parameters: Processing of Model Parameters

title: "Extracting, Computing and Exploring the Parameters of Statistical Models using R" authors: - affiliation: 1 name: Daniel Lüdecke orcid: 0000-0002-8895-3206 - affiliation: 2 name: Mattan S. Ben-Shachar orcid: 0000-0002-4287-4801 - affiliation: 3 name: Indrajeet Patil orcid: 0000-0003-1995-6531 - affiliation: 4 name: Dominique Makowski orcid: 0000-0001-5375-9967

date: "01 July 2020" output: pdf_document bibliography: paper.bib csl: apa.csl tags: - R - easystats - parameters - regression - linear models - coefficients affiliations: - index: 1 name: University Medical Center Hamburg-Eppendorf, Germany - index: 2 name: Ben-Gurion University of the Negev, Israel - index: 3 name: Max Planck Institute for Human Development, Germany - index: 4 name: Nanyang Technological University, Singapore

Summary

The recent growth of data science is partly fueled by the ever-growing amount of data and the joint important developments in statistical modeling, with new and powerful models and frameworks becoming accessible to users. Although there exist some generic functions to obtain model summaries and parameters, many package-specific modeling functions do not provide such methods to allow users to access such valuable information.

Aims of the Package

parameters is an R-package [@rcore] that fills this important gap. Its primary goal is to provide utilities for processing the parameters of various statistical models. Beyond computing p-values, standard errors, confidence intervals (CI), Bayesian indices and other measures for a wide variety of models, this package implements features like parameters bootstrapping and engineering (such as variables reduction and/or selection), as well as tools for data reduction like functions to perform cluster, factor or principal component analysis.

Another important goal of the parameters package is to facilitate and streamline the process of reporting results of statistical models, which includes the easy and intuitive calculation of standardized estimates in addition to robust standard errors and p-values. parameters therefor offers a simple and unified syntax to process a large variety of (model) objects from many different packages.

parameters is part of the easystats ecosystem, a collaborative project created to facilitate the usage of R for statistical analyses.

Comparison to other Packages

parameters functionality is in part comparable to packages like broom [@robinson_broom_2020], finalfit [@harrison2020finalfit] or stargazer [@hlavac_stargazer_2018] (and maybe some more). Yet, there are some notable differences, e.g.:

broom (via glance()), finalfit (via ff_metrics()) and stargazer (via stargazer()) report fit indices (such as R2 or AIC) by default, while parameters does not. However, there is a dedicated package in the easystats project for assessing regression model quality and fit indices, performance [@luedecke2020performance].
parameters easily allows to compute standardized estimates, robust estimation, small-sample-size corrections for degrees of freedom (like Satterthwaite or Kenward-Roger), bootstrapping or simulating parameters, and feature reduction. Furthermore, parameters provides functions to test for the presence or absence of an effect [equivalence testing, see @lakens2020equivalence].
For most functions, easy-to-use plot()-methods exist to quickly create nice looking plots (powered by the see package [@ludecke2020see]).
parameters is a very lightweight package. Its main functionality only relies on the insight, the bayestestR, and the effectsize packages [@ludecke2019insight; @makowski2019bayetestR; @benshachar2020effecsize] to access and process information contained in models, and these packages in turn only depend on R core packages. However, additional features that do not belong to the core functions of parameters require the installation of other packages, such as sandwich [@zeileis2006] for robust estimation, psych [@revelle_psych_2019] for factor analysis or PCA or cAIC4 [@saefken_caic4_2018] for parameter selection for mixed models.

Examples of Features

As stated above, parameters creates summary tables of many different statistical models. The workflow is simple: fit a model and pass it to the model_parameters() function (or its shortcut, parameters()) to obtain information about the model's parameters.

In the following, we show some brief examples. However, a comprehensive overview including in-depth examples are accessible via the dedicated website (https://easystats.github.io/parameters/).

model_parameters() allows you to extract the parameters and their characteristics from various models in a consistent way.

library(parameters)

model <- lm(Sepal.Length ~ Species, data = iris)
parameters(model)

#> Parameter            | Coefficient |   SE |       95% CI |      p
#> -----------------------------------------------------------------
#> (Intercept)          |        5.01 | 0.07 | [4.86, 5.15] | < .001
#> Species [versicolor] |        0.93 | 0.10 | [0.73, 1.13] | < .001
#> Species [virginica]  |        1.58 | 0.10 | [1.38, 1.79] | < .001

Extraction of robust indices is possible for many models, in particular models supported by the sandwich [@zeileis2006] and clubSandwich [@pustejovsky2020] packages.

parameters(model, robust = TRUE)

#> Parameter            | Coefficient |   SE |       95% CI |      p
#> -----------------------------------------------------------------
#> (Intercept)          |        5.01 | 0.05 | [4.91, 5.11] | < .001
#> Species [versicolor] |        0.93 | 0.09 | [0.75, 1.11] | < .001
#> Species [virginica]  |        1.58 | 0.10 | [1.38, 1.79] | < .001

For linear mixed models, parameters() also allows to specify the method for approximating degrees of freedom, which may improve the accurracy for calculated standard errors or p-values.

library(lme4)
model <- lmer(
  Sepal.Length ~ Sepal.Width * Petal.Length + (1 | Species), 
  data = iris
)

parameters(model, digits = 3)

#> Parameter                  | Coefficient |    SE |         95% CI |      p
#> --------------------------------------------------------------------------
#> (Intercept)                |       0.707 | 0.652 | [-0.57,  1.98] | 0.278 
#> Sepal.Width                |       0.731 | 0.156 | [ 0.43,  1.04] | < .001
#> Petal.Length               |       1.023 | 0.143 | [ 0.74,  1.30] | < .001
#> Sepal.Width * Petal.Length |      -0.084 | 0.040 | [-0.16, -0.01] | 0.035 

parameters(model, digits = 3, df_method = "kenward")

#> Parameter                  | Coefficient |    SE |         95% CI |      p
#> --------------------------------------------------------------------------
#> (Intercept)                |       0.707 | 0.654 | [-0.70,  2.11] | 0.298 
#> Sepal.Width                |       0.731 | 0.157 | [ 0.42,  1.04] | < .001
#> Petal.Length               |       1.023 | 0.145 | [ 0.74,  1.31] | < .001
#> Sepal.Width * Petal.Length |      -0.084 | 0.040 | [-0.16, -0.01] | 0.037

parameters functions also include plotting capabilities via the see package [@ludecke2020see]. A complete overview of plotting functions is available at the see website (https://easystats.github.io/see/articles/parameters.html).

library(see)

model <- lm(Sepal.Length ~ Petal.Width * Species, data=iris)
plot(parameters(model))

Licensing and Availability

parameters is licensed under the GNU General Public License (v3.0), with all source code stored at GitHub (https://github.com/easystats/parameters), and with a corresponding issue tracker for bug reporting and feature enhancements. In the spirit of honest and open science, we encourage requests/tips for fixes, feature updates, as well as general questions and concerns via direct interaction with contributors and developers.