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

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)

Helper functions for MST Assembly and Simulation

Description

helper functions for MST assembly and simulation

mst_get_form_index maps the input form indices to the actual indices

Usage

mst_get_form_index(x, indices, method)

Arguments

Value

mst_get_form_index returns a matrix of form index with rows being routes and columns the modules.

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

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

set.seed(123456)
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=30)

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)