ability: Estimate abilities

In dexter: Data Management and Analysis of Tests

Estimate abilities

Description

Computes estimates of ability for persons or for booklet scores

Usage

ability(
  dataSrc,
  parms,
  predicate = NULL,
  method = c("MLE", "EAP", "WLE"),
  prior = c("normal", "Jeffreys"),
  parms_draw = "average",
  mu = 0,
  sigma = 4,
  merge_within_persons = FALSE
)

ability_tables(
  parms,
  design = NULL,
  method = c("MLE", "EAP", "WLE"),
  prior = c("normal", "Jeffreys"),
  parms_draw = "average",
  mu = 0,
  sigma = 4
)

Arguments

dataSrc	a connection to a dexter database, a matrix, or a data.frame with columns: person_id, item_id, item_score
parms	object produced by fit_enorm or a data.frame with columns item_id, item_score and, depending on parametrization, a column named either beta/delta, eta or b
predicate	An optional expression to subset data, if NULL all data is used
method	Maximum Likelihood (MLE), Expected A posteriori (EAP) or Weighted Likelihood (WLE)
prior	If an EAP estimate is produced one can choose a normal prior or Jeffreys prior; i.e., a prior proportional to the square root of test information.
parms_draw	When parms is Bayesian, parms_draw can be the index of the posterior sample of the item parameters that will be used for generating abilities. If parms_draw='average', the posterior mean is used.
mu	Mean of the normal prior
sigma	Standard deviation of the normal prior
merge_within_persons	for persons who were administered multiple booklets, whether to provide just one ability value (TRUE) or one per booklet(FALSE)
design	A data.frame with columns item_id and optionally booklet_id. If the column booklet_id is not included, the score transformation table will be based on all items found in the design. If design is NULL and parms is an enorm fit object the score transformation table will be computed based on the test design that was used to fit the items.

Details

MLE estimates of ability will produce -Inf and Inf estimates for the minimum (=0) and the maximum score on a booklet. If this is undesirable, we advise to use WLE. The WLE was proposed by Warm (1989) to reduce bias in the MLE and is also known as the Warm estimator.

Value

ability

a data.frame with columns: booklet_id, person_id, booklet_score, theta and optionally se (standard error)

ability_tables

a data.frame with columns: booklet_id, booklet_score, theta and optionally se (standard error)

References

Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54(3), 427-450.

Examples

db = start_new_project(verbAggrRules, ":memory:")
add_booklet(db, verbAggrData, "agg")

f = fit_enorm(db)

mle = ability_tables(f, method="MLE")
eap = ability_tables(f, method="EAP", mu=0, sigma=1)
wle = ability_tables(f, method="WLE")

plot(wle$booklet_score, wle$theta, xlab="test-score", ylab="ability est.", pch=19)
points(mle$booklet_score, mle$theta, col="red", pch=19,)
points(eap$booklet_score, eap$theta, col="blue", pch=19)
legend("topleft", legend = c("WLE", "MLE", "EAP N(0,1)"), 
        col = c("black", "red", "blue"), bty = "n",pch = 19)

close_project(db)

dexter documentation built on Sept. 11, 2024, 6:42 p.m.