log_likelihood_shash

This function computes the negative log-likelihood for a Sinh-Arcsinh regression model
where the location, scale, skewness, and (optionally) tail weight parameters
are modeled as functions of predictors.

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_likelihood_shash function

<dl><dt>params</dt>
<dd>A numeric vector containing all model parameters</dd>
<dt>X_mu</dt>
<dd>Design matrix for location parameter</dd>
<dt>X_sigma</dt>
<dd>Design matrix for scale parameter</dd>
<dt>X_epsilon</dt>
<dd>Design matrix for skewness parameter</dd>
<dt>X_delta</dt>
<dd>Design matrix for tail weight parameter (or NULL for fixed delta)</dd>
<dt>y</dt>
<dd>Response vector</dd>
<dt>weights</dt>
<dd>Observation weights</dd>
<dt>fixed_delta</dt>
<dd>If not NULL, the delta parameter is fixed to this value</dd></dl>

Arguments

Calculate the negative log-likelihood for a shash regression model — log_likelihood_shash

<dl>

<dt>params</dt>
<dd>A numeric vector containing all model parameters</dd>


<dt>X_mu</dt>
<dd>Design matrix for location parameter</dd>


<dt>X_sigma</dt>
<dd>Design matrix for scale parameter</dd>


<dt>X_epsilon</dt>
<dd>Design matrix for skewness parameter</dd>


<dt>X_delta</dt>
<dd>Design matrix for tail weight parameter (or NULL for fixed delta)</dd>


<dt>y</dt>
<dd>Response vector</dd>


<dt>weights</dt>
<dd>Observation weights</dd>


<dt>fixed_delta</dt>
<dd>If not NULL, the delta parameter is fixed to this value</dd>

</dl>

log_likelihood_shash: Calculate the negative log-likelihood for a shash regression model

Description

Usage

Value

Arguments