% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/1_model_parameters.R
\name{model_parameters.default}
\alias{model_parameters.default}
\title{Parameters from (General) Linear Models}
\usage{
\method{model_parameters}{default}(
  model,
  ci = 0.95,
  ci_method = NULL,
  bootstrap = FALSE,
  iterations = 1000,
  standardize = NULL,
  exponentiate = FALSE,
  p_adjust = NULL,
  vcov = NULL,
  vcov_args = NULL,
  include_info = getOption("parameters_info", FALSE),
  keep = NULL,
  drop = NULL,
  verbose = TRUE,
  ...
)
}
\arguments{
\item{model}{Model object.}

\item{ci}{Confidence Interval (CI) level. Default to \code{0.95} (\verb{95\%}).}

\item{ci_method}{Method for computing degrees of freedom for
confidence intervals (CI) and the related p-values. Allowed are following
options (which vary depending on the model class): \code{"residual"},
\code{"normal"}, \code{"likelihood"}, \code{"satterthwaite"}, \code{"kenward"}, \code{"wald"},
\code{"profile"}, \code{"boot"}, \code{"uniroot"}, \code{"ml1"}, \code{"betwithin"}, \code{"hdi"},
\code{"quantile"}, \code{"ci"}, \code{"eti"}, \code{"si"}, \code{"bci"}, or \code{"bcai"}. See section
\emph{Confidence intervals and approximation of degrees of freedom} in
\code{\link[=model_parameters]{model_parameters()}} for further details. When \code{ci_method=NULL}, in most
cases \code{"wald"} is used then.}

\item{bootstrap}{Should estimates be based on bootstrapped model? If \code{TRUE},
then arguments of \link[=model_parameters.brmsfit]{Bayesian regressions} apply
(see also \code{\link[=bootstrap_parameters]{bootstrap_parameters()}}).}

\item{iterations}{The number of bootstrap replicates. This only apply in the
case of bootstrapped frequentist models.}

\item{standardize}{The method used for standardizing the parameters. Can be
\code{NULL} (default; no standardization), \code{"refit"} (for re-fitting the model
on standardized data) or one of \code{"basic"}, \code{"posthoc"}, \code{"smart"},
\code{"pseudo"}. See 'Details' in \code{\link[=standardize_parameters]{standardize_parameters()}}.
\strong{Importantly}:
\itemize{
\item The \code{"refit"} method does \emph{not} standardize categorical predictors (i.e.
factors), which may be a different behaviour compared to other R packages
(such as \strong{lm.beta}) or other software packages (like SPSS). to mimic
such behaviours, either use \code{standardize="basic"} or standardize the data
with \code{datawizard::standardize(force=TRUE)} \emph{before} fitting the model.
\item For mixed models, when using methods other than \code{"refit"}, only the fixed
effects will be standardized.
\item Robust estimation (i.e., \code{vcov} set to a value other than \code{NULL}) of
standardized parameters only works when \code{standardize="refit"}.
}}

\item{exponentiate}{Logical, indicating whether or not to exponentiate the
coefficients (and related confidence intervals). This is typical for
logistic regression, or more generally speaking, for models with log or
logit links. It is also recommended to use \code{exponentiate = TRUE} for models
with log-transformed response values. For models with a log-transformed
response variable, when \code{exponentiate = TRUE}, a one-unit increase in the
predictor is associated with multiplying the outcome by that predictor's
coefficient. \strong{Note:} Delta-method standard errors are also computed (by
multiplying the standard errors by the transformed coefficients). This is
to mimic behaviour of other software packages, such as Stata, but these
standard errors poorly estimate uncertainty for the transformed
coefficient. The transformed confidence interval more clearly captures this
uncertainty. For \code{compare_parameters()}, \code{exponentiate = "nongaussian"}
will only exponentiate coefficients from non-Gaussian families.}

\item{p_adjust}{Character vector, if not \code{NULL}, indicates the method to
adjust p-values. See \code{\link[stats:p.adjust]{stats::p.adjust()}} for details. Further
possible adjustment methods are \code{"tukey"}, \code{"scheffe"},
\code{"sidak"} and \code{"none"} to explicitly disable adjustment for
\code{emmGrid} objects (from \strong{emmeans}).}

