README.md
In xluo11/Rata: Automated Test Assembly
Rata: Automated Test Assembly
Overview
Rata applies mixed integer programming (MIP) to automatically build test
forms for educational and psychological assessment. Rata is designed as
a general automated test assembly (ATA) framework, and it can be used to
assemble linear tests, support linear-on-the-fly testing (LOFT), prepare
item pools for computerized adaptive testing (CAT), and assemble panels
in multistage testing (MST).
In Rata, users first define a MIP model by adding the objective and
constraints sequentially, and then solve the MIP model using either
lp_solve or
GLPK.
Rata supports mixed format item pool. Currently, the mixed format item
pool supports a mixture of 3PL, GPCM, and GRM items. Key dependencies of
Rata include Rirt,
lpSolveAPI, and
glpkAPI.
Installation
Install the stable version from CRAN:
install.packages("Rata")
Install the most recent version from
github:
devtools::install_github("xluo11/Rata")
Quickstart
Users would use the following functions to build and solve MIP models:
ata: initiate a MIP modelata_relative_objective: add relative test assembly objective to
the modelata_absolute_objective: add absolute test assembly objective to
the modelata_constraint: add constraints pertaining to categorical and
continuous item attributes to the modelata_item_use: add constraints pertaining to item usage to the
modelata_item_enemy: add constraints pertaining to enemy items to the
modelata_item_fix: fix the value of the decision variable in the modelata_solve: solve the model using a MIP solver. Rata currently
supports lp_solve and GLPKplot: plot the TIF of the assembled test forms
Usage
First, we write a helper function for generating item pools which is
used in following examples. By default, the pool includes 300 3PL items,
20 GPCM items, and 20 GRM items. Each item has a categorical item
attribute (content area) and a continuous attribute (response time). In
addition, items are randomly grouped to form item sets.
library(Rirt)
library(dplyr, warn.conflicts=FALSE)
item_pool <- function(types=c('3pl', 'gpcm', 'grm'), n_3pl=300, n_gpcm=20, n_grm=20, seed=21578) {
set.seed(seed)
items <- model_mixed_gendata(1, n_3pl, n_gpcm, n_grm, n_c=4)$items
items$'3pl' <- cbind(items$'3pl', id=seq(n_3pl), content=sample(3, n_3pl, replace=TRUE),
time=round(rlnorm(n_3pl, 4, .38)), group=sort(sample(n_3pl/2, n_3pl, replace=TRUE)))
items$'gpcm' <- cbind(items$'gpcm', id=seq(n_gpcm), content=sample(3, n_gpcm, replace=TRUE),
time=round(rlnorm(n_gpcm, 4, .38)), group=sort(sample(n_gpcm/2, n_gpcm, replace=TRUE)))
items$'grm' <- cbind(items$'grm', id=seq(n_grm), content=sample(3, n_grm, replace=TRUE),
time=round(rlnorm(n_grm, 4, .38)), group=sort(sample(n_grm/2, n_grm, replace=TRUE)))
items[names(items) %in% types]
}
Example 1: Assemble linear tests
Assemble 4 non-overlapping forms that should have maximum test
information function (TIF) from -1.28 to 1.28 on the scale which covers
80% of the population. Each form includes 10 items, with 3, 3, and 4
items in the content area 1 to 3 respectively. Additionally, each form
has an average response time of 60 +/- 5 seconds per item.
x <- ata(item_pool(), n_forms=4, test_len=10, max_use=1)
x <- ata_relative_objective(x, seq(-1.28, 1.28, length.out=4), 'max')
x <- ata_constraint(x, 'content', min=3, max=3, level=1)
x <- ata_constraint(x, 'content', min=3, max=3, level=2)
x <- ata_constraint(x, 'content', min=4, max=4, level=3)
x <- ata_constraint(x, 'time', min=55*10, max=65*10)
x <- ata_solve(x, 'lpsolve', return_format='model', time_limit=30)
## the model is sub-optimal, optimum: 2.373 (3.509, 1.136)
rbind(if(nrow(x$items$'3pl') > 0) select(x$items$'3pl', content, time, form) else NULL,
if(nrow(x$items$'gpcm') > 0) select(x$items$'gpcm', content, time, form) else NULL,
if(nrow(x$items$'grm') > 0) select(x$items$'grm', content, time, form) else NULL) %>%
group_by(form) %>%
summarise(con1=sum(content==1), con2=sum(content==2), con3=sum(content==3), time=mean(time))
## # A tibble: 4 x 5
## form con1 con2 con3 time
## <int> <int> <int> <int> <dbl>
## 1 1 3 3 4 63.6
## 2 2 3 3 4 65
## 3 3 3 3 4 60.3
## 4 4 3 3 4 55.6
plot(x)
To obtain a flatter TIF over the same region so that the test produces
more comparable measurement errors, we give ATA a TIF target that is
about 60% of the optimum found in the previous solution.
