estimate_performance: Estimate psychometric parameters of an identification system...

In mcbeem/giftedCalcs: Psychometrics for Gifted Program Identification

Estimate psychometric parameters of an identification system given the observed scores of the identified students using bootstrapping to provide uncertainty estimates.

Description

Estimate psychometric parameters of an identification system given the observed scores of the identified students using bootstrapping to provide uncertainty estimates.

Usage

estimate_performance(
  x,
  id.rate,
  nom.rate,
  reps,
  relyt = 1,
  pop.mean = 0,
  pop.sd = 1,
  adjust = 1,
  CI = 0.95
)

Arguments

x	Numeric vector of observed scores.
id.rate	The proportion of students who have been identified. Range (0, 1). Must be less than or equal to nom.rate.
nom.rate	The proportion of students who have been nominated. Range (0, 1). Used to calculate the nomination cutoff.
reps	The number of bootstrap samples.
relyt	Confirmatory test reliability coefficient. Range (0,1]. Must not be exactly 0. Used in the calculation of sensitivity. Defaults to 1, in which case the reported sensitivity is relative to a universal screening system and does not include sensitivity loss from imperfect test reliability. If <1, the test reliability is included in the sensitivity calculation.
pop.mean	The known general population mean of the x. Defaults to 0.
pop.sd	The known general population standard deviation of the x. Defaults to 1.
adjust	Number that controls the amount of smoothing in the density estimation. Defaults to 1.0, which has been found to work well in simulation.
CI	The confidence limit. Must be between 0 and 1. Defaults to .95.

Value

This function stimates the psychometric parameters of an identification system given the observed scores of the identified students. This function calculates statistics using the estimate_valid function with bootstrapping. The resulting nomination validity (valid) estimates are passed to the marginal_psychometrics function in order to calculate the implied performance statistics.

At least 500 bootstrapped samples are suggested. This can take a while.

Examples

# generate some data
set.seed(123)
x <- r_identified(
  n = 300, test.cutoff = .9, valid = .5,
  nom.cutoff = .9
)

# calculate the identification rate implied by the system parameters
id.rate <- marginal_psychometrics(
  test.cutoff = .9, valid = .5,
  nom.cutoff = .9
)$identification.rate

# calculate the nomination rate implied by the system parameters
nom.rate <- marginal_psychometrics(
  test.cutoff = .9, valid = .5,
  nom.cutoff = .9
)$nom.rate

# estimate the system parameters with 200 bootstrapped samples
#  this uses one CPU
a <- estimate_performance(
  x = x, id.rate = id.rate,
  nom.rate = nom.rate, reps = 200
)
a

# plot the results for each parameter
plot(a)

# plot with histograms
plot(a, type = "hist")

# the width argument controls the x-limits
plot(a, type = "hist", width = .0)

# for type="density", the bandwidth is adjustable
#  (default is 1.2, see ?density for details)
plot(a, type = "density", width = .05, adjust = .5)
plot(a, type = "density", width = .05, adjust = 1.5)

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