| Type: | Package |
| Title: | Generate Simulated Data for IRT-Enabled Exams |
| Version: | 1.0.0 |
| Author: | Waldir Leoncio <waldir.leoncio@gmail.com> |
| Maintainer: | Waldir Leoncio <waldir.leoncio@gmail.com> |
| Description: | Generates binary test data based on Item Response Theory using the two-parameter logistic model (Lord, 1980 <doi:10.4324/9780203056615>). Useful functions for test equating are included, e.g. functions for generating internal and external common items between test forms and a function to create a linkage plans between those forms. Ancillary functions for generating true item and person parameters as well as for calculating the probability of a person correctly answering an item are also included. |
| Imports: | stats, Matrix, msm |
| BugReports: | https://github.com/wleoncio/simExam/issues |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 6.1.1 |
| NeedsCompilation: | no |
| Packaged: | 2019-07-31 13:12:27 UTC; wleoncio |
| Repository: | CRAN |
| Date/Publication: | 2019-08-02 09:20:02 UTC |
Creates linkage plan
Description
Creates linkage plan
Usage
createLinkagePlan(forms, J, C, forms.linked, wrap.around = FALSE)
Arguments
forms |
number of forms |
J |
number of items per form |
C |
number of items in common between two forms |
forms.linked |
maximum number of forms linked to one form |
wrap.around |
if |
Value
matrix with the number of items in common between two forms
Examples
# Linkage plan for 10 forms, 40 items per form, 5 items in common between
# each pair of forms, and with each form being connected at most to its 4
# closest neighbors.
createLinkagePlan(10, 40, 5, 4)
Fill matrix of true.items with values from a custom linkage plan
Description
Fill matrix of true.items with values from a custom linkage plan
Usage
fillCustomLinkagePlan(t.tot, true.items, linkage.plan, min.a, max.a, mu.b,
sd.b, ...)
Arguments
t.tot |
number of tests |
true.items |
matrix containing all items in the rows and all test forms in the columns |
linkage.plan |
matrix containing the number of items each test form has in common with itself and another test form |
min.a |
Lower bound for the (uniform) distribution of item discrimination parameter |
max.a |
Upper bound for the (uniform) distribution of item discrimination parameter |
mu.b |
Mean of (normally-distributed) item difficulty parameter |
sd.b |
Standard deviation of (normally-distributed) item difficulty parameter |
... |
Arguments to pass to genItemParameter |
Fill matrix of true.items with values for a random linkage plan
Description
Fill matrix of true.items with values for a random linkage plan
Usage
fillRandomLinkagePlan(t.tot, J, C, true.items, min.a, max.a, mu.b, sd.b,
...)
Arguments
t.tot |
number of tests |
J |
number of total items (unique + common) per test |
C |
number of common items between two test |
true.items |
matrix containing all items in the rows and all test forms in the columns |
min.a |
Lower bound for the (uniform) distribution of item discrimination parameter |
max.a |
Upper bound for the (uniform) distribution of item discrimination parameter |
mu.b |
Mean of (normally-distributed) item difficulty parameter |
sd.b |
Standard deviation of (normally-distributed) item difficulty parameter |
... |
Arguments to pass to genItemParameter |
Generate True Ability Parameters
Description
Generate True Ability Parameters
Usage
genAbilityParms(forms.n, mu.first, sd.first, mu.last = mu.first,
sd.last = sd.first)
Arguments
forms.n |
number of forms |
mu.first |
mean ability of first form |
sd.first |
standard deviation of ability of first form |
mu.last |
mean ability of last form |
sd.last |
standard deviation of ability of last form |
Value
List containing means and standard deviations per form
Simulate exam test answers
Description
Simulates answers for a test, given the true item parameters (2PL model) as well as the examinee skills per test.
Usage
genExamAnswers(true.item.parms, true.skills, join.anchors = FALSE)
Arguments
true.item.parms |
true item parameters per form |
true.skills |
true examinee skill per form |
join.anchors |
join answers for anchor items on each test? |
Value
List of size equal to the number of forms. Each element of the list contains a matrix of dichotomic answers (right or wrong) per examinee and item.
