log_likelihood2

This function computes the negative log-likelihood for a beta-binomial
regression model where both the alpha and beta parameters are modeled as
functions of predictors (mode 2).

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

log_likelihood2 function

<dl><dt>params</dt>
<dd>A numeric vector containing all model parameters. The first
n_alpha elements are coefficients for the alpha model, and the remaining
elements are coefficients for the beta model.</dd>
<dt>X</dt>
<dd>A matrix of predictors for the alpha model.</dd>
<dt>Z</dt>
<dd>A matrix of predictors for the beta model.</dd>
<dt>y</dt>
<dd>A numeric vector of response values.</dd>
<dt>n</dt>
<dd>The maximum score (number of trials).</dd>
<dt>weights</dt>
<dd>A numeric vector of weights for each observation
(NULL = equal weights).</dd>
<dt>lch</dt>
<dd>Optional precomputed <code>lchoose(n, y)</code>. Since this term does
not depend on the parameters, passing it once avoids recomputation in
every optimizer iteration.</dd></dl>

Arguments

Calculate the negative log-likelihood for a beta-binomial regression model — log_likelihood2

<dl>

<dt>params</dt>
<dd>A numeric vector containing all model parameters. The first
n_alpha elements are coefficients for the alpha model, and the remaining
elements are coefficients for the beta model.</dd>


<dt>X</dt>
<dd>A matrix of predictors for the alpha model.</dd>


<dt>Z</dt>
<dd>A matrix of predictors for the beta model.</dd>


<dt>y</dt>
<dd>A numeric vector of response values.</dd>


<dt>n</dt>
<dd>The maximum score (number of trials).</dd>


<dt>weights</dt>
<dd>A numeric vector of weights for each observation
(NULL = equal weights).</dd>


<dt>lch</dt>
<dd>Optional precomputed <code>lchoose(n, y)</code>. Since this term does
not depend on the parameters, passing it once avoids recomputation in
every optimizer iteration.</dd>

</dl>

log_likelihood2: Calculate the negative log-likelihood for a beta-binomial regression model

Description

Usage

Value

Arguments

Details