betaCoefficients

This function calculates the \(\alpha\) (a) and \(\beta\) (b)
parameters of a beta binomial distribution, along with the mean (m) and
standard deviation (sd) based on the input vector <code>x</code> and the maximum
number <code>n</code>.

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

betaCoefficients function

<dl><dt>x</dt>
<dd>A numeric vector of non-negative integers representing observed
counts.</dd>
<dt>n</dt>
<dd>The maximum number or the maximum possible value of <code>x</code>.
If not specified, uses max(x) instead.</dd></dl>

Arguments

Compute Parameters of a Beta Binomial Distribution — betaCoefficients

<dl>

<dt>x</dt>
<dd>A numeric vector of non-negative integers representing observed
counts.</dd>


<dt>n</dt>
<dd>The maximum number or the maximum possible value of <code>x</code>.
If not specified, uses max(x) instead.</dd>

</dl>

betaCoefficients: Compute Parameters of a Beta Binomial Distribution

Description

Usage

Value

Arguments

Details