\item{vcov}{Variance-covariance matrix used to compute uncertainty estimates
(e.g., for robust standard errors). This argument accepts a covariance
matrix, a function which returns a covariance matrix, or a string which
identifies the function to be used to compute the covariance matrix.
\itemize{
\item A covariance matrix
\item A function which returns a covariance matrix (e.g., \code{stats::vcov()})
\item A string which indicates the kind of uncertainty estimates to return.
\itemize{
\item Heteroskedasticity-consistent: \code{"HC"}, \code{"HC0"}, \code{"HC1"}, \code{"HC2"},
\code{"HC3"}, \code{"HC4"}, \code{"HC4m"}, \code{"HC5"}. See \code{?sandwich::vcovHC}
\item Cluster-robust: \code{"CR"}, \code{"CR0"}, \code{"CR1"}, \code{"CR1p"}, \code{"CR1S"},
\code{"CR2"}, \code{"CR3"}. See \code{?clubSandwich::vcovCR}
\item Bootstrap: \code{"BS"}, \code{"xy"}, \code{"residual"}, \code{"wild"}, \code{"mammen"},
\code{"fractional"}, \code{"jackknife"}, \code{"norm"}, \code{"webb"}. See
\code{?sandwich::vcovBS}
\item Other \code{sandwich} package functions: \code{"HAC"}, \code{"PC"}, \code{"CL"}, \code{"OPG"},
\code{"PL"}.
}
}}

\item{vcov_args}{List of arguments to be passed to the function identified by
the \code{vcov} argument. This function is typically supplied by the
\strong{sandwich} or \strong{clubSandwich} packages. Please refer to their
documentation (e.g., \code{?sandwich::vcovHAC}) to see the list of available
arguments. If no estimation type (argument \code{type}) is given, the default
type for \code{"HC"} equals the default from the \strong{sandwich} package; for type
\code{"CR"}, the default is set to \code{"CR3"}.}

\item{include_info}{Logical, if \code{TRUE}, prints summary information about the
model (model formula, number of observations, residual standard deviation
and more).}

\item{keep}{Character containing a regular expression pattern that
describes the parameters that should be included (for \code{keep}) or excluded
(for \code{drop}) in the returned data frame. \code{keep} may also be a
named list of regular expressions. All non-matching parameters will be
removed from the output. If \code{keep} is a character vector, every parameter
name in the \emph{"Parameter"} column that matches the regular expression in
\code{keep} will be selected from the returned data frame (and vice versa,
all parameter names matching \code{drop} will be excluded). Furthermore, if
\code{keep} has more than one element, these will be merged with an \code{OR}
operator into a regular expression pattern like this: \code{"(one|two|three)"}.
If \code{keep} is a named list of regular expression patterns, the names of the
list-element should equal the column name where selection should be
applied. This is useful for model objects where \code{model_parameters()}
returns multiple columns with parameter components, like in
\code{\link[=model_parameters.lavaan]{model_parameters.lavaan()}}. Note that the regular expression pattern
should match the parameter names as they are stored in the returned data
frame, which can be different from how they are printed. Inspect the
\verb{$Parameter} column of the parameters table to get the exact parameter
names.}

\item{drop}{See \code{keep}.}

\item{verbose}{Toggle warnings and messages.}

\item{...}{Arguments passed to or from other methods. For instance, when
\code{bootstrap = TRUE}, arguments like \code{type} or \code{parallel} are passed down to
\code{bootstrap_model()}.

Further non-documented arguments are:
\itemize{
\item \code{digits}, \code{p_digits}, \code{ci_digits} and \code{footer_digits} to set the number of
digits for the output. \code{groups} can be used to group coefficients. These
arguments will be passed to the print-method, or can directly be used in
\code{print()}, see documentation in \code{\link[=print.parameters_model]{print.parameters_model()}}.
\item If \code{s_value = TRUE}, the p-value will be replaced by the S-value in the
output (cf. \emph{Rafi and Greenland 2020}).
\item \code{pd} adds an additional column with the \emph{probability of direction} (see
\code{\link[bayestestR:p_direction]{bayestestR::p_direction()}} for details). Furthermore, see 'Examples' for
this function.
\item For developers, whose interest mainly is to get a "tidy" data frame of
model summaries, it is recommended to set \code{pretty_names = FALSE} to speed
up computation of the summary table.
}}
}
\value{
A data frame of indices related to the model's parameters.
}
\description{
Extract and compute indices and measures to describe parameters
of (generalized) linear models (GLMs).
}
\section{Confidence intervals and approximation of degrees of freedom}{

There are different ways of approximating the degrees of freedom depending
on different assumptions about the nature of the model and its sampling
distribution. The \code{ci_method} argument modulates the method for computing degrees
of freedom (df) that are used to calculate confidence intervals (CI) and the
related p-values. Following options are allowed, depending on the model
class:

\strong{Classical methods:}

Classical inference is generally based on the \strong{Wald method}.
The Wald approach to inference computes a test statistic by dividing the
parameter estimate by its standard error (Coefficient / SE),
then comparing this statistic against a t- or normal distribution.
This approach can be used to compute CIs and p-values.

