assembly {Rmst}

Assemble Computerized Adaptive Multistage Testing

Description

mst creates a multistage (MST) assembly model

mst_route adds/removes a route to/from the assembly model

mst_objective adds an objective to the assembly model

mst_constraint adds constraints to the assembly model

mst_stage_length sets length limits on stages

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

mst_module_info sets the information requirements for modules

mst_assemble tries to solve the assembly model

mst_get_items retrieves items from the assembly results

Usage

mst(pool, design, n_panels = 1, method = c("topdown", "bottomup"),
  test_len = NULL, max_use = NULL, ...)

mst_route(x, route, op = c("+", "-"))

mst_objective(x, coef, mode = c("max", "min"), indices = NULL,
  target = NULL, method = NULL, ...)

mst_constraint(x, coef, min = NA, max = NA, level = NULL,
  indices = NULL, method = NULL)

mst_stage_length(x, stages, min = NA, max = NA)

mst_rdp(x, theta, indices, tol = 0.5)

mst_module_info(x, theta, min = NA, max = NA, indices)

mst_assemble(x, solver = c("lpsolve", "glpk"), silent = FALSE,
  time_limit = 30, message = FALSE, ...)

mst_get_items(x, panel_ix = NULL, stage_ix = NULL, module_ix = NULL,
  route_ix = NULL)

## S3 method for class 'mst'
print(x, ...)

## S3 method for class 'mst'
plot(x, ...)

Arguments

pool

the item pool (a list of '3pl', 'gpcm', and 'grm' items)

design

the MST design (string): e.g., "1-3", "1-2-2", "1-2-3"

n_panels

the number of panels (integer)

method

the design method (string): 'topdown' or 'bottomup'

test_len

the module/route length (integer)

max_use

the maximum selection of items (integer)

...

additional arguments

x

the MST object

route

a MST route (a vector of module index)

op

"+" to add a route and "-" to remove a route

coef

the coefficients (numeric vector or string)

mode

the optimization direction: "max" or "min"

indices

the indices of the route (topdown) or the module (bottomup) where the objective is added

target

the target values of the absolute objectives, NULL for the relative objective

min

the lower bound of the constraint

max

the upper bound of the constraint

level

the constrained level of categorical item attribute, NULL for continuous item attributes

stages

the stage indices

theta

the theta point where TIF is controlled

tol

tolerance parameter (numeric)

solver

the MIP solver: "lpsolve" or "glpk"

silent

TRUE to mute solving status

time_limit

the time limit for solving the model in seconds

message

TRUE to print messages from the solver

panel_ix

the panel index (int vector)

stage_ix

the stage index (int vector)

module_ix

the module index (int vector)

route_ix

the route index (int vector)

Details

A mst object stores the definitions of the MST. When mst_assemble is called, definitions are converted to a real mixed integer programming model for assembly. If the model is solved, assembled items are appended to the original object.
The bottom-up approach adds objectives and constraints on individual modules, and the top-down approach adds objectives and constraints on routes.

coef in mst_objective can be a vector of theta points where TIFs are optimized, or a continuous variable in the pool where the item attribute is optimized, or a numeric value with the same length of the pool at either item or group level.

plot.mst draws module information functions when byroute=FALSE and route information functions when byroute=TRUE. Use label=TRUE to put labels on routes and modules.

Value

mst returns a mst object.

mst_get_items returns the assembled forms in a list of 3pl, gpcm, and grm items

Examples

## generate item pool
set.seed(123456)
items <- Rirt::model_mixed_gendata(1, n_3pl=200)$items

## Ex. 1: 1-2-2 MST, 2 panels, 20 items, topdown
## maximize info. at -1 and 1 for easy and hard routes
x <- mst(items, "1-2-2", n_panels=2, method='topdown', test_len=10, max_use=1)
x <- mst_objective(x, -1, indices=1:2)
x <- mst_objective(x, 1, indices=3:4)
x <- mst_assemble(x, 'lpsolve', time_limit=30)
plot(x, byroute=TRUE, label=TRUE)

## Ex. 2: 1-2-3 MST, 2 panels, bottomup,
## remove two routes with large theta change: 1-2-6, 1-3-4
## 10 items in each module, content= and 3 items in content area 1 in each module
## maximize info. at -1, 0 and 1 for easy, medium, and hard modules
x <- mst(items, "1-2-3", 1, 'bottomup', len=10, max_use=1)
x <- mst_route(x, c(1, 2, 6), "-")
x <- mst_route(x, c(1, 3, 4), "-")
x <- mst_objective(x,  0, indices=c(1, 5))
x <- mst_objective(x, -1, indices=c(2, 4))
x <- mst_objective(x,  1, indices=c(3, 6))
x <- mst_assemble(x, timeout=30)
plot(x, byroute=FALSE)
plot(x, byroute=TRUE)