xxIRT (version 2.0.1)

mst: Computerized Multistage Testing (MST)

Description

mst creates a multistage (MST) object

mst_route adds and removes routes in the mst

mst_objective adds objective functions to the mst

mst_constraint adds constraints to the mst

mst_stage_length sets the minimum and maximum length for a stage

mst_set_rdp anchors the routing decision point (rdp) between adjacent modules

mst_module_mininfo sets the minimum information for modules

mst_assemble assembles the mst

mst_get_items extracts items from results

Usage

mst(pool, design, npanel, method, len = NULL, maxselect = NULL)
mst_route(x, route, op)
mst_objective(x, theta, indices = NULL, target = NULL, flatten = NULL,
  theta.step = 2)
mst_constraint(x, coef, min = NA, max = NA, level = NULL,
  indices = NULL)
mst_stage_length(x, stages, min = NA, max = NA)
mst_set_rdp(x, theta, indices, tol)
mst_module_mininfo(x, theta, mininfo, indices)
mst_assemble(x, solver = "lpsolve", verbose = "none", ...)
# S3 method for mst
print(x, ...)
# S3 method for mst
plot(x, ...)
mst_get_items(x, panel, stage = NULL, module = NULL, route = NULL)

Arguments

pool

a data frame of item parameters

design

a numeric vector of the MST design (e.g., 1-2-3, or 1-2-2)

npanel

the number of panels

method

the design method (i.e., 'topdown' or 'bottomup')

len

the module/route length

maxselect

the maximum selection of items

x

the mst object

route

a vector of form indices to represent the route

op

"+" for adding a route and "-" for removing a route

theta

a theta point or interval for optimization

indices

the index of the route (topdown) or the module (bottomup) for adding objectives

target

the target valus of the TIF objectives. NULL for maximization

flatten

the parameter for getting a flat TIF

theta.step

the step parameters to process theta interval

coef

the coefficients of the constraint

min

the minimum value of the contraint

max

the maximum value of the contraint

level

the level value for a categorical constraint

stages

the stage index

tol

tolerance parameter

mininfo

the minimum information treshold

solver

the ata solver

verbose

the verbose parameter

...

further arguments

panel

the panel index

stage

the stage index

module

the module index

Details

The mst object contains an item pool (pool), a test assembler (assembler), a route map (route), a stage-module map (module), a design method (method), and several constants such as npanel, nstage, nmodule, nroute. Two indices are used to index modules/testlets. form number is a unique identifier for all modules, which is used for automated test assembly. index is a panel-wise unique identifier, which is used for routing.

There are two design methods for mst: 'bottomup' and 'topdown'. In the bottomup approach, constraitns are imposed on individual modules. Conversely, in the topdown approach, constraints are imposed on routes.

plot.mst draws module information functions if byroute=FALSE and route information functions if byroute=TRUE

Examples

# NOT RUN {
# generate a 300-item pool
pool <- irt_model("3pl")$gendata(1,300)$items
pool$content <- sample(1:3, nrow(pool), replace=TRUE)
pool$time <- round(exp(rnorm(nrow(pool), log(60), .2)))

## ex. 1: 1-2-2 MST, 2 panels, topdown
## 20 items, content = c(10, 5, 5)
## maximize information at -1 and 1 for easy and hard routes
x <- mst(pool, design=c(1, 2, 2), npanel=2, method='topdown', len=20, maxselect=1)
x <- mst_objective(x, theta=-1, indices=1:2)
x <- mst_objective(x, theta= 1, indices=3:4)
x <- mst_constraint(x, coef="content", min=10, max=10, level=1)
x <- mst_constraint(x, coef="content", min=5, max=5, level=2)
x <- mst_constraint(x, coef="content", min=5, max=5, level=3)
x <- mst_stage_length(x, stages=c(1, 2, 3), min=1)
x <- mst_assemble(x, timeout=10)
x$items
plot(x)
plot(x, byroute=TRUE)
freq(mst_get_items(x, panel=1, route=1)$content, 1:3)$freq
freq(mst_get_items(x, panel=2, route=4)$content, 1:3)$freq

## ex. 2: 1-2-3 MST, 2 panels, bottomup, 
## 10 items in each module, content = c(4, 3, 3)
## maximize information at -1, 0 and 1 for easy, medium, and hard modules
x <- mst(pool, design=c(1, 2, 3), npanel=2, method='bottomup', len=10, maxselect=1)
x <- mst_route(x, c(1, 2, 6), "-")
x <- mst_route(x, c(1, 3, 4), "-")
x <- mst_objective(x, theta= 0, indices=1)
x <- mst_objective(x, theta=-1, indices=c(2,4))
x <- mst_objective(x, theta= 1, indices=c(3,5))
x <- mst_constraint(x, coef="content", min=4, max=4, level=1)
x <- mst_constraint(x, coef="content", min=3, max=3, level=2)
x <- mst_constraint(x, coef="content", min=3, max=3, level=3)
x <- mst_assemble(x, timeout=10)
plot(x)
plot(x, byroute=TRUE)
freq(mst_get_items(x, panel=1, route=1)$content, 1:3)$freq
freq(mst_get_items(x, panel=2, route=4)$content, 1:3)$freq

## ex. 3: 1-2-3 MST, 2 panels, topdown, 30 items, 
## 10 items in each content area
## target information at 18 at -1, 0, and 1 for easy, medium and hard routes
x <- mst(pool, design=c(1, 2, 3), npanel=2, method='topdown', len=30, maxselect=1)
x <- mst_route(x, c(1, 2, 6), "-")
x <- mst_route(x, c(1, 3, 4), "-")
x <- mst_objective(x, theta=-1, indices=1, target=16)
x <- mst_objective(x, theta= 0, indices=2:3, target=16)
x <- mst_objective(x, theta= 1, indices=4, target=16)
x <- mst_constraint(x, coef="content", min=10, max=10, level=1)
x <- mst_constraint(x, coef="content", min=10, max=10, level=2)
x <- mst_constraint(x, coef="content", min=10, max=10, level=3)
x <- mst_stage_length(x, stages=c(1, 2, 3), min=3)
x <- mst_assemble(x, timeout=20)
plot(x)
plot(x, byroute=TRUE)
freq(mst_get_items(x, panel=1, route=1)$content, 1:3)$freq
freq(mst_get_items(x, panel=2, route=4)$content, 1:3)$freq
# }