efficiency {optical}

Efficiency of optimal design

Description

This function computes the efficiency of the D, I, and A optimal designs compared to the random design.

Usage

efficiency(
  yyy,
  ip,
  uncert = FALSE,
  ipop,
  oc = "D",
  L = NULL,
  items = FALSE,
  integ = TRUE
)

Arguments

yyy

a optical object; the output of a call optical()

ip

matrix with item parameters for all items (number of rows determines number of items; number of columns is 2 (for 2PL; or 1PL with common a-parameter when NA in first column from second item) or 3 (for 3PL; or mixed 2/3-PL with NA for 2PL-items in third column)

uncert

if false (default), abilities are assumed to be known; if true, handling of uncertainties of Bjermo et al. (2021) is used.

ipop

matrix with item parameters for operational items (used if uncert=TRUE, only).

oc

optimality criterion: "D" (D-optimality, default), "I" (I-optimality with standard normal weight function), "A" (A-optimality).

L

L-matrix (not used for D-optimality)

items

if false (default), only total block efficiency is returned; if true, criteria for optimal and random and the efficiency for each item are reported in each column of output. Last column are then total criteria and efficiency. D-, L-, I-, A-optimality

integ

if true (default), integrate() is used for computation of partial information matrices; if false, Riemann rule is used.

Value

A numerical value is displayed.

See Also

optical

Examples

# 2PL-models for two items; parameters (a, b)=(1.6, -1) and (1.6, 1), respectively
ip <- cbind(c(1.6, 1.6),c(-1, 1))

yyy <- optical(ip)

# Efficiency of A-optimal design compared to random design
efficiency(yyy, ip, oc="A")


# Efficiency of D-optimal design compared to random design
efficiency(yyy, ip, oc="D")

# Efficiency of I-optimal design compared to random design
efficiency(yyy, ip, oc="I")