Package '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
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=2)
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)

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Simulate the Administration of Multistage Tests

Description

mst_sim simulates the administration of the assembled MST panel(s)

Usage

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

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

mst_sim(x, true, rdp = NULL, estimator = model_mixed_eap, ...)

Arguments

x	the assembled MST object
...	additional option/control parameters
true	the true theta parameter (numeric)
rdp	routing decision points (list)
estimator	the estimator of the ability parameter (function)

Details

Use theta to set the initial theta, panel to select the MST panel, prior to set the prior for theta estimation, bounds to set the bounds of theta estimation, and D to set the scaling constant.

Value

a list of true and estimated ability theta, administered items, and end-of-stage statistics

Examples

## assemble a MST
items <- Rirt::model_mixed_gendata(1, n_3pl=150)$items
x <- mst(items, "1-3", 2, 'topdown', len=20, max_use=1)
x <- mst_objective(x, -1, indices=1)
x <- mst_objective(x,  0, indices=2)
x <- mst_objective(x,  1, indices=3)
x <- mst_stage_length(x, 1:2, min=5)
x <- mst_assemble(x, 'lpsolve', time_limit=2)

sim1 <- mst_sim(x, true=.5)
print(sim1)
plot(sim1)

sim2 <- mst_sim(x, true=-.5, rdp=list('stage2'=c(-.44, .44)))
print(sim2)
plot(sim2)

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