tif_tar <- x$obj_var[1] * .6
x <- ata(item_pool(), n_forms=4, test_len=10, max_use=1)
x <- ata_absolute_objective(x, seq(-1.28, 1.28, length.out=4), target=tif_tar)
x <- ata_constraint(x, 'content', min=3, max=3, level=1)
x <- ata_constraint(x, 'content', min=3, max=3, level=2)
x <- ata_constraint(x, 'content', min=4, max=4, level=3)
x <- ata_constraint(x, 'time', min=55*10, max=65*10)
x <- ata_solve(x, 'lpsolve', return_format='model', time_limit=30)
## the model is sub-optimal, optimum: 0.174 (0.059, 0.115)
rbind(if(nrow(x$items$'3pl') > 0) select(x$items$'3pl', content, time, form) else NULL,
if(nrow(x$items$'gpcm') > 0) select(x$items$'gpcm', content, time, form) else NULL,
if(nrow(x$items$'grm') > 0) select(x$items$'grm', content, time, form) else NULL) %>%
group_by(form) %>%
summarise(con1=sum(content==1), con2=sum(content==2), con3=sum(content==3), time=mean(time))
## # A tibble: 4 x 5
## form con1 con2 con3 time
## <int> <int> <int> <int> <dbl>
## 1 1 3 3 4 59.5
## 2 2 3 3 4 64.7
## 3 3 3 3 4 55.2
## 4 4 3 3 4 62.7
plot(x)
We can also use difficulty parameters, as opposed to TIF, to control the
psychometric characteristics of the test forms. In this example, we
assemble four parallel test forms in which the mean and SD of difficulty
parameters are equal to 0 and 1
respectively.
x <- ata(item_pool('3pl', n_3pl=300), n_forms=4, test_len=10, max_use=1) # generate 300 3PL items
x <- ata_absolute_objective(x, x$pool$'3pl'$b, target=0*10)
x <- ata_absolute_objective(x, (x$pool$'3pl'$b-0)^2, target=1^2*10)
x <- ata_constraint(x, 'content', min=3, max=3, level=1)
x <- ata_constraint(x, 'content', min=3, max=3, level=2)
x <- ata_constraint(x, 'content', min=4, max=4, level=3)
x <- ata_constraint(x, 'time', min=55*10, max=65*10)
x <- ata_solve(x, 'lpsolve', return_format='model', time_limit=30)
## the model is sub-optimal, optimum: 0.043 (0.043, 0)
group_by(x$items$'3pl', form) %>%
summarise(b_mean=mean(b), b_std=sd(b), con1=sum(content==1), con2=sum(content==2), con3=sum(content==3), time=mean(time)) %>% round(., 2)
## # A tibble: 4 x 7
## form b_mean b_std con1 con2 con3 time
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 1.05 3 3 4 55.8
## 2 2 0 1.05 3 3 4 59.6
## 3 3 0 1.05 3 3 4 60.5
## 4 4 0 1.05 3 3 4 55.2
Example 2: Model item relational constraints
In this example, we demonstrate how to control item relational
constraints in ATA. First is the item set constraints, which treats
items associated with the same stimulus as a group. Setting ata(...,
group=) to the name of the item set grouping variable would add the
relevant constraints to the MIP model automatically in the ensuing model
building
process.
