normTable.betabinomial

This function generates a norm table for specific ages based on the beta
binomial regression model. In case a confidence coefficient (CI, default
.9) and the reliability is specified, confidence intervals are computed
for the true score estimates, including a correction for regression to
the mean (Eid &amp; Schmidt, 2012, p. 272).

Generates continuous test norms in
psychometrics and biometrics, and analyzing model fit. The package offers
both distribution-free modeling using Taylor polynomials and parametric
modeling using the beta-binomial and the 'Sinh-Arcsinh' distribution.
Originally developed for achievement tests, it is applicable to a wide
range of mental, physical, or other test scores dependent on continuous or
discrete explanatory variables. The package provides several advantages:
It minimizes deviations from representativeness in subsamples, interpolates
between discrete levels of explanatory variables, and significantly reduces
the required sample size compared to conventional norming per age group.
cNORM enables graphical and analytical evaluation of model fit,
accommodates a wide range of scales including those with negative and
descending values, and as well supports conventional norming. It generates
norm tables including confidence intervals. Methods for addressing
representativeness issues are available through Iterative Proportional
Fitting. Based on Lenhard et al. (2016)
<doi:10.1177/1073191116656437>, Lenhard et al. (2019)
<doi:10.1371/journal.pone.0222279>, Lenhard and Lenhard (2021)
<doi:10.1177/0013164420928457> and Gary et al. (2023)
<doi:10.1007/s00181-023-02456-0>.

Wolfgang Lenhard

cNORM

Continuous Norming

Alexandra Lenhard

Sebastian Gary

WPS Publisher

normTable.betabinomial function

<dl><dt>model</dt>
<dd>The model, fitted with <code>cnorm.betabinomial</code>.</dd>
<dt>ages</dt>
<dd>A numeric vector of age points at which to compute the tables.</dd>
<dt>n</dt>
<dd>The number of items resp. the maximum score.</dd>
<dt>m</dt>
<dd>An optional stop criterion in table generation. Positive integer
lower than n. Please note: The probabilities are always computed on the
full support 0 to n; m only truncates the output table.</dd>
<dt>range</dt>
<dd>The range of the norm scores in standard deviations.
Default is 3. Thus, scores in the range of +/- 3 standard deviations
are considered.</dd>
<dt>CI</dt>
<dd>Confidence coefficient, ranging from 0 to 1, default .9.</dd>
<dt>reliability</dt>
<dd>Reliability coefficient, ranging between 0 to 1.</dd></dl>

Arguments

Calculate Cumulative Probabilities, Density, Percentiles, and Z-Scores for
Beta-Binomial Distribution — normTable.betabinomial

<dl>

<dt>model</dt>
<dd>The model, fitted with <code>cnorm.betabinomial</code>.</dd>


<dt>ages</dt>
<dd>A numeric vector of age points at which to compute the tables.</dd>


<dt>n</dt>
<dd>The number of items resp. the maximum score.</dd>


<dt>m</dt>
<dd>An optional stop criterion in table generation. Positive integer
lower than n. Please note: The probabilities are always computed on the
full support 0 to n; m only truncates the output table.</dd>


<dt>range</dt>
<dd>The range of the norm scores in standard deviations.
Default is 3. Thus, scores in the range of +/- 3 standard deviations
are considered.</dd>


<dt>CI</dt>
<dd>Confidence coefficient, ranging from 0 to 1, default .9.</dd>


<dt>reliability</dt>
<dd>Reliability coefficient, ranging between 0 to 1.</dd>

</dl>

normTable.betabinomial: Calculate Cumulative Probabilities, Density, Percentiles, and Z-Scores for Beta-Binomial Distribution

Description

Usage

Value

Arguments