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Added model speficicatiion
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### Gaussian Noise Model (GN)
According to GN, $y$ is subject to additive noise and assumed to be normally distributed
around the decision evidence value $x$ with a standard deviation $\sigma$ (Maniscalco & Lau, 2016).
$\sigma$ is an additional free parameter.

#' ### \strong{Weighted Evidence and Visibility model (WEV)}
#' WEV assumes that the observer combines evidence about decision-relevant features
#' of the stimulus with the strength of evidence about choice-irrelevant features
#' to generate confidence (Rausch et al., 2018). Thus, the WEV model assumes that \eqn{y} is normally
#' distributed with a mean of \eqn{(1-w)\times x+w \times d_k\times R} and standard deviation \eqn{\sigma}.
#' The standard deviation quantifies the amount of unsystematic variability
#' contributing to confidence judgments but not to the discrimination judgments.
#' The parameter \eqn{w} represents the weight that is put on the choice-irrelevant
#' features in the confidence judgment. \eqn{w} and \eqn{\sigma} are fitted in
#' addition to the set of shared parameters.
#'
#' ### \strong{Post-decisional accumulation model (PDA)}
#' PDA represents the idea of on-going information accumulation after the
#' discrimination choice (Rausch et al., 2018). The parameter \eqn{a} indicates the amount of additional
#' accumulation. The confidence variable is normally distributed with mean
#' \eqn{x+S\times d_k\times a} and variance \eqn{a}.
#' For this model the parameter \eqn{a} is fitted in addition to the shared
#' parameters.
#'
#' ### \strong{Independent Gaussian Model (IG)}
#' According to IG, \eqn{y} is sampled independently
#' from \eqn{x} (Rausch & Zehetleitner, 2017). \eqn{y} is normally distributed with a mean of \eqn{a\times d_k} and variance
#' of 1 (again as it would scale with \eqn{m}). The additional parameter \eqn{m}
#' represents the amount of information available for confidence judgment
#' relative to amount of evidence available for the discrimination decision and can
#' be smaller as well as greater than 1.
#'
#' ### \strong{Independent Truncated Gaussian Model: HMetad-Version (ITGc)}
#' According to the version of ITG consistent
#' with the HMetad-method (Fleming, 2017; see Rausch et al., 2023), \eqn{y} is sampled independently
#' from \eqn{x} from a truncated Gaussian distribution with a location parameter
#' of \eqn{S\times d_k \times m/2} and a scale parameter of 1. The Gaussian distribution of \eqn{y}
#' is truncated in a way that it is impossible to sample evidence that contradicts
#' the original decision: If \eqn{R = -1}, the distribution is truncated to the
#' right of \eqn{c}. If \eqn{R = 1}, the distribution is truncated to the left
#' of \eqn{c}. The additional parameter \eqn{m} represents metacognitive efficiency,
#' i.e., the amount of information available for confidence judgments relative to
#' amount of evidence available for discrimination decisions and can be smaller
#' as well as greater than 1.
#'
#' ### \strong{Independent Truncated Gaussian Model: Meta-d'-Version (ITGcm)}
#' According to the version of the ITG consistent
#' with the original meta-d' method (Maniscalco & Lau, 2012, 2014; see Rausch et al., 2023),
#' \eqn{y} is sampled independently from \eqn{x} from a truncated Gaussian distribution with a location parameter
#' of \eqn{S\times d_k \times m/2} and a scale parameter
#' of 1. If \eqn{R = -1}, the distribution is truncated to the right of \eqn{m\times c}.
#' If \eqn{R = 1}, the distribution is truncated to the left of \eqn{m\times c}.
#' The additional parameter \eqn{m} represents metacognitive efficiency, i.e.,
#' the amount of information available for confidence judgments relative to
#' amount of evidence available for the discrimination decision and can be smaller
#' as well as greater than 1.
#'
#' ### \strong{Logistic Noise Model (logN)}
#' According to logN, the same sample
#' of sensory evidence is used to generate response and confidence, i.e.,
#' \eqn{y=x} just as in SDT (Shekhar & Rahnev, 2021). However, according to logN, the confidence criteria
#' are not assumed to be constant, but instead they are affected by noise drawn from
#' a lognormal distribution. In each trial, \eqn{\theta_{-1,i}} is given
#' by \eqn{c - \epsilon_i}. Likewise, \eqn{\theta_{1,i}} is given by
#' \eqn{c + \epsilon_i}. \eqn{\epsilon_i} is drawn from a lognormal distribution with
#' the location parameter
#' \eqn{\mu_{R,i}=log(|\overline{\theta}_{R,i}- c|) - 0.5 \times \sigma^{2}} and
#' scale parameter \eqn{\sigma}. \eqn{\sigma} is a free parameter designed to
#' quantify metacognitive ability. It is assumed that the criterion noise is perfectly
#' correlated across confidence criteria, ensuring that the confidence criteria
#' are always perfectly ordered. Because \eqn{\theta_{-1,1}}, ..., \eqn{\theta_{-1,L-1}},
#' \eqn{\theta_{1,1}}, ..., \eqn{\theta_{1,L-1}} change from trial to trial, they are not estimated
#' as free parameters. Instead, we estimate the means of the confidence criteria, i.e., \eqn{\overline{\theta}_{-1,1}, ...,
#' \overline{\theta}_{-1,L-1}, \overline{\theta}_{1,1}, ... \overline{\theta}_{1,L-1}},
#' as free parameters.
#'
#' ### \strong{Logistic Weighted Evidence and Visibility model (logWEV)}
#' logWEV is a combination of logN and WEV proposed by Shekhar and Rahnev (2023).
#' Conceptually, logWEV assumes that the observer combines evidence about decision-relevant features
#' of the stimulus with the strength of evidence about choice-irrelevant features (Rausch et al., 2018).
#' The model also assumes that noise affecting the confidence decision variable is lognormal
#' in accordance with Shekhar and Rahnev (2021).
#' According to logWEV, the confidence decision variable is \eqn{y} is equal to
#' \eqn{y^*\times R}. \eqn{y^*} is sampled from a lognormal distribution with a location parameter
#' of \eqn{(1-w)\times x\times R + w \times d_k} and a scale parameter of \eqn{\sigma}.
#' The parameter \eqn{\sigma} quantifies the amount of unsystematic variability
#' contributing to confidence judgments but not to the discrimination judgments.
#' The parameter \eqn{w} represents the weight that is put on the choice-irrelevant
#' features in the confidence judgment. \eqn{w} and \eqn{\sigma} are fitted in
#' addition to the set of shared parameters.
around the decision evidence value $x$ with a standard deviation $\sigma$,
which is an additional free parameter (Maniscalco & Lau, 2016).