x <- ata(item_pool('3pl', n_3pl=200), n_forms=4, test_len=10, max_use=1, group='group') # generate 200 3PL items
x <- ata_relative_objective(x, seq(-.68, .68, length.out=3), 'max') # maximize TIF over [-.68, .68] which covers 50% of the population
x <- ata_solve(x, 'lpsolve', 'model', time_limit=30)
## the model is sub-optimal, optimum: 2.938 (3.661, 0.723)
# ATA = number of items associated with the group id in assembled forms
# Pool = number of items associated with the group id in the item pool
merge(group_by(x$items$'3pl', form, group) %>% summarise(ATA=n()),
group_by(x$pool$'3pl', group) %>% summarise(Pool=n()),
by='group', all.x=TRUE) %>% arrange(form, group)
## group form ATA Pool
## 1 5 1 1 1
## 2 7 1 1 1
## 3 27 1 4 4
## 4 55 1 3 3
## 5 61 1 1 1
## 6 14 2 1 1
## 7 25 2 1 1
## 8 39 2 4 4
## 9 73 2 1 1
## 10 75 2 1 1
## 11 80 2 1 1
## 12 94 2 1 1
## 13 42 3 3 3
## 14 44 3 5 5
## 15 49 3 1 1
## 16 64 3 1 1
## 17 11 4 1 1
## 18 21 4 1 1
## 19 50 4 1 1
## 20 68 4 2 2
## 21 69 4 2 2
## 22 76 4 1 1
## 23 81 4 2 2
plot(x)
To have a set of common items shared across all forms, use ata(...,
common_items=). To have a set of common items shared between adjacent
forms, use ata(..., overlap_items).
# 5 common items among all forms
x <- ata(item_pool('3pl', n_3pl=200), n_forms=4, test_len=10, max_use=1, common_items=5)
x <- ata_relative_objective(x, seq(-.68, .68, length.out=3), 'max')
x <- ata_solve(x, 'lpsolve', 'model', time_limit=30)
## the model is sub-optimal, optimum: 3.729 (4.424, 0.695)
plot(x)
counts <- with(x$items$'3pl', table(id, form))
# expect 10 items each test form
colSums(counts)
## 1 2 3 4
## 10 10 10 10
# expect 5 items that appear in all test forms
counts[rowSums(counts)==4, ]
## form
## id 1 2 3 4
## 112 1 1 1 1
## 117 1 1 1 1
## 128 1 1 1 1
## 150 1 1 1 1
## 158 1 1 1 1
To avoid enemy items in the same form, use the ata_item_enemy
function.
x <- ata(item_pool('3pl', n_3pl=15), n_forms=5, test_len=3, max_use=1)
x <- ata_relative_objective(x, x$pool$'3pl'$b, 'max')
x <- ata_item_enemy(x, 1:5) # do not put item 1-5 in the same form
x <- ata_item_enemy(x, 6:10) # do not put item 6-10 in the same form
x <- ata_item_enemy(x, 11:15) # do not put item 11-15 in the same form
x <- ata_solve(x, 'lpsolve', 'model', time_limit=30)
## optimal solution found, optimum: 0.021 (0.146, 0.125)
# expect each form have one item from 1-5, 6-10, and 11-15
select(x$items$'3pl', form, id) %>% arrange(form, id)
## form id
## 1 1 2
## 2 1 10
## 3 1 12
## 4 2 3
## 5 2 8
## 6 2 11
## 7 3 4
## 8 3 7
## 9 3 13
## 10 4 5
## 11 4 9
## 12 4 14
## 13 5 1
## 14 5 6
## 15 5 15
To allow item reuse, use ata(..., max_use=) or the ata_item_use
function.
x <- ata(item_pool('3pl', n_3pl=15), n_forms=2, test_len=5, max_use=2) # allow items to be used up to twice
x <- ata_relative_objective(x, x$pool$'3pl'$b, 'max')
x <- ata_solve(x, 'lpsolve', 'model', time_limit=30)
## optimal solution found, optimum: 3.348 (3.348, 0)
# expect two identical forms, since the best items are reused
with(x$items$'3pl', table(id, form))
## form
## id 1 2
## 1 1 1
## 4 1 1
## 6 1 1
## 11 1 1
## 14 1 1
To force an item to be select or not selected, use the ata_item_fix
function.
x <- ata(item_pool('3pl', n_3pl=15), n_forms=2, test_len=5, max_use=2)
x <- ata_relative_objective(x, x$pool$'3pl'$b, 'max')
x <- ata_item_fix(x, 1:5, min=1, forms=1) # use item 1-5 in form 1
x <- ata_item_fix(x, 1:5, max=0, forms=2) # do not use 1-5 in form 2
x <- ata_solve(x, 'lpsolve', 'model', time_limit=30)
## optimal solution found, optimum: 1.138 (1.152, 0.014)
# expect item 1-5 in form 1 but not form 2
with(x$items$'3pl', table(id, form))
## form
## id 1 2
## 1 1 0
## 2 1 0
## 3 1 0
## 4 1 0
## 5 1 0
## 6 0 1
## 7 0 1
## 10 0 1
## 12 0 1
## 14 0 1
Getting help
If you encounter a bug, please post a code example that exposes the bug
on github. You can post your
questions and feature requests on
github or contact the
author.
xluo11/Rata documentation built on Nov. 5, 2019, 12:29 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Rata: Automated Test Assembly
Overview
Rata applies mixed integer programming (MIP) to automatically build test forms for educational and psychological assessment. Rata is designed as a general automated test assembly (ATA) framework, and it can be used to assemble linear tests, support linear-on-the-fly testing (LOFT), prepare item pools for computerized adaptive testing (CAT), and assemble panels in multistage testing (MST).
