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📊 Computation and processing of models' parameters
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easystats/parameters
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Describe and understand your model’s parameters!
parameters’ primary goal is to provide utilities for processing theparameters of various statistical models (seehere for a list of supportedmodels). Beyond computingp-values,CIs,Bayesian indices andother measures for a wide variety of models, this package implementsfeatures likebootstrapping of parameters and models,featurereduction (feature extraction and variable selection), or tools fordata reduction like functions to perform cluster, factor or principalcomponent analysis.
Another important goal of theparameters package is to facilitateand streamline the process of reporting results of statistical models,which includes the easy and intuitive calculation of standardizedestimates or robust standard errors and p-values.parameterstherefor offers a simple and unified syntax to process a large varietyof (model) objects from many different packages.
| Type | Source | Command |
|---|---|---|
| Release | CRAN | install.packages("parameters") |
| Development | r - universe | install.packages("parameters", repos = "https://easystats.r-universe.dev") |
| Development | GitHub | remotes::install_github("easystats/parameters") |
Tip
Instead of
library(parameters), uselibrary(easystats). This willmake all features of the easystats-ecosystem available.To stay updated, use
easystats::install_latest().
Click on the buttons above to access the packagedocumentation and theeasystats blog, and check-outthese vignettes:
- Summary of ModelParameters
- Parameter and ModelStandardization
- Robust Estimation of Standard Errors, Confidence Intervals andp-values
- Model Parameters and MissingData
- Feature reduction (PCA, cMDS,ICA…)
- Structural models (EFA, CFA,SEM…)
- Parametersselection
- A Practical Guide for Panel DataAnalysis
- Plottingfunctions
In case you want to file an issue or contribute in another way to thepackage, please followthisguide.For questions about the functionality, you may either contact us viaemail or also file an issue.
Themodel_parameters()function (that can be accessed via theparameters() shortcut) allowsyou to extract the parameters and their characteristics from variousmodels in a consistent way. It can be considered as a lightweightalternative tobroom::tidy(),with some notable differences:
- The column names of the returned data frame arespecific to theircontent. For instance, the column containing the statistic is namedfollowing the statistic name, i.e.,t,z, etc., instead of ageneric name such asstatistic (however, you can get standardized(generic) column names using
standardize_names()). - It is able to compute or extract indices not available by default,such asp-values,CIs, etc.
- It includesfeature engineering capabilities, including parametersbootstrapping.
model<- lm(Sepal.Width~Petal.Length*Species+Petal.Width,data=iris)# regular model parametersmodel_parameters(model)#> Parameter | Coefficient | SE | 95% CI | t(143) | p#> -------------------------------------------------------------------------------------------#> (Intercept) | 2.89 | 0.36 | [ 2.18, 3.60] | 8.01 | < .001#> Petal Length | 0.26 | 0.25 | [-0.22, 0.75] | 1.07 | 0.287#> Species [versicolor] | -1.66 | 0.53 | [-2.71, -0.62] | -3.14 | 0.002#> Species [virginica] | -1.92 | 0.59 | [-3.08, -0.76] | -3.28 | 0.001#> Petal Width | 0.62 | 0.14 | [ 0.34, 0.89] | 4.41 | < .001#> Petal Length × Species [versicolor] | -0.09 | 0.26 | [-0.61, 0.42] | -0.36 | 0.721#> Petal Length × Species [virginica] | -0.13 | 0.26 | [-0.64, 0.38] | -0.50 | 0.618# standardized parametersmodel_parameters(model,standardize="refit")#> Parameter | Coefficient | SE | 95% CI | t(143) | p#> -------------------------------------------------------------------------------------------#> (Intercept) | 3.59 | 1.30 | [ 1.01, 6.17] | 2.75 | 