Generate item bank for NEAT with external anchor items
Description
Generate item bank for NEAT with external anchor items
Usage
genItemBankExt(C, U, t.tot, min.a, max.a, mu.b, sd.b)
Arguments
C |
number of common items between two tests |
U |
number of unique items per test |
t.tot |
number of forms |
min.a |
Lower bound for the (uniform) distribution of item discrimination parameter |
max.a |
Upper bound for the (uniform) distribution of item discrimination parameter |
mu.b |
Mean of (normally-distributed) item difficulty parameter |
sd.b |
Standard deviation of (normally-distributed) item difficulty parameter |
Value
list containing 2PL item parameters per form
Generate item bank for NEAT with internal anchor items
Description
Generate item bank for NEAT with internal anchor items
Usage
genItemBankInt(C, J, t.tot, min.a, max.a, mu.b, sd.b, leading0 = TRUE,
num.digits = 4, linkage.plan = NULL, ...)
Arguments
C |
number of common items between two test |
J |
number of total items (unique + common) per test |
t.tot |
number of tests |
min.a |
Lower bound for the (uniform) distribution of item discrimination parameter |
max.a |
Upper bound for the (uniform) distribution of item discrimination parameter |
mu.b |
Mean of (normally-distributed) item difficulty parameter |
sd.b |
Standard deviation of (normally-distributed) item difficulty parameter |
leading0 |
format item names with leading zeros for better ordering? |
num.digits |
number of digits for representing items |
linkage.plan |
square matrix or order t.tot representing the number of items each form has in common with another form. If NULL, links between forms will be chosen randomly. |
... |
parameters to pass to child functions |
Value
list containing 2PL item parameters per form
Generate Item Parameter Values
Description
Generate Item Parameter Values
Usage
genItemParameter(type, parms, quantity = 1, truncate.b = c(-Inf, Inf))
Arguments
type |
Either "a" for the item discrimination or "b" for the item difficulty |
parms |
vector of length two. If type = "a", parms must be setup such
that |
quantity |
number of item parameters to generate |
truncate.b |
vector of length 2 containing the limits for the difficulty distribution |
Value
scalar containing one item parameter
Generate true item parameters for NEAT design
Description
Creates true item parameters for a 2-parameters IRT model for posterior generation of item responses, IRT implementation and equating. Compatible with the common-item, non-equivalent group design (see Kolen et. al. 2004).
Usage
genTrueItems(C, J, U, num.forms, min.a = 0.5, max.a = 2, mu.b = 0,
sd.b = 1, anchor.type = "internal", output = "list",
linkage.plan = NULL, ...)
Arguments
C |
number of common items between two forms |
J |
number of items per form |
U |
number of unique items per form (only valid for external anchor) |
num.forms |
number of forms |
min.a |
Lower bound for the (uniform) distribution of item discrimination parameter |
max.a |
Upper bound for the (uniform) distribution of item discrimination parameter |
mu.b |
Mean of (normally-distributed) item difficulty parameter |
sd.b |
Standard deviation of (normally-distributed) item difficulty parameter |
anchor.type |
type of anchor item set ("internal" or "external") |
output |
type of output; "list" gives a list of used items per form, "matrix" gives a joint matrix (data.frame). |
linkage.plan |
matrix containing linkage plan |
... |
extra parameters to be passed to genItemBankInt() or genItemBankExt() |
Value
List of true item parameters per form
Author(s)
Waldir Leoncio
Simulates true examinee skills per form
Description
Generates a matrix containing the true (latent) skill per administration for a given group of examinees.
Usage
genTrueSkills(I, num.forms, mu.skill = rep(0, num.forms),
sd.skill = rep(1, num.forms))
Arguments
I |
number of test takers per form. It can have length 1, so all forms will have the same number of test takers, or be a larger vector with the respective number of examinees on each form |
num.forms |
number of test forms |
mu.skill |
mean skill per form |
sd.skill |
standard deviation of skills per form |
Value
List of examinee skill per form
Probability of Getting an Item Correct
Description
Calculates the probability of getting an item correct under a 2-parameter IRT model.
Usage
probIRT(theta, a, b)
Arguments
theta |
examinee skill |
a |
item discimination |
b |
item difficulty |
Value
Probability of getting a correct item.