bb_distribution

Computes the (normalized) probability mass function, the cumulative
distribution function and mid-p percentiles of a beta-binomial
distribution in a numerically stable way (log space).

internal

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

bb_distribution function

<dl><dt>a</dt>
<dd>Alpha parameter (&gt; 0).</dd>
<dt>b</dt>
<dd>Beta parameter (&gt; 0).</dd>
<dt>n</dt>
<dd>Number of trials / maximum score.</dd></dl>

Arguments

Beta-binomial distribution on the full support 0:n — bb_distribution

<dl>

<dt>a</dt>
<dd>Alpha parameter (&gt; 0).</dd>


<dt>b</dt>
<dd>Beta parameter (&gt; 0).</dd>


<dt>n</dt>
<dd>Number of trials / maximum score.</dd>

</dl>

bb_distribution: Beta-binomial distribution on the full support 0:n

Description

Usage

Value

Arguments