In Rata, users first define a MIP model by adding the objective and constraints sequentially, and then solve the MIP model using either lp_solve or GLPK.
Rata supports mixed format item pool. Currently, the mixed format item pool supports a mixture of 3PL, GPCM, and GRM items. Key dependencies of Rata include Rirt, lpSolveAPI, and glpkAPI.
Installation
Install the stable version from CRAN:
install.packages("Rata")
Install the most recent version from github:
devtools::install_github("xluo11/Rata")
Quickstart
Users would use the following functions to build and solve MIP models:
ata: initiate a MIP modelata_relative_objective: add relative test assembly objective to the modelata_absolute_objective: add absolute test assembly objective to the modelata_constraint: add constraints pertaining to categorical and continuous item attributes to the modelata_item_use: add constraints pertaining to item usage to the modelata_item_enemy: add constraints pertaining to enemy items to the modelata_item_fix: fix the value of the decision variable in the modelata_solve: solve the model using a MIP solver. Rata currently supports lp_solve and GLPKplot: plot the TIF of the assembled test forms
Usage
First, we write a helper function for generating item pools which is used in following examples. By default, the pool includes 300 3PL items, 20 GPCM items, and 20 GRM items. Each item has a categorical item attribute (content area) and a continuous attribute (response time). In addition, items are randomly grouped to form item sets.
library(Rirt)
library(dplyr, warn.conflicts=FALSE)
item_pool <- function(types=c('3pl', 'gpcm', 'grm'), n_3pl=300, n_gpcm=20, n_grm=20, seed=21578) {
set.seed(seed)
items <- model_mixed_gendata(1, n_3pl, n_gpcm, n_grm, n_c=4)$items
items$'3pl' <- cbind(items$'3pl', id=seq(n_3pl), content=sample(3, n_3pl, replace=TRUE),
time=round(rlnorm(n_3pl, 4, .38)), group=sort(sample(n_3pl/2, n_3pl, replace=TRUE)))
items$'gpcm' <- cbind(items$'gpcm', id=seq(n_gpcm), content=sample(3, n_gpcm, replace=TRUE),
time=round(rlnorm(n_gpcm, 4, .38)), group=sort(sample(n_gpcm/2, n_gpcm, replace=TRUE)))
items$'grm' <- cbind(items$'grm', id=seq(n_grm), content=sample(3, n_grm, replace=TRUE),
time=round(rlnorm(n_grm, 4, .38)), group=sort(sample(n_grm/2, n_grm, replace=TRUE)))
items[names(items) %in% types]
}
Example 1: Assemble linear tests
Assemble 4 non-overlapping forms that should have maximum test information function (TIF) from -1.28 to 1.28 on the scale which covers 80% of the population. Each form includes 10 items, with 3, 3, and 4 items in the content area 1 to 3 respectively. Additionally, each form has an average response time of 60 +/- 5 seconds per item.
x <- ata(item_pool(), n_forms=4, test_len=10, max_use=1)
x <- ata_relative_objective(x, seq(-1.28, 1.28, length.out=4), 'max')
x <- ata_constraint(x, 'content', min=3, max=3, level=1)
x <- ata_constraint(x, 'content', min=3, max=3, level=2)
x <- ata_constraint(x, 'content', min=4, max=4, level=3)
x <- ata_constraint(x, 'time', min=55*10, max=65*10)
x <- ata_solve(x, 'lpsolve', return_format='model', time_limit=30)
## the model is sub-optimal, optimum: 2.373 (3.509, 1.136)
rbind(if(nrow(x$items$'3pl') > 0) select(x$items$'3pl', content, time, form) else NULL,
if(nrow(x$items$'gpcm') > 0) select(x$items$'gpcm', content, time, form) else NULL,
if(nrow(x$items$'grm') > 0) select(x$items$'grm', content, time, form) else NULL) %>%
group_by(form) %>%
summarise(con1=sum(content==1), con2=sum(content==2), con3=sum(content==3), time=mean(time))
## # A tibble: 4 x 5
## form con1 con2 con3 time
## <int> <int> <int> <int> <dbl>
## 1 1 3 3 4 63.6
## 2 2 3 3 4 65
## 3 3 3 3 4 60.3
## 4 4 3 3 4 55.6
plot(x)
To obtain a flatter TIF over the same region so that the test produces more comparable measurement errors, we give ATA a TIF target that is about 60% of the optimum found in the previous solution.
