Compute and extract model parameters. See the documentation for your object's class:

Correlations, t-tests, ... (

`htest`

,`pairwise.htest`

)ANOVAs (

`aov`

,`anova`

, afex, ...)Regression models (

`lm`

,`glm`

, survey, ...)Additive models (

`gam`

,`gamm`

, ...)Zero-inflated models (

`hurdle`

,`zeroinfl`

,`zerocount`

)Multinomial, ordinal and cumulative link models (

`bracl`

,`multinom`

,`mlm`

, ...)Other special models (

`model.avg`

,`betareg`

,`glmx`

, ...)Mixed models (lme4, nlme, glmmTMB, afex, ...)

Bayesian tests (BayesFactor)

Bayesian models (rstanarm, brms, MCMCglmm, blavaan, ...)

PCA and FA (psych)

CFA and SEM (lavaan)

Cluster models (k-means, ...)

Meta-Analysis via linear (mixed) models (

`rma`

,`metaplus`

, metaBMA, ...)Hypothesis testing (

`glht`

, PMCMRplus)Robust statistical tests (WRS2)

```
model_parameters(model, ...)
parameters(model, ...)
```

model | Statistical Model. |
---|---|

... | Arguments passed to or from other methods. Non-documented
arguments are |

A data frame of indices related to the model's parameters.

Standardization is based on `effectsize::standardize_parameters()`

.
In case of `standardize = "refit"`

, the data used to fit the model
will be standardized and the model is completely refitted. In such cases,
standard errors and confidence intervals refer to the standardized
coefficient. The default, `standardize = "refit"`

, never standardizes
categorical predictors (i.e. factors), which may be a different behaviour
compared to other R packages or other software packages (like SPSS).
To mimic behaviour of SPSS or packages such as lm.beta, use
`standardize = "basic"`

.

For full details, please refer to `effectsize::standardize_parameters()`

.

**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).The

`robust`

argument (default to`FALSE`

) enables a robust standardization of data, i.e., based on the`median`

and`MAD`

instead of the`mean`

and`SD`

.**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`robust=TRUE`

) of the outcome (which becomes their expression 'unit'). Then, the coefficients related to numeric variables are additionally multiplied by the standard deviation (or MAD) of the related terms, so that they correspond to changes of 1 SD of the predictor. 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.**smart**(Standardization of Model's parameters with Adjustment, Reconnaissance and Transformation -

*experimental*): Similar to`method="posthoc"`

in that it does not involve model refitting. The difference is that the SD (or MAD) 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.**basic**This method is similar to

`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`lm.beta::lm.beta()`

.**pseudo**(*for 2-level (G)LMMs only*)In this (post-hoc) method, the response and the predictor are standardized based on the level of prediction: Predictors are standardized based on their SD at level of prediction (see also

`datawizard::demean()`

). The outcome (in linear LMMs) is standardized based on a fitted random-intercept-model, where`sqrt(random-intercept-variance)`

is used for level 2 predictors, and`sqrt(residual-variance)`

is used for level 1 predictors (Hoffman 2015, page 342). A warning is given when a within-group variable is found to have access between-group variance.

The `print()`

method has several
arguments to tweak the output. There is also a
`plot()`

-method
implemented in the
see-package, and a dedicated
method for use inside rmarkdown files,
`print_md()`

.

Throughout the parameters package, we decided to label the residual
degrees of freedom *df_error*. The reason for this is that these degrees
of freedom not always refer to the residuals. For certain models, they refer
to the estimate error - in a linear model these are the same, but in - for
instance - any mixed effects model, this isn't strictly true. Hence, we
think that `df_error`

is the most generic label for these degrees of
freedom.

Note that the *interpretation* of interaction terms depends on many
characteristics of the model. The number of parameters, and overall
performance of the model, can differ *or not* between `a * b`

`a : b`

, and `a / b`

, suggesting that sometimes interaction terms
give different parameterizations of the same model, but other times it gives
completely different models (depending on `a`

or `b`

being factors
of covariates, included as main effects or not, etc.). Their interpretation
depends of the full context of the model, which should not be inferred
from the parameters table alone - rather, we recommend to use packages
that calculate estimated marginal means or marginal effects, such as
modelbased, emmeans or ggeffects. To raise
awareness for this issue, you may use `print(...,show_formula=TRUE)`

to add the model-specification to the output of the
`print()`

method for `model_parameters()`

.

Hoffman, L. (2015). Longitudinal analysis: Modeling within-person fluctuation and change. Routledge.

Neter, J., Wasserman, W., & Kutner, M. H. (1989). Applied linear regression models.

`insight::standardize_names()`

to
rename columns into a consistent, standardized naming scheme.