d_identified: Conditional density of true or observed scores for identified...

In mcbeem/giftedCalcs: Psychometrics for Gifted Program Identification

Conditional density of true or observed scores for identified students

Description

d_identified is the conditional probability density function (pdf) for identified students.

Usage

d_identified(
  x,
  relyt = 1,
  test.cutoff,
  mu = 0,
  valid = 1e-07,
  nom.cutoff = 1e-07,
  normalize = TRUE
)

Arguments

x	The student's score on a standardized (z-score) metric. Interpreted as a true score if a value is specified for relyt, otherwise intepreted as an observed score.
relyt	Confirmatory test reliability coefficient. Range (0, 1]. Must not be exactly 0. Defaults to 1; in this case, x is assumed to be an observed score. If an alternative value is supplied for relyt, x is assumed to be a true score.
test.cutoff	Confirmatory test cutoff percentile. Range (0, 1). Must not be exactly 0 or 1.
mu	Population mean true score on a standardized (z-score) metric. Defaults to zero.
valid	Nomination validity coefficient. Controls the relatedness of the nomination scores and the confirmatory test scores. Range (0, 1). Must not be exactly 0 or 1, and must be less than the square root of the test reliability. Defaults to 1e-7 for a single- stage identification system.
nom.cutoff	Nomination cutoff percentile. Range (0, 1). Must not be exactly 0 or 1. Defaults to 1e-7 for a single- stage identification system.
normalize	Logical. Should the density be normalized to have a total area of one? Defaults to TRUE.

Details

See also p_identified for the cumulative density, q_identified for the quantile function, and r_identified for random generation.

Examples

# un-normalized density for true score=1.5
d_identified(
  relyt = .9, x = 1.5, test.cutoff = .9,
  nom.cutoff = .9, valid = .5, mu = 0, normalize = FALSE
)

# normalized density for observed score=1.5
d_identified(
  x = 1.5, test.cutoff = .9,
  nom.cutoff = .9, valid = .5, mu = 0, normalize = TRUE
)

# compare the density of identified students for universal
# screening vs. a poor-performing nomination stage
#
# area of each curve is proportion to the identification rate
# under each system

# create vector of true scores
Tscores <- seq(0, 4, length.out = 200)

# # plot the un-normed density for universal screening
p.universal <- sapply(Tscores, d_identified,
  relyt = .9,
  test.cutoff = .9, normalize = FALSE
)

plot(
  x = Tscores, y = p.universal, type = "l", xlab = "true score",
  col = "blue"
)

# add the un-normed density for the bad system
p.bad <- sapply(Tscores, d_identified,
  relyt = .9,
  test.cutoff = .9, nom.cutoff = .9, valid = .5, normalize = FALSE
)

points(x = Tscores, y = p.bad, type = "l", col = "red")

mcbeem/giftedCalcs documentation built on Nov. 29, 2024, 3:48 a.m.