0.007#> Petal Length | 1.07 | 1.00 | [-0.91, 3.04] | 1.07 | 0.287#> Species [versicolor] | -4.62 | 1.31 | [-7.21, -2.03] | -3.53 | < .001#> Species [virginica] | -5.51 | 1.38 | [-8.23, -2.79] | -4.00 | < .001#> Petal Width | 1.08 | 0.24 | [ 0.59, 1.56] | 4.41 | < .001#> Petal Length × Species [versicolor] | -0.38 | 1.06 | [-2.48, 1.72] | -0.36 | 0.721#> Petal Length × Species [virginica] | -0.52 | 1.04 | [-2.58, 1.54] | -0.50 | 0.618# heteroscedasticity-consitent SE and CImodel_parameters(model,vcov="HC3")#> Parameter | Coefficient | SE | 95% CI | t(143) | p#> -------------------------------------------------------------------------------------------#> (Intercept) | 2.89 | 0.43 | [ 2.03, 3.75] | 6.66 | < .001#> Petal Length | 0.26 | 0.29 | [-0.30, 0.83] | 0.92 | 0.357#> Species [versicolor] | -1.66 | 0.53 | [-2.70, -0.62] | -3.16 | 0.002#> Species [virginica] | -1.92 | 0.77 | [-3.43, -0.41] | -2.51 | 0.013#> Petal Width | 0.62 | 0.12 | [ 0.38, 0.85] | 5.23 | < .001#> Petal Length × Species [versicolor] | -0.09 | 0.29 | [-0.67, 0.48] | -0.32 | 0.748#> Petal Length × Species [virginica] | -0.13 | 0.31 | [-0.73, 0.48] | -0.42 | 0.675
library(lme4)model<- lmer(Sepal.Width~Petal.Length+ (1|Species),data=iris)# model parameters with CI, df and p-values based on Wald approximationmodel_parameters(model)#> # Fixed Effects#>#> Parameter | Coefficient | SE | 95% CI | t(146) | p#> ------------------------------------------------------------------#> (Intercept) | 2.00 | 0.56 | [0.89, 3.11] | 3.56 | < .001#> Petal Length | 0.28 | 0.06 | [0.16, 0.40] | 4.75 | < .001#>#> # Random Effects#>#> Parameter | Coefficient | SE | 95% CI#> -----------------------------------------------------------#> SD (Intercept: Species) | 0.89 | 0.46 | [0.33, 2.43]#> SD (Residual) | 0.32 | 0.02 | [0.28, 0.35]# model parameters with CI, df and p-values based on Kenward-Roger approximationmodel_parameters(model,ci_method="kenward",effects="fixed")#> # Fixed Effects#>#> Parameter | Coefficient | SE | 95% CI | t | df | p#> -------------------------------------------------------------------------#> (Intercept) | 2.00 | 0.57 | [0.07, 3.93] | 3.53 | 2.67 | 0.046#> Petal Length | 0.28 | 0.06 | [0.16, 0.40] | 4.58 | 140.98 | < .001
Besides many types of regression models and packages, it also works forother types of models, such asstructuralmodels(EFA, CFA, SEM…).
library(psych)model<-psych::fa(attitude,nfactors=3)model_parameters(model)#> # Rotated loadings from Factor Analysis (oblimin-rotation)#>#> Variable | MR1 | MR2 | MR3 | Complexity | Uniqueness#> ------------------------------------------------------------#> rating | 0.90 | -0.07 | -0.05 | 1.02 | 0.23#> complaints | 0.97 | -0.06 | 0.04 | 1.01 | 0.10#> privileges | 0.44 | 0.25 | -0.05 | 1.64 | 0.65#> learning | 0.47 | 0.54 | -0.28 | 2.51 | 0.24#> raises | 0.55 | 0.43 | 0.25 | 2.35 | 0.23#> critical | 0.16 | 0.17 | 0.48 | 1.46 | 0.67#> advance | -0.11 | 0.91 | 0.07 | 1.04 | 0.22#>#> The 3 latent factors (oblimin rotation) accounted for 66.60% of the total variance of the original data (MR1 = 38.19%, MR2 = 22.69%, MR3 = 5.72%).
select_parameters()can help you quickly select and retain the most relevant predictorsusing methods tailored for the model type.
lm(disp~.,data=mtcars)|> select_parameters()|> model_parameters()#> Parameter | Coefficient | SE | 95% CI | t(26) | p#> -----------------------------------------------------------------------#> (Intercept) | 141.70 | 125.67 | [-116.62, 400.02] | 1.13 | 0.270#> cyl | 13.14 | 7.90 | [ -3.10, 29.38] | 1.66 | 0.108#> hp | 0.63 | 0.20 | [ 0.22, 1.03] | 3.18 | 0.004#> wt | 80.45 | 12.22 | [ 55.33, 105.57] | 6.58 | < .001#> qsec | -14.68 | 6.14 | [ -27.31, -2.05] | -2.39 | 0.024#> carb | -28.75 | 5.60 | [ -40.28, -17.23] | -5.13 | < .001
There is no standardized approach to drawing conclusions based on theavailable data and statistical models. A frequently chosen but also muchcriticized approach is to evaluate results based on their statisticalsignificance (Amrhein, Korner-Nievergelt, & Roth, 2017).
