% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/standardize_parameters.R
\name{standardize_parameters}
\alias{standardize_parameters}
\alias{standardize_posteriors}
\title{Parameters standardization}
\usage{
standardize_parameters(
  model,
  method = "refit",
  ci = 0.95,
  robust = FALSE,
  two_sd = FALSE,
  verbose = TRUE,
  parameters,
  ...
)

standardize_posteriors(
  model,
  method = "refit",
  robust = FALSE,
  two_sd = FALSE,
  verbose = TRUE,
  ...
)
}
\arguments{
\item{model}{A statistical model.}

\item{method}{The method used for standardizing the parameters. Can be
\code{"refit"} (default), \code{"posthoc"}, \code{"smart"}, \code{"basic"} or \code{"pseudo"}. See
'Details'.}

\item{ci}{Confidence Interval (CI) level}

\item{robust}{Logical, if \code{TRUE}, centering is done by subtracting the
median from the variables and dividing it by the median absolute deviation
(MAD). If \code{FALSE}, variables are standardized by subtracting the
mean and dividing it by the standard deviation (SD).}

\item{two_sd}{If \code{TRUE}, the variables are scaled by two times the deviation
(SD or MAD depending on \code{robust}). This method can be useful to obtain
model coefficients of continuous parameters comparable to coefficients
related to binary predictors, when applied to \strong{the predictors} (not the
outcome) (Gelman, 2008).}

\item{verbose}{Toggle warnings and messages on or off.}

\item{parameters}{Deprecated.}

\item{...}{For \code{standardize_parameters()}, arguments passed to
\link[parameters:model_parameters]{parameters::model_parameters}, such as:
\itemize{
\item \code{ci_method}, \code{centrality} for Bayesian models...
\item \code{df_method} for Mixed models ...
\item \code{exponentiate}, ...
\item etc.
}}
}
\value{
A data frame with the standardized parameters (\verb{Std_*}, depending on
the model type) and their CIs (\code{CI_low} and \code{CI_high}). Where applicable,
standard errors (SEs) are returned as an attribute (\code{attr(x, "standard_error")}).
}
\description{
Compute standardized model parameters (coefficients).
}
\details{
\subsection{Methods:}{
\itemize{
\item \strong{refit}: This method is based on a complete model re-fit with a
standardized version of the data. Hence, this method is equal to
standardizing the variables before fitting the model. It is the "purest" and
the most accurate (Neter et al., 1989), but it is also the most
computationally costly and long (especially for heavy models such as Bayesian
models). This method is particularly recommended for complex models that
include interactions or transformations (e.g., polynomial or spline terms).
The \code{robust} (default to \code{FALSE}) argument enables a robust standardization
of data, i.e., based on the \code{median} and \code{MAD} instead of the \code{mean} and
\code{SD}. \strong{See \code{\link[=standardize]{standardize()}} for more details.}
\item \strong{posthoc}: Post-hoc standardization of the parameters, aiming at
emulating the results obtained by "refit" without refitting the model. The
coefficients are divided by the standard deviation (or MAD if \code{robust}) of
the outcome (which becomes their expression 'unit'). Then, the coefficients
related to numeric variables are additionally multiplied by the standard
deviation (or MAD if \code{robust}) of the related terms, so that they correspond
to changes of 1 SD of the predictor (e.g., "A change in 1 SD of \code{x} is
related to a change of 0.24 of the SD of \code{y}). This does not apply to binary
variables or factors, so the coefficients are still related to changes in
levels. This method is not accurate and tend to give aberrant results when
interactions are specified.
\item \strong{smart} (Standardization of Model's parameters with Adjustment,
Reconnaissance and Transformation - \emph{experimental}): Similar to \code{method = "posthoc"} in that it does not involve model refitting. The difference is
that the SD (or MAD if \code{robust}) of the response is computed on the relevant
section of the data. For instance, if a factor with 3 levels A (the
intercept), B and C is entered as a predictor, the effect corresponding to B
vs. A will be scaled by the variance of the response at the intercept only.
As a results, the coefficients for effects of factors are similar to a Glass'
delta.
\item \strong{basic}: This method is similar to \code{method = "posthoc"}, but treats all
variables as continuous: it also scales the coefficient by the standard
deviation of model's matrix' parameter of factors levels (transformed to
integers) or binary predictors. Although being inappropriate for these cases,
this method is the one implemented by default in other software packages,
such as \code{\link[lm.beta:lm.beta]{lm.beta::lm.beta()}}.
\item \strong{pseudo} (\emph{for 2-level (G)LMMs only}): In this (post-hoc) method, the
response and the predictor are standardized based on the level of prediction
(levels are detected with \code{\link[parameters:demean]{parameters::check_heterogeneity()}}): Predictors
are standardized based on their SD at level of prediction (see also
\code{\link[parameters:demean]{parameters::demean()}}); The outcome (in linear LMMs) is standardized based
on a fitted random-intercept-model, where \code{sqrt(random-intercept-variance)}
is used for level 2 predictors, and \code{sqrt(residual-variance)} is used for
level 1 predictors (Hoffman 2015, page 342). A warning is given when a
within-group varialbe is found to have access between-group variance.
}
}

