Item-class {irt} | R Documentation |
An S4 class to represent an Item
Description
Item
is a class to represent an item. An object in Item class should
have a model
name and parameters
.
The model that item parameters
represents. Currently,
following models are available:
"Rasch"
-
Rasch Model.
Required parameters:
"b"
Item difficulty parameter.
Probability of correct response at ability estimate
\theta
:P(\theta) = \frac{e^{(\theta - b)}}{1+e^{(\theta - b)}}
Model family: Unidimensional Item Response Theory (UIRT) Models
"1PL"
-
Unidimensional One-Parameter Logistic Model.
Required parameters:
"b"
Item difficulty parameter.
"D"
Scaling constant. Default value is
1
.
Probability of correct response at ability estimate
\theta
:P(\theta) = \frac{e^{D(\theta - b)}}{1+e^{D(\theta - b)}}
Model family: Unidimensional Item Response Theory (UIRT) Models
"2PL"
-
Unidimensional Two-Parameter Logistic Model.
Required parameters:
"a"
Item discrimination parameter.
"b"
Item difficulty parameter.
"D"
Scaling constant. Default value is
1
.
Probability of correct response at ability estimate
\theta
:P(\theta) = \frac{e^{Da(\theta - b)}}{1+e^{Da(\theta - b)}}
Model family: Unidimensional Item Response Theory (UIRT) Models
"3PL"
-
Unidimensional Three-Parameter Logistic Model.
Required parameters:
"a"
Item discrimination parameter.
"b"
Item difficulty parameter.
"c"
Pseudo-guessing parameter (lower asymptote).
"D"
Scaling constant. Default value is
1
.
Probability of correct response at ability estimate
\theta
:P(\theta) = c + (1-c) \frac{e^{Da(\theta - b)}}{1+e^{Da(\theta - b)}}
Model family: Unidimensional Item Response Theory (UIRT) Models
"4PL"
-
Unidimensional Four-Parameter Logistic Model.
Required parameters:
"a"
Item discrimination parameter.
"b"
Item difficulty parameter.
"c"
Pseudo-guessing parameter (lower asymptote).
"d"
Upper asymptote parameter.
"D"
Scaling constant. Default value is
1
.
Probability of correct response at ability estimate
\theta
:P(\theta) = c + (d-c) \frac{e^{Da(\theta - b)}}{1+e^{Da(\theta - b)}}
Model family: Unidimensional Item Response Theory (UIRT) Models
"GRM"
-
Graded Response Model
Required parameters:
"a"
Item discrimination parameter.
"b"
Item threshold parameters (a vector of values). Each value refers to the ability level for which the probability of responding at or above that category is equal to 0.5.
"D"
Scaling constant. Default value is
1
.
Probability of scoring at or above the category
k
:P^*_k(\theta) = \frac{e^{Da(\theta - b_k)}}{1+e^{Da(\theta - b_k)}}
Probability of responding at category
k
where the possible scores are0, \ldots, m
:P_0(\theta) = 1 - P^*_1(\theta)
P_1(\theta) = P^*_1(\theta) - P^*_2(\theta)
\cdots
P_k(\theta) = P^*_{k}(\theta) - P^*_{k+1}(\theta)
\cdots
P_m(\theta) = P^*_{m}(\theta)
Model family: Polytomous Item Response Theory (PIRT) Models
"GPCM"
-
Generalized Partial Credit Model
Required parameters:
"a"
Item discrimination parameter.
"b"
Item step difficulty parameters (a vector of values).
"D"
Scaling constant. Default value is
1
.
Probability of scoring at category
k
:P_k(\theta) = \frac{exp[\sum_{v = 0}^{k} Da(\theta - b_v)]} {\sum_{c = 0}^{m-1}exp[\sum_{v = 0}^{c}Da(\theta - b_v)]}
Model family: Polytomous Item Response Theory (PIRT) Models
"PCM"
-
Partial Credit Model (Masters, 1982)
Required parameters:
"b"
Item step difficulty parameters (a vector of values).
Probability of scoring at category
k
:P_k(\theta) = \frac{exp[\sum_{v = 0}^{k} (\theta - b_v)]}{\sum_{c = 0}^{m-1}exp[\sum_{v = 0}^{c}(\theta - b_v)]}
Model family: Polytomous Item Response Theory (PIRT) Models
"GPCM2"
-
An alternative parametrization of Generalized Partial Credit Model
"GPCM"
whereb_k = b - d_k
. See Muraki (1997), Equation 15 on page 164.Required parameters:
"a"
Item discrimination parameter.
"b"
Location parameter.
"d"
A vector of threshold parameters.
"D"
Scaling constant. Default value is
1
.
Probability of scoring at category
k
:P_k(\theta) = \frac{exp[\sum_{v = 0}^{k} Da(\theta - b + d_v)]}{\sum_{c = 0}^{m-1}exp[\sum_{v = 0}^{c}Da(\theta - b + d_v)]}
Model family: Polytomous Item Response Theory (PIRT) Models
A model must be specified for the construction of an Item
object.
Slots
item_id
Item ID. Default value is
NULL
.content
Content information for the Item object.
misc
This slot is a list where one can put any information about the Item object. For example, one can enter the ID's of the enemies of the current Item as
misc = list(enemies = c("i1", i2))
. Or, one can enter Sympson-Hetter exposure control parameter K:misc = list(sympson_hetter_k = .75)
.
Author(s)
Emre Gonulates
References
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.
Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159–176.