Package 'repsd'

Title: Root Expected Proportion Squared Difference for Detecting DIF
Description: Root Expected Proportion Squared Difference (REPSD) is a nonparametric differential item functioning (DIF) method that (a) allows practitioners to explore for DIF related to small, fine-grained focal groups of examinees, and (b) compares the focal group directly to the composite group that will be used to develop the reported test score scale. Using your provided response matrix with a column that identifies focal group membership, this package provides the REPSD values, a simulated null distribution of possible REPSD values, and the simulated p-values identifying items possibly displaying DIF without requiring enormous sample sizes.
Authors: Anne Corrine Huggins-Manley [aut], Anthony William Raborn [aut, cre]
Maintainer: Anthony William Raborn <[email protected]>
License: MIT + file LICENSE
Version: 1.0.1
Built: 2025-03-04 02:46:37 UTC
Source: https://github.com/anthonyraborn/repsd

Help Index

Estimate the effect size difference between focal and composite group abilities

Description

Estimate the effect size difference between focal and composite group abilities

Usage

estimate_impact(responses = timmsData, focal_column = 21, focal_id = 1)

Arguments

responses

The data.frame of responses, including the focal_column.
focal_column

The numeric location of the focal column.
focal_id

The numeric, character, or logical value that identifies the focal group.

Value

A numeric estimate of the impact as the effect size D, e.g., the standardized mean theta difference between the focal group and the composite (total) group abilities. This estimate is rounded to 3 decimal places.

null_repsd

Description

null_repsd

Usage

null_repsd(
  item_count = 20,
  focal_sample = 88,
  focal_prop = 0.09,
  numStrata = 4,
  impact = estimate_impact(),
  item_params_a = timmsDiscrim,
  item_params_b = timmsDiffic,
  anchorItems = NULL,
  iterations = 10000,
  verbose = TRUE
)

Arguments

item_count

numeric. How many items?
focal_sample

numeric. How large is the focal sample?
focal_prop

numeric, between 0 and 1 (exclusive). What is the proportion of the focal sample compared to the rest of the data?
numStrata

numeric. How many strata for matching should be used?
impact

numeric. What is the expected, standardized mean difference between the focal group's mean theta and the composite group's mean theta (i.e., standardized focal mean - composite mean). See details for further explanation.
item_params_a

numeric vector. What are the discrimination parameters of the items in the data set?
item_params_b

numeric vector. What are the difficulty parameters of the items in the data set?
anchorItems

either NULL or a vector of the anchorItems names or numeric column locations. If NULL, all items are used for calculating the total test score for stratifying individuals. If a vector, the specified items are used to calculate the total test score for stratifying individuals.
iterations

numeric. How many iterations for the function to run? Defaults to 10000.
verbose

logical. If TRUE (default), prints a progress::progress_bar() in the console to allow tracking of the state of the distribution generation.

Value

An item_count x iterations data.frame with simulated repsd values for each item.

REPSD Null vs Observed Histogram

Description

REPSD Null vs Observed Histogram

Usage

plot_repsd(repsd_values, null_values, pvalues, which_item, bins = 30)

Arguments

repsd_values

A numerical vector of repsd values, the output of repsd()$repsd_each_item.
null_values

A matrix of the repsd null distribution, the output of null_repsd().
pvalues

A numerical vector of the repds p-values, the output of repsd_pval()$p.value
which_item

A numerical indicator of the specific item to plot.
bins

A numerical indicator on the number of bins to output in the histogram.

Value

A plot of the REPSD null distribution for the indicated item with the observed REPSD value as a red line and the observed p-value

Examples

example_repsd <-
    repsd()
example_null <-
    null_repsd(iterations = 100)
example_pvals <-
    repsd_pval(
               alpha = .05,
               null_dist = example_null,
               items_repsd = example_repsd$repsd_each_item
               )
# Only one plot
plot_repsd(repsd_values = example_repsd$repsd_each_item,
           null_values = example_null,
           pvalues = example_pvals$p.value,
           which_item = 18,
           bins = 10)
# Multiple plots on the same plot
oldpar <- par()
par(mfrow = c(2,2))
for (i in c(1,8,16,18)) {
  plot_repsd(
             repsd_values = example_repsd$repsd_each_item,
             null_values = example_null,
             pvalues = example_pvals$p.value,
             which_item = 18,
             bins = 10
             )
}
par(mfrow = oldpar$mfrow)

repsd

Description

repsd

Usage

repsd(
  responses = timmsData,
  focalColumn = 21,
  focalGroupID = 1,
  anchorItems = NULL,
  numStrata = 4
)