tif_tar <- x$obj_var[1] * .6
x <- ata(item_pool(), n_forms=4, test_len=10, max_use=1)
x <- ata_absolute_objective(x, seq(-1.28, 1.28, length.out=4), target=tif_tar)
x <- ata_constraint(x, 'content', min=3, max=3, level=1)
x <- ata_constraint(x, 'content', min=3, max=3, level=2)
x <- ata_constraint(x, 'content', min=4, max=4, level=3)
x <- ata_constraint(x, 'time', min=55*10, max=65*10)
x <- ata_solve(x, 'lpsolve', return_format='model', time_limit=30)
## the model is sub-optimal, optimum: 0.174 (0.059, 0.115)
rbind(if(nrow(x$items$'3pl') > 0) select(x$items$'3pl', content, time, form) else NULL,
if(nrow(x$items$'gpcm') > 0) select(x$items$'gpcm', content, time, form) else NULL,
if(nrow(x$items$'grm') > 0) select(x$items$'grm', content, time, form) else NULL) %>%
group_by(form) %>%
summarise(con1=sum(content==1), con2=sum(content==2), con3=sum(content==3), time=mean(time))
## # A tibble: 4 x 5
## form con1 con2 con3 time
## <int> <int> <int> <int> <dbl>
## 1 1 3 3 4 59.5
## 2 2 3 3 4 64.7
## 3 3 3 3 4 55.2
## 4 4 3 3 4 62.7
plot(x)
We can also use difficulty parameters, as opposed to TIF, to control the psychometric characteristics of the test forms. In this example, we assemble four parallel test forms in which the mean and SD of difficulty parameters are equal to 0 and 1 respectively.
x <- ata(item_pool('3pl', n_3pl=300), n_forms=4, test_len=10, max_use=1) # generate 300 3PL items
x <- ata_absolute_objective(x, x$pool$'3pl'$b, target=0*10)
x <- ata_absolute_objective(x, (x$pool$'3pl'$b-0)^2, target=1^2*10)
x <- ata_constraint(x, 'content', min=3, max=3, level=1)
x <- ata_constraint(x, 'content', min=3, max=3, level=2)
x <- ata_constraint(x, 'content', min=4, max=4, level=3)
x <- ata_constraint(x, 'time', min=55*10, max=65*10)
x <- ata_solve(x, 'lpsolve', return_format='model', time_limit=30)
## the model is sub-optimal, optimum: 0.043 (0.043, 0)
group_by(x$items$'3pl', form) %>%
summarise(b_mean=mean(b), b_std=sd(b), con1=sum(content==1), con2=sum(content==2), con3=sum(content==3), time=mean(time)) %>% round(., 2)
## # A tibble: 4 x 7
## form b_mean b_std con1 con2 con3 time
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0 1.05 3 3 4 55.8
## 2 2 0 1.05 3 3 4 59.6
## 3 3 0 1.05 3 3 4 60.5
## 4 4 0 1.05 3 3 4 55.2
Example 2: Model item relational constraints
In this example, we demonstrate how to control item relational
constraints in ATA. First is the item set constraints, which treats
items associated with the same stimulus as a group. Setting ata(...,
group=) to the name of the item set grouping variable would add the
relevant constraints to the MIP model automatically in the ensuing model
building
process.