\code{"wald"}:
\itemize{
\item Applies to \emph{non-Bayesian models}. For \emph{linear models}, CIs
computed using the Wald method (SE and a \emph{t-distribution with residual df});
p-values computed using the Wald method with a \emph{t-distribution with residual df}.
For other models, CIs computed using the Wald method (SE and a \emph{normal distribution});
p-values computed using the Wald method with a \emph{normal distribution}.
}

\code{"normal"}
\itemize{
\item Applies to \emph{non-Bayesian models}. Compute Wald CIs and p-values,
but always use a normal distribution.
}

\code{"residual"}
\itemize{
\item Applies to \emph{non-Bayesian models}. Compute Wald CIs and p-values,
but always use a \emph{t-distribution with residual df} when possible. If the
residual df for a model cannot be determined, a normal distribution is
used instead.
}

\strong{Methods for mixed models:}

Compared to fixed effects (or single-level) models, determining appropriate
df for Wald-based inference in mixed models is more difficult.
See \href{https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#what-are-the-p-values-listed-by-summaryglmerfit-etc.-are-they-reliable}{the R GLMM FAQ}
for a discussion.

Several approximate methods for computing df are available, but you should
also consider instead using profile likelihood (\code{"profile"}) or bootstrap ("\verb{boot"})
CIs and p-values instead.

\code{"satterthwaite"}
\itemize{
\item Applies to \emph{linear mixed models}. CIs computed using the
Wald method (SE and a \emph{t-distribution with Satterthwaite df}); p-values
computed using the Wald method with a \emph{t-distribution with Satterthwaite df}.
}

\code{"kenward"}
\itemize{
\item Applies to \emph{linear mixed models}. CIs computed using the Wald
method (\emph{Kenward-Roger SE} and a \emph{t-distribution with Kenward-Roger df});
p-values computed using the Wald method with \emph{Kenward-Roger SE and t-distribution with Kenward-Roger df}.
}

\code{"ml1"}
\itemize{
\item Applies to \emph{linear mixed models}. CIs computed using the Wald
method (SE and a \emph{t-distribution with m-l-1 approximated df}); p-values
computed using the Wald method with a \emph{t-distribution with m-l-1 approximated df}.
See \code{\link[=ci_ml1]{ci_ml1()}}.
}

\code{"betwithin"}
\itemize{
\item Applies to \emph{linear mixed models} and \emph{generalized linear mixed models}.
CIs computed using the Wald method (SE and a \emph{t-distribution with between-within df});
p-values computed using the Wald method with a \emph{t-distribution with between-within df}.
See \code{\link[=ci_betwithin]{ci_betwithin()}}.
}

\strong{Likelihood-based methods:}

Likelihood-based inference is based on comparing the likelihood for the
maximum-likelihood estimate to the the likelihood for models with one or more
parameter values changed (e.g., set to zero or a range of alternative values).
Likelihood ratios for the maximum-likelihood and alternative models are compared
to a \eqn{\chi}-squared distribution to compute CIs and p-values.

\code{"profile"}
\itemize{
\item Applies to \emph{non-Bayesian models} of class \code{glm}, \code{polr}, \code{merMod} or \code{glmmTMB}.
CIs computed by \emph{profiling the likelihood curve for a parameter}, using
linear interpolation to find where likelihood ratio equals a critical value;
p-values computed using the Wald method with a \emph{normal-distribution} (note:
this might change in a future update!)
}

\code{"uniroot"}
\itemize{
\item Applies to \emph{non-Bayesian models} of class \code{glmmTMB}. CIs
computed by \emph{profiling the likelihood curve for a parameter}, using root
finding to find where likelihood ratio equals a critical value; p-values
computed using the Wald method with a \emph{normal-distribution} (note: this
might change in a future update!)
}

\strong{Methods for bootstrapped or Bayesian models:}

Bootstrap-based inference is based on \strong{resampling} and refitting the model
to the resampled datasets. The distribution of parameter estimates across
resampled datasets is used to approximate the parameter's sampling
distribution. Depending on the type of model, several different methods for
bootstrapping and constructing CIs and p-values from the bootstrap
distribution are available.

