To install giftedCalcs, run the following code in the R console.

install.packages("devtools")
devtools::install_github("mcbeem/giftedCalcs")

library(giftedCalcs)

?giftedCalcs

Click on index at the bottom of the page to see all the functions in the package.

?marginal_psychometrics

• Every help file contains example code
• Open function help ?functionname
• Highlight Examples code at the bottom of the help file
• Press Ctrl-Enter (windows) or Cmd-Return (Mac)
• Code executes in the console

The marginal_psychometrics() function calculates:

• sensitivity
• incorrect identification rate (IIR)
• nomination rate
• nomination pass rate
• identification rate

These equations come from McBee, Peters, & Miller (2016)

The user specifies one of:

• nomination observed score
• confirmatory test observed score
• test true score

The first and second moments (e.g., expected value and variance) of the joint multivariate normal distribution of the other two variables is calculated.

conditional_moments(t.true=1.5, relyt=.9, valid=.6)

## $conditional.mean
##            [,1]
## n.obs 0.9486833
## t.obs 1.4230249
## 
## $conditional.cov
##       n.obs t.obs
## n.obs   0.6   0.0
## t.obs   0.0   0.1

Calculates the probability of identification for a student with a particular true score.

conditional_p_id(x=2, relyt=.9, test.cutoff=.9,
   nom.cutoff=.9, valid=.5)

## [1] 0.3843284

The conditional_p_id() function can be used to calculate a conditional identification curve.

# create vector of true scores
Tscores <- seq(0,3, length.out=100)

# calculate the identification probability for each
p.id <- conditional_p_id(x=Tscores, relyt=.9,
  test.cutoff=.9, nom.cutoff=.9, valid=.5)

# make a plot
plot(x=Tscores, y=p.id, type="l", xlab="true score",
  ylab="p identified", ylim=c(0,1))

# add a reference line for the test cutoff
abline(v=qnorm(.9), col="red")

The following functions allow you to work with the statistical distribution of scores for identified students.

• d_identified(): density
• p_identified(): cumulative density
• q_identified(): quantile function
• r_identified(): random samples

The density function can be plotted to visualize the probability density of true scores for identified students.

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

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

plot(x=Tscores, y=pdf, type="l", col="blue", 
     main="Distribution of true scores")

abline(v=qnorm(.9), col="red")

It can also be used to visualize the distribution of observed scores. Many of the functions work this way. This is triggered by not providing a value for the relyt= argument.

# create vector of true scores
Tscores <- seq(0,4, length.out=500)

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

plot(x=Tscores, y=pdf, type="l", col="blue", 
     main="Distribution of observed scores")

abline(v=qnorm(.9), col="red")

This is the cumulative density function for identified students.

Given a true (or observed) score, it returns the percentile.

p_identified(x=1.5, relyt=.95, test.cutoff=.9, 
             nom.cutoff=.9, valid=.5)

## [1] 0.2617256

This is the quantile function for identified students.

Given a percentile, it returns the associated true (or observed) score for identified students.

q_identified(percentile=.8, relyt=.95, test.cutoff=.9, 
             nom.cutoff=.9, valid=.5)

## [1] 2.243256

This samples random values from the distribution of true or observed scores of identified students.

This is useful for simulation purposes.

r_identified(n=10, relyt=.95, test.cutoff=.9, 
             nom.cutoff=.9, valid=.5)

##  [1] 1.672412 2.395773 1.550169 1.933561 1.952277 1.214970 2.106214
##  [8] 1.525831 1.437669 1.833512

• mean_identified(): mean or expected value for identified students
• sd_identified(): standard deviation for identified students

mean_identified(relyt=.95, test.cutoff=.9, 
             nom.cutoff=.9, valid=.5)

## [1] 1.850697

sd_identified(relyt=.95, test.cutoff=.9, 
             nom.cutoff=.9, valid=.5)

## [1] 0.5055684

Infer identification system nomination validity and performance from observed data

estimate_performance(x=data, id.rate=.032,
  nom.rate=0.1, reps=500)

## $summary
##              Estimate  StdErr CI.95.lower CI.95.upper
## valid         0.50836 0.01345     0.48199     0.53473
## sensitivity   0.33044 0.00842     0.31393     0.34695
## nom.passrate  0.32645 0.00832     0.31014     0.34275
## test.cutoff   0.90121      NA          NA          NA
## nom.cutoff    0.90000      NA          NA          NA
## 
## $note
## [1] "Since the test reliability was not specified, the sensitivity value is interpreted as relative to universal screening. Achieved sensitivity is dependent on the test reliability."

Optimal identification is a method for designing an identification process for maximal psychometric performance.

1. Multiple assessments for confirmation.
2. Mean combination rule
3. Nominate on the basis of one of the consituent assessments

Functions:

• reliability_mean()
• var_mean()
• cor_mean()
• shrinkage_mean()