### Weighted Evidence and Visibility model (WEV)
WEV assumes that the observer combines evidence about decision-relevant features
of the stimulus with the strength of evidence about choice-irrelevant features
to generate confidence (Rausch et al., 2018). Thus, the WEV model assumes that $Y$ is normally
distributed with a mean of $(1-w)\times x+w \times d_k\times R} and standard deviation $\sigma$.
The standard deviation quantifies the amount of unsystematic variability
contributing to confidence judgments but not to the discrimination judgments.
The parameter $w$ represents the weight that is put on the choice-irrelevant
features in the confidence judgment. $w$ and $\sigma$ are fitted in
addition to the set of shared parameters.

### \strong{Post-decisional accumulation model (PDA)}
PDA represents the idea of on-going information accumulation after the
discrimination choice (Rausch et al., 2018). The parameter $a$ indicates the amount of additional
accumulation. The confidence variable is normally distributed with mean
$x+S\times d_k\times a$ and variance $a$.
For this model the parameter $a$ is fitted in addition to the shared
parameters.

### \strong{Independent Gaussian Model (IG)
According to IG, $y$ is sampled independently
from $x$ (Rausch & Zehetleitner, 2017). $y$ is normally distributed with a mean of $a\times d_k$ and variance
of 1 (again as it would scale with $m$). The additional parameter $m$
represents the amount of information available for confidence judgment
relative to amount of evidence available for the discrimination decision and can
be smaller as well as greater than 1.

