| Title: | The R Package for "The Basics of Item Response Theory Using R" |
|---|---|
| Description: | R functions for "The Basics of Item Response Theory Using R" by Frank B. Baker and Seock-Ho Kim (Springer, 2017, ISBN-13: 978-3-319-54204-1) including iccplot(), icccal(), icc(), iccfit(), groupinv(), tcc(), ability(), tif(), and rasch(). For example, iccplot() plots an item characteristic curve under the two-parameter logistic model. |
| Authors: | Seock-Ho Kim [aut, cre] |
| Maintainer: | Seock-Ho Kim <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0.0 |
| Built: | 2024-12-09 06:42:40 UTC |
| Source: | CRAN |
Estimates the ability parameter and obtains the standard error of the estimate given the item characteristic curve model, the response vector, and the set of known item parameters under the one-, two-, or three-parameter logistic model.
ability(mdl, u, b, a, c)ability(mdl, u, b, a, c)
mdl |
1, 2, or 3 representing the number of the model parameters. |
u |
a numeric vector of 0s and 1s representing the responses to items. |
b |
a numeric vector representing the values of item difficulty. |
a |
a numeric vector representing the values of item discrimination. |
c |
a numeric vector representing the values of lower asymptote. |
With the number of item characteristic curve model parameters mdl,
the response vector u, and the set of item parameters b,
a, and c, the ability parameter is estimated and reported
as th by the maximum likelilhood procedure.
The estimated standard error se is also obtained and reported.
The length of u should be the same as that of b, a,
and c.
Each parameter c has a theoretical range from 0 to 1, but in
practice values above .35 are not considered acceptable, hence use the
range from 0 to .35 for each c.
Under the one-parameter logisric model, a = rep(1, length(b)) and
c = rep(0, length(b)).
Under the two-parameter logistic model, c = rep(0, lenght(b)).
Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1
u <- c(1, 0, 1) b <- c(-1.0, 0.0, 1.0) a <- c(1.0, 1.2, 0.8) ability(2, u, b, a) # ability(2, u, b, a, c = rep(0, length(b))) theta.se <- ability(2, u, b, a) theta.seu <- c(1, 0, 1) b <- c(-1.0, 0.0, 1.0) a <- c(1.0, 1.2, 0.8) ability(2, u, b, a) # ability(2, u, b, a, c = rep(0, length(b))) theta.se <- ability(2, u, b, a) theta.se
The birtr package provides nine important functions:
iccplot(), icccal(), icc(), iccfit(), groupinv(),
tcc(), ability(), tif(), and rasch().
The iccplot() function plots an item characteristic curve under the
two-parameter logistic model.
The icccal() function computes the logistic deviate L, the
exponent of negative L, the denominator, and the value of probability
of correct response for each of seven ability levels evenly spaced from
-3 to +3 under the one-, two-, or three-parameter logistic item
characteristic curve model.
The icc() function plots an item characteristic curve under the one-,
two-, or three-parameter logistic model.
The iccfit() function plots the item characteristic curve and the
simulated observed proportions of correct response from the one-, two-,
or three-parameter logistic model.
The groupinv() function plots the item characteristic curve and
the two sets of simulated observed proportions of correct response from
two groups under the one-, two-, or three-parameter logistic model.
The tcc() function plots a test characteristic curve from a set of
item parameters under the one-, two-, or three-parameter logistic model.
The ability() function estimates the ability parameter and obtains
the standard error of the estimate given the item characteristic curve
model, the response vector, and the set of known item parameters under
the one-, two-, or three-parameter logistic model.
The tif() function plots a test information function from a set of
item parameters under the one-, two-, or three-parameter logistic model.
The rasch() function yields estimates of item difficulty parameters
and ability parameters under the one-parameter logistic Rasch model
by the Birnbaum paradigm.
Seock-Ho Kim [email protected]
Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1
Plots the item characteristic curve and the two sets of simulated observed proportions of correct response from two groups under the one-, two-, or three-parameter logistic model.
groupinv(mdl, t1l, t1u, t2l, t2u)groupinv(mdl, t1l, t1u, t2l, t2u)
mdl |
1, 2, or 3 representing the number of the model parameters. |
t1l |
a number indicating the lower bound of ability for group 1. |
t1u |
a number indicating the upper bound of ability for group 1. |
t2l |
a number indicating the lower bound of ability for group 2. |
t2u |
a number indicating the upper bound of ability for group 2. |
While the theoretical range of ability is from negative infinity to positive
infinity, practical considerations usually limit the range of values
from -3 to +3.
The default values are t1l = -3, t1u = -1, t2l = 1,
and t2u = 3.
With the number of item characteristic curve model parameters mdl
the item parameters are randomly sampled from the uniform distributions; for
example, under the three-parameter logistic model, b from the -3 to
3 range, a from the 0.2 to 2.8 range, and c from the 0 to
.35 range.