x <- ata(item_pool('3pl', n_3pl=200), n_forms=4, test_len=10, max_use=1, group='group') # generate 200 3PL items
x <- ata_relative_objective(x, seq(-.68, .68, length.out=3), 'max') # maximize TIF over [-.68, .68] which covers 50% of the population
x <- ata_solve(x, 'lpsolve', 'model', time_limit=30)
## the model is sub-optimal, optimum: 2.938 (3.661, 0.723)
# ATA = number of items associated with the group id in assembled forms
# Pool = number of items associated with the group id in the item pool
merge(group_by(x$items$'3pl', form, group) %>% summarise(ATA=n()),
group_by(x$pool$'3pl', group) %>% summarise(Pool=n()),
by='group', all.x=TRUE) %>% arrange(form, group)
## group form ATA Pool
## 1 5 1 1 1
## 2 7 1 1 1
## 3 27 1 4 4
## 4 55 1 3 3
## 5 61 1 1 1
## 6 14 2 1 1
## 7 25 2 1 1
## 8 39 2 4 4
## 9 73 2 1 1
## 10 75 2 1 1
## 11 80 2 1 1
## 12 94 2 1 1
## 13 42 3 3 3
## 14 44 3 5 5
## 15 49 3 1 1
## 16 64 3 1 1
## 17 11 4 1 1
## 18 21 4 1 1
## 19 50 4 1 1
## 20 68 4 2 2
## 21 69 4 2 2
## 22 76 4 1 1
## 23 81 4 2 2
plot(x)
To have a set of common items shared across all forms, use ata(...,
common_items=). To have a set of common items shared between adjacent
forms, use ata(..., overlap_items).
# 5 common items among all forms
x <- ata(item_pool('3pl', n_3pl=200), n_forms=4, test_len=10, max_use=1, common_items=5)
x <- ata_relative_objective(x, seq(-.68, .68, length.out=3), 'max')
x <- ata_solve(x, 'lpsolve', 'model', time_limit=30)
## the model is sub-optimal, optimum: 3.729 (4.424, 0.695)
plot(x)
counts <- with(x$items$'3pl', table(id, form))
# expect 10 items each test form
colSums(counts)
## 1 2 3 4
## 10 10 10 10
# expect 5 items that appear in all test forms
counts[rowSums(counts)==4, ]
## form
## id 1 2 3 4
## 112 1 1 1 1
## 117 1 1 1 1
## 128 1 1 1 1
## 150 1 1 1 1
## 158 1 1 1 1
To avoid enemy items in the same form, use the ata_item_enemy
function.
x <- ata(item_pool('3pl', n_3pl=15), n_forms=5, test_len=3, max_use=1)
x <- ata_relative_objective(x, x$pool$'3pl'$b, 'max')
x <- ata_item_enemy(x, 1:5) # do not put item 1-5 in the same form
x <- ata_item_enemy(x, 6:10) # do not put item 6-10 in the same form
x <- ata_item_enemy(x, 11:15) # do not put item 11-15 in the same form
x <- ata_solve(x, 'lpsolve', 'model', time_limit=30)
## optimal solution found, optimum: 0.021 (0.146, 0.125)
# expect each form have one item from 1-5, 6-10, and 11-15
select(x$items$'3pl', form, id) %>% arrange(form, id)
## form id
## 1 1 2
## 2 1 10
## 3 1 12
## 4 2 3
## 5 2 8
## 6 2 11
## 7 3 4
## 8 3 7
## 9 3 13
## 10 4 5
## 11 4 9
## 12 4 14
## 13 5 1
## 14 5 6
## 15 5 15
To allow item reuse, use ata(..., max_use=) or the ata_item_use
function.
x <- ata(item_pool('3pl', n_3pl=15), n_forms=2, test_len=5, max_use=2) # allow items to be used up to twice
x <- ata_relative_objective(x, x$pool$'3pl'$b, 'max')
x <- ata_solve(x, 'lpsolve', 'model', time_limit=30)
## optimal solution found, optimum: 3.348 (3.348, 0)
# expect two identical forms, since the best items are reused
with(x$items$'3pl', table(id, form))
## form
## id 1 2
## 1 1 1
## 4 1 1
## 6 1 1
## 11 1 1
## 14 1 1
To force an item to be select or not selected, use the ata_item_fix
function.
x <- ata(item_pool('3pl', n_3pl=15), n_forms=2, test_len=5, max_use=2)
x <- ata_relative_objective(x, x$pool$'3pl'$b, 'max')
x <- ata_item_fix(x, 1:5, min=1, forms=1) # use item 1-5 in form 1
x <- ata_item_fix(x, 1:5, max=0, forms=2) # do not use 1-5 in form 2
x <- ata_solve(x, 'lpsolve', 'model', time_limit=30)
## optimal solution found, optimum: 1.138 (1.152, 0.014)
# expect item 1-5 in form 1 but not form 2
with(x$items$'3pl', table(id, form))
## form
## id 1 2
## 1 1 0
## 2 1 0
## 3 1 0
## 4 1 0
## 5 1 0
## 6 0 1
## 7 0 1
## 10 0 1
## 12 0 1
## 14 0 1
Getting help
If you encounter a bug, please post a code example that exposes the bug on github. You can post your questions and feature requests on github or contact the author.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.