A more sophisticated way would be to test whether estimated effectsexceed the “smallest effect size of interest”, to avoid even thesmallest effects being considered relevant simply because they arestatistically significant, but clinically or practically irrelevant(Lakens, 2024; Lakens, Scheel, & Isager, 2018). A rather unconventionalapproach, which is nevertheless advocated by various authors, is tointerpret results from classical regression models in terms ofprobabilities, similar to the usual approach in Bayesian statistics(Greenland, Rafi, Matthews, & Higgs, 2022; Rafi & Greenland, 2020;Schweder, 2018; Schweder & Hjort, 2003; Vos & Holbert, 2022).
Theparameters package provides several options or functions to aidstatistical inference. These are, for example:
equivalence_test(),to compute the (conditional) equivalence test for frequentist modelsp_significance(),to compute the probability ofpractical significance, which can beconceptualized as a unidirectional equivalence testp_function(),orconsonance function, to compute p-values and compatibility(confidence) intervals for statistical models- the
pdargument (settingpd = TRUE) inmodel_parameters()includes a column with theprobability of direction, i.e. theprobability that a parameter is strictly positive or negative. SeebayestestR::p_direction()for details. - the
s_valueargument (settings_value = TRUE) inmodel_parameters()replaces the p-values with their relatedS-values (@ Rafi & Greenland, 2020) - finally, it is possible to generate distributions of modelcoefficients by generating bootstrap-samples (setting
bootstrap = TRUE) or simulating draws from model coefficients usingsimulate_model().These samples can then be treated as “posterior samples” and used inmany functions from thebayestestR package.
Most of the above shown options or functions derive from methodsoriginally implemented for Bayesian models (Makowski, Ben-Shachar, Chen,& Lüdecke, 2019). However, assuming that model assumptions are met(which means, the model fits well to the data, the correct model ischosen that reflects the data generating process (distributional modelfamily) etc.), it seems appropriate to interpret results from classicalfrequentist models in a “Bayesian way” (more details: documentation inp_function()).
In order to cite this package, please use the following command:
citation("parameters")Tocitepackage'parameters'inpublicationsuse:LüdeckeD,Ben-ShacharM,PatilI,Makowski D (2020)."Extracting, Computing and Exploring the Parameters of Statistical Models using R."_JournalofOpenSourceSoftware_,*5*(53),2445.doi:10.21105/joss.02445<https://doi.org/10.21105/joss.02445>.ABibTeXentryforLaTeXusersis@Article{,title= {Extracting,ComputingandExploringtheParametersofStatisticalModelsusing {R}.},volume= {5},doi= {10.21105/joss.02445},number= {53},journal= {JournalofOpenSourceSoftware},author= {DanielLüdeckeandMattanS.Ben-ShacharandIndrajeetPatilandDominiqueMakowski},year= {2020},pages= {2445}, }
Please note that the parameters project is released with aContributorCode ofConduct.By contributing to this project, you agree to abide by its terms.
Amrhein, V., Korner-Nievergelt, F., & Roth, T. (2017). The earth is flat(p > 0.05): Significance thresholds and the crisis of unreplicableresearch.PeerJ,5, e3544.https://doi.org/10.7717/peerj.3544
Greenland, S., Rafi, Z., Matthews, R., & Higgs, M. (2022).To AidScientific Inference, Emphasize Unconditional Compatibility Descriptionsof Statistics. Retrieved fromhttp://arxiv.org/abs/1909.08583
Lakens, D. (2024).Improving Your Statistical Inferences.https://doi.org/10.5281/ZENODO.6409077
Lakens, D., Scheel, A. M., & Isager, P. M. (2018). Equivalence testingfor psychological research: A tutorial.Advances in Methods andPractices in Psychological Science,1(2), 259–269.https://doi.org/10.1177/2515245918770963
Makowski, D., Ben-Shachar, M. S., Chen, S. H. A., & Lüdecke, D. (2019).Indices of Effect Existence and Significance in the Bayesian Framework.Frontiers in