Arguments

responses

data.frame, matrix, or similar object which includes the item responses and the focal group ID column.
focalColumn

numeric or character. The location or name of the column that holds the focal group data.
focalGroupID

numeric or character. The value that identifies the focal group.
anchorItems

either NULL or a vector of the anchorItems names or numeric column locations. If NULL, all items are used for calculating the total test score for stratifying individuals. If a vector, the specified items are used to calculate the total test score for stratifying individuals.
numStrata

numeric. How many strata for matching should be used?

Value

Matrix of repsd values for each item.

Calculating p-values for repsd

Description

Calculating p-values for repsd

Usage

repsd_pval(
  alpha = 0.05,
  null_dist = null_repsd(),
  items_repsd = repsd()$repsd_each_item,
  responses = timmsData,
  focalColumn = 21,
  verbose = TRUE
)

Arguments

alpha

numeric. The alpha level to calculate significance.
null_dist

A data.frame-type object with the null distribution simulation for each item as columns.
items_repsd

A numeric vector of the repsd values for each item.
responses

The data.frame of item responses and the focal column.
focalColumn

The column number for the focal column. Removed from the final data.
verbose

Logical. Do you want to print the results to console (TRUE, default) or return the results invisibly (FALSE)?

Details

Calculates the p-values for repsd for the data set. It can be used as a wrapper function by providing the null_repsd() function and the repsd_each_item output of the repsd() function (each with proper arguments) as the arguments to null_dist and items_repsd, respectively.

Value

If the colorDF package is installed and accessible, a colorDF with the significant items highlighted. Otherwise, a data.frame. Both have columns with the items names, the repsd value, the p.value, and the sig (0 = false, 1 = true) for each item.

Sample data from TIMMS

Description

Dataset including 977 observations on 20 items and 1 group identifying variable.

Usage

timmsData

Format

A data frame with 977 rows and 21 columns:

MA13011

0 (incorrect) or 1 (correct) response on this math item

MA13012

0 (incorrect) or 1 (correct) response on this math item

MA13013

0 (incorrect) or 1 (correct) response on this math item

MA13015

0 (incorrect) or 1 (correct) response on this math item

MA13016

0 (incorrect) or 1 (correct) response on this math item

MA13017

0 (incorrect) or 1 (correct) response on this math item

MA13018

0 (incorrect) or 1 (correct) response on this math item

MA33086

0 (incorrect) or 1 (correct) response on this math item

MA33225C

0 (incorrect) or 1 (correct) response on this math item

MA33225E

0 (incorrect) or 1 (correct) response on this math item

MA33142

0 (incorrect) or 1 (correct) response on this math item

MA33044

0 (incorrect) or 1 (correct) response on this math item

MA33179

0 (incorrect) or 1 (correct) response on this math item

MA33076

0 (incorrect) or 1 (correct) response on this math item

MA33140

0 (incorrect) or 1 (correct) response on this math item

MA33007

0 (incorrect) or 1 (correct) response on this math item

MA33214

0 (incorrect) or 1 (correct) response on this math item

MA33171

0 (incorrect) or 1 (correct) response on this math item

MA33039

0 (incorrect) or 1 (correct) response on this math item

MA33180

0 (incorrect) or 1 (correct) response on this math item

middle_school_or_lower_for_parents_highest_ed

0 (higher than middle school) or 1 (middle school or lower) indicator for parents' highest education level

Sample TIMMS item difficulties

Description

A vector of the 20 item difficulty parameters b for the timmsData items.

Usage

timmsDiffic

Format

An object of class numeric of length 20.

Sample TIMMS item discriminations

Description

A vector of the 20 item discrimination parameters a for the timmsData items.

Usage

timmsDiscrim

Format

An object of class numeric of length 20.