\subsection{Transformed Variables}{

When the model's formula contains transformations (e.g. \code{y ~ exp(X)})
\code{method = "refit"} might give different results compared to
\code{method = "basic"} (\code{"posthoc"} and \code{"smart"} do not support such
transformations): where \code{"refit"} standardizes the data prior to the
transformation (e.g. equivalent to \code{exp(scale(X))}), the \code{"basic"} method
standardizes the transformed data (e.g. equivalent to \code{scale(exp(X))}). See
\code{\link[=standardize]{standardize()}} for more details on how different transformations are dealt
with.
}
}
\section{Generalized Linear Models}{
When standardizing coefficients of a generalized model (GLM, GLMM, etc), only
the predictors are standardized, maintaining the interpretability of the
coefficients (e.g., in a binomial model: the exponent of the standardized
parameter is the OR of a change of 1 SD in the predictor, etc.)
}

\examples{
library(effectsize)

model <- lm(len ~ supp * dose, data = ToothGrowth)
standardize_parameters(model, method = "refit")
\donttest{
standardize_parameters(model, method = "posthoc")
standardize_parameters(model, method = "smart")
standardize_parameters(model, method = "basic")

# Robust and 2 SD
standardize_parameters(model, robust = TRUE)
standardize_parameters(model, two_sd = TRUE)


model <- glm(am ~ cyl * mpg, data = mtcars, family = "binomial")
standardize_parameters(model, method = "refit")
standardize_parameters(model, method = "posthoc")
standardize_parameters(model, method = "basic", exponentiate = TRUE)
}

\donttest{
if (require("lme4")) {
  m <- lmer(mpg ~ cyl + am + vs + (1 | cyl), mtcars)
  standardize_parameters(m, method = "pseudo", df_method = "satterthwaite")
}


\dontrun{
if (require("rstanarm")) {
  model <- stan_glm(rating ~ critical + privileges, data = attitude, refresh = 0)
  standardize_posteriors(model, method = "refit")
  standardize_posteriors(model, method = "posthoc")
  standardize_posteriors(model, method = "smart")
  head(standardize_posteriors(model, method = "basic"))
}
}
}

}
\references{
\itemize{
\item Hoffman, L. (2015). Longitudinal analysis: Modeling within-person fluctuation and change. Routledge.
\item Neter, J., Wasserman, W., & Kutner, M. H. (1989). Applied linear regression models.
\item Gelman, A. (2008). Scaling regression inputs by dividing by two standard deviations. Statistics in medicine, 27(15), 2865-2873.
}
}
\seealso{
\code{\link[=standardize_info]{standardize_info()}}

Other standardize: 
\code{\link{standardize_info}()},
\code{\link{standardize}()}

Other effect size indices: 
\code{\link{cohens_d}()},
\code{\link{effectsize}()},
\code{\link{eta_squared}()},
\code{\link{phi}()},
\code{\link{rank_biserial}()}
}
\concept{effect size indices}
\concept{standardize}