Each of the 33 ability levels from the -3 to +3 range with .1875 interval,
the observed proportion of correct response is generated from the binomial
distribution for sample size of 21.
The ability levels and the observed proportions of correct response between
t1l and t1u are used as the group 1 data, and
the ability levels and the observed proportions of correct response between
t2l and t2u are used as the group 2 data.
The data from the pooled groups are used to obatin the plot that displays
the set of item parameters.
Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1
groupinv(1) # groupinv(1, -3, -1, 1, 3) groupinv(2) # groupinv(2, -3, -1, 1, 3) groupinv(3) # groupinv(3, -3, -1, 1, 3) groupinv(2, -2, 1, -1, 2)groupinv(1) # groupinv(1, -3, -1, 1, 3) groupinv(2) # groupinv(2, -3, -1, 1, 3) groupinv(3) # groupinv(3, -3, -1, 1, 3) groupinv(2, -2, 1, -1, 2)
Plots an item characteristic curve under the one-, two-, or three-parameter logistic model.
icc(b, a, c)icc(b, a, c)
b |
a single number representing the value of item difficulty. |
a |
a single number representing the value of item discrimination. |
c |
a single number representing the value of lower asymptote. |
While the theoretical range of ability is from negative infinity to positive
infinity, practical considerations usually limit the range of values
from -3 to +3.
Under the one-parameter logistic model, a = 1 and c = 0.
Under the two-parameter logistic model, c = 0.
The parameter c has a theoretical range from 0 to 1, but in practice
values above .35 are not considered acceptable, hence use the range from 0
to .35 for c.
The vertical dotted line corresponds to the value of the item difficulty
parameter.
Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1
icc(1.5, 1.3, .2) icc(a = 1.3, b = 1.5, c = .2) icc(1) # icc(1, 1, 0) icc(1, 0.5) # icc(1, 0.5, 0)icc(1.5, 1.3, .2) icc(a = 1.3, b = 1.5, c = .2) icc(1) # icc(1, 1, 0) icc(1, 0.5) # icc(1, 0.5, 0)
Computes the logistic deviate L, the exponent of negative L, the denominator, and the value of probability of correct response for each of seven ability levels evenly spaced from -3 to +3 under the one-, two-, or three-parameter logistic item characteristic curve model.
icccal(b, a, c)icccal(b, a, c)
b |
a single number representing the value of item difficulty. |
a |
a single number representing the value of item discrimination. |
c |
a single number representing the value of lower asymptote. |
While the theoretical range of ability is from negative infinity to positive
infinity, practical considerations usually limit the range of values
from -3 to +3.
Under the one-parameter logistic model, a = 1 and c = 0.
Under the two-parameter logistic model, c = 0.
The parameter c has a theoretical range from 0 to 1, but in practice
values above .35 are not considered acceptable, hence use the range from 0
to .35 for c.
Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1
icccal(1.5, 1.3, .2) icccal(a = 1.3, b = 1.5, c = .2) icccal(1) # icccal(1, 1, 0) icccal(1, 0.5) # icccal(1, 0.5, 0)icccal(1.5, 1.3, .2) icccal(a = 1.3, b = 1.5, c = .2) icccal(1) # icccal(1, 1, 0) icccal(1, 0.5) # icccal(1, 0.5, 0)
Plots the item characteristic curve and the simulated observed proportions of correct response from the one-, two-, or three-parameter logistic model.
iccfit(mdl)iccfit(mdl)
mdl |
1, 2, or 3 representing the number of the model parameters. |
While the theoretical range of ability is from negative infinity to positive
infinity, practical considerations usually limit the range of values
from -3 to +3.
With the number of item characteristic curve model parameters mdl
the item parameters are randomly sampled from the uniform distributions; for
example, under the three-parameter logistic model, b from the -3 to
3 range, a from the 0.2 to 2.8 range, and c from the 0 to
.35 range.
Each of the 33 ability levels from the -3 to +3 range with .1875 interval,
the observed proportion of correct response is generated from the binomial
distribution for sample size of 21.
The chi-square goodness-of-fit index is obtained and reported with the
set of item parameters.
Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1
iccfit(1) iccfit(2) iccfit(3)iccfit(1) iccfit(2) iccfit(3)
Plots an item characteristic curve under the two-parameter logistic model.
iccplot(b, a)iccplot(b, a)
b |
a single number representing the value of item difficulty. |
a |
a single number representing the value of item discrimination. |
While the theoretical range of ability is from negative infinity to positive infinity, practical considerations usually limit the range of values from -3 to +3.
Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1
iccplot(0, 1) iccplot(a = 1, b = 0) iccplot(0, 1); par(new = TRUE); iccplot(-1.5, 1)iccplot(0, 1) iccplot(a = 1, b = 0) iccplot(0, 1); par(new = TRUE); iccplot(-1.5, 1)
Yields estimates of item difficulty parameters and ability parameters under the one-parameter logistic Rasch model by the Birnbaum paradigm.
rasch(s, f)rasch(s, f)
s |
a numeric vector representing the column sum for the |
f |
a numeric vector representing the frequencies for the scores from
1 to |
With data editing command lines, the item response data matrix of
N by J is to be converted to the two vectors of the column
sum s and the frequencies for the scores f.
The two vectors are the input for the Birnbaum paradigm to calibrate
the test.
The function contains two other required functions, stage1 and
stage2.
After obtaining the item and ability parameter estimates from the Birnbaum
paradigm, bias correction methods are applied to the item parameter
estimates and then to the ability parameter estimates.
The estimates of item difficulty parameters b are reported in
the console window.
The estimates of ability parameters theta are not for individual
examinees but for the raw score groups ranged from 1 to J-1.
The function prints out the mean and the standard deviation of the item
parameter estimates as well as those of the ability parameter estimates.
Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1
rm(list = ls()) # remove the existing objects in workspace s <- c(13, 8, 8, 5, 10, 7, 7, 6, 7, 3) f <- c(1, 2, 2, 4, 1, 1, 0, 0, 4) rasch(s, f)rm(list = ls()) # remove the existing objects in workspace s <- c(13, 8, 8, 5, 10, 7, 7, 6, 7, 3) f <- c(1, 2, 2, 4, 1, 1, 0, 0, 4) rasch(s, f)
Plots a test characteristic curve from a set of item parameters under the one-, two-, or three-parameter logistic model.
tcc(b, a, c)tcc(b, a, c)
b |
a numeric vector representing the values of item difficulty. |
a |
a numeric vector representing the values of item discrimination. |
c |
a numeric vector representing the values of lower asymptote. |
While the theoretical range of ability is from negative infinity to positive
infinity, practical considerations usually limit the range of values
from -3 to +3.
The length of b should be the same as that of a and c.
Each parameter c has a theoretical range from 0 to 1, but in practice
values above .35 are not considered acceptable, hence use the range from 0
to .35 for each c.
Under the one-parameter logistic model, a = rep(1, length(b)) and
c = rep(0, length(b)).
Under the two-parameter logistic model, c = rep(0, length(b)).
Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1
b <- c(-2.0, -1.0, 0.0, 1.0, 2.0) a <- c(0.5, 0.75, 1.0, 0.75, 0.5) c <- c(.2, .2, .2, .2, .2) tcc(b, a, c) tcc(a = a, b = b, c = c) tcc(b) # tcc(b, a = rep(1, length(b)), c = rep(0, length(b))) tcc(b, a) # tcc(b, a, c = rep(0, length(b)))b <- c(-2.0, -1.0, 0.0, 1.0, 2.0) a <- c(0.5, 0.75, 1.0, 0.75, 0.5) c <- c(.2, .2, .2, .2, .2) tcc(b, a, c) tcc(a = a, b = b, c = c) tcc(b) # tcc(b, a = rep(1, length(b)), c = rep(0, length(b))) tcc(b, a) # tcc(b, a, c = rep(0, length(b)))
Plots a test information function from a set of item parameters under the one-, two-, or three-parameter logistic model.
tif(b, a, c)tif(b, a, c)
b |
a numeric vector representing the values of item difficulty. |
a |
a numeric vector representing the values of item discrimination. |
c |
a numeric vector representing the values of lower asymptote. |
While the theoretical range of ability is from negative infinity to positive
infinity, practical considerations usually limit the range of values
from -3 to +3.
The length of b should be the same as that of a and c.
Each parameter c has a theoretical range from 0 to 1, but in practice
values above .35 are not considered acceptable, hence use the range from 0
to .35 for each c.
Under the one-parameter logistic model, a = rep(1, length(b)) and
c = rep(0, length(b)).
Under the two-parameter logistic model, c = rep(0, length(b)).
In case b to be a single number, then the plot contains the item
informaiton function.
Note that the maximum of the information value on the vertical axis of
the graph is arbitrarily set to 10.
Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1
b <- c(-1.0, -0.5, 0.0, 0.5, 1.0) a <- c(2.0, 1.5, 1.5, 1.5, 2.0) c <- c(.2, .2, .2, .2, .2) tif(b, a, c) tif(a = a, b = b, c = c) tif(b) # tif(b, a = rep(1, length(b)), c = rep(0, length(b))) tif(b, a) # tif(b, a, c = rep(0, length(b)))b <- c(-1.0, -0.5, 0.0, 0.5, 1.0) a <- c(2.0, 1.5, 1.5, 1.5, 2.0) c <- c(.2, .2, .2, .2, .2) tif(b, a, c) tif(a = a, b = b, c = c) tif(b) # tif(b, a = rep(1, length(b)), c = rep(0, length(b))) tif(b, a) # tif(b, a, c = rep(0, length(b)))