For Bayesian models, inference is based on drawing samples from the model
posterior distribution.

\code{"quantile"} (or \code{"eti"})
\itemize{
\item Applies to \emph{all models (including Bayesian models)}.
For non-Bayesian models, only applies if \code{bootstrap = TRUE}. CIs computed
as \emph{equal tailed intervals} using the quantiles of the bootstrap or
posterior samples; p-values are based on the \emph{probability of direction}.
See \code{\link[bayestestR:eti]{bayestestR::eti()}}.
}

\code{"hdi"}
\itemize{
\item Applies to \emph{all models (including Bayesian models)}. For non-Bayesian
models, only applies if \code{bootstrap = TRUE}. CIs computed as \emph{highest density intervals}
for the bootstrap or posterior samples; p-values are based on the \emph{probability of direction}.
See \code{\link[bayestestR:hdi]{bayestestR::hdi()}}.
}

\code{"bci"} (or \code{"bcai"})
\itemize{
\item Applies to \emph{all models (including Bayesian models)}.
For non-Bayesian models, only applies if \code{bootstrap = TRUE}. CIs computed
as \emph{bias corrected and accelerated intervals} for the bootstrap or
posterior samples; p-values are based on the \emph{probability of direction}.
See \code{\link[bayestestR:bci]{bayestestR::bci()}}.
}

\code{"si"}
\itemize{
\item Applies to \emph{Bayesian models} with proper priors. CIs computed as
\emph{support intervals} comparing the posterior samples against the prior samples;
p-values are based on the \emph{probability of direction}. See \code{\link[bayestestR:si]{bayestestR::si()}}.
}

\code{"boot"}
\itemize{
\item Applies to \emph{non-Bayesian models} of class \code{merMod}. CIs computed
using \emph{parametric bootstrapping} (simulating data from the fitted model);
p-values computed using the Wald method with a \emph{normal-distribution)}
(note: this might change in a future update!).
}

For all iteration-based methods other than \code{"boot"}
(\code{"hdi"}, \code{"quantile"}, \code{"ci"}, \code{"eti"}, \code{"si"}, \code{"bci"}, \code{"bcai"}),
p-values are based on the probability of direction (\code{\link[bayestestR:p_direction]{bayestestR::p_direction()}}),
which is converted into a p-value using \code{\link[bayestestR:pd_to_p]{bayestestR::pd_to_p()}}.
}

\examples{
\dontshow{if (require("boot", quietly = TRUE) && require("sandwich") && require("clubSandwich") && require("brglm2")) (if (getRversion() >= "3.4") withAutoprint else force)(\{ # examplesIf}
library(parameters)
model <- lm(mpg ~ wt + cyl, data = mtcars)

model_parameters(model)

# bootstrapped parameters
model_parameters(model, bootstrap = TRUE)

# standardized parameters
model_parameters(model, standardize = "refit")

# robust, heteroskedasticity-consistent standard errors
model_parameters(model, vcov = "HC3")

model_parameters(model,
  vcov = "vcovCL",
  vcov_args = list(cluster = mtcars$cyl)
)

# different p-value style in output
model_parameters(model, p_digits = 5)
model_parameters(model, digits = 3, ci_digits = 4, p_digits = "scientific")

# report S-value or probability of direction for parameters
model_parameters(model, s_value = TRUE)
model_parameters(model, pd = TRUE)

\donttest{
# logistic regression model
model <- glm(vs ~ wt + cyl, data = mtcars, family = "binomial")
model_parameters(model)

# show odds ratio / exponentiated coefficients
model_parameters(model, exponentiate = TRUE)

# bias-corrected logistic regression with penalized maximum likelihood
model <- glm(
  vs ~ wt + cyl,
  data = mtcars,
  family = "binomial",
  method = "brglmFit"
)
model_parameters(model)
}
\dontshow{\}) # examplesIf}
}
\seealso{
\code{\link[insight:standardize_names]{insight::standardize_names()}} to rename columns into a
consistent, standardized naming scheme.
}