### \strong{Independent Truncated Gaussian Model: HMetad-Version (ITGc)
According to the version of ITG consistent
with the HMetad-method (Fleming, 2017; see Rausch et al., 2023), $y$ is sampled independently
from $x$ from a truncated Gaussian distribution with a location parameter
of $S\times d_k \times m/2$ and a scale parameter of 1. The Gaussian distribution of $y$
is truncated in a way that it is impossible to sample evidence that contradicts
the original decision: If $R = -1$, the distribution is truncated to the
right of $c$. If $R = 1$, the distribution is truncated to the left
of $c$. The additional parameter $m$ represents metacognitive efficiency,
i.e., the amount of information available for confidence judgments relative to
amount of evidence available for discrimination decisions and can be smaller
as well as greater than 1.

### \strong{Independent Truncated Gaussian Model: Meta-d'-Version (ITGcm)
According to the version of the ITG consistent
with the original meta-d' method (Maniscalco & Lau, 2012, 2014; see Rausch et al., 2023),
$y$ is sampled independently from $x$ from a truncated Gaussian distribution with a location parameter
of $S\times d_k \times m/2$ and a scale parameter
of 1. If $R = -1$, the distribution is truncated to the right of $m\times c$.
If $R = 1$, the distribution is truncated to the left of $m\times c$.
The additional parameter $m$ represents metacognitive efficiency, i.e.,
the amount of information available for confidence judgments relative to
amount of evidence available for the discrimination decision and can be smaller
as well as greater than 1.

### \strong{Logistic Noise Model (logN)
According to logN, the same sample
of sensory evidence is used to generate response and confidence, i.e.,
$y=x$ just as in SDT (Shekhar & Rahnev, 2021). However, according to logN, the confidence criteria
are not assumed to be constant, but instead they are affected by noise drawn from
a lognormal distribution. In each trial, $\theta_{-1,i}$ is given
by $c - \epsilon_i$. Likewise, $\theta_{1,i}$ is given by
$c + \epsilon_i$. $\epsilon_i$ is drawn from a lognormal distribution with
the location parameter
$\mu_{R,i}=log(|\overline{\theta}_{R,i}- c|) - 0.5 \times \sigma^{2}$ and
scale parameter $\sigma$. $\sigma$ is a free parameter designed to
quantify metacognitive ability. It is assumed that the criterion noise is perfectly
correlated across confidence criteria, ensuring that the confidence criteria
are always perfectly ordered. Because $\theta_{-1,1}$, ..., $\theta_{-1,L-1}$,
$\theta_{1,1}$, ..., $\theta_{1,L-1}$ change from trial to trial, they are not estimated
as free parameters. Instead, we estimate the means of the confidence criteria, i.e., $\overline{\theta}_{-1,1}, ...,
\overline{\theta}_{-1,L-1}, \overline{\theta}_{1,1}, ... \overline{\theta}_{1,L-1}$,
as free parameters.

### \strong{Logistic Weighted Evidence and Visibility model (logWEV)
The logWEV model is a combination of logN and WEV, proposed by Shekhar and Rahnev (2023).
Conceptually, logWEV assumes that the observer combines evidence about decision-relevant features
of the stimulus with the strength of evidence about choice-irrelevant features (Rausch et al., 2018).
The model also assumes that noise affecting the confidence decision variable is lognormal
in accordance with Shekhar and Rahnev (2021).
According to logWEV, the confidence decision variable is $y$ is equal to
$y^*\times R$. $y^*$ is sampled from a lognormal distribution with a location parameter
of $(1-w)\times x\times R + w \times d_k$ and a scale parameter of $\sigma$.
The parameter $\sigma$ quantifies the amount of unsystematic variability
contributing to confidence judgments but not to the discrimination judgments.
The parameter $w$ represents the weight that is put on the choice-irrelevant
features in the confidence judgment. $w$ and $\sigma$ are free parameters.

## Installation

The latest released version of the package is available on CRAN via
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