plot(result.IRT, type = "ICC", items = 1:6, nc = 2, nr = 3)
# Plot Item Information Curves (IIC) for items 1-6 in a 2x3 grid
plot(result.IRT, type = "IIC", items = 1:6, nc = 2, nr = 3)
# Plot the Test Information Curve (TIC) for all items
plot(result.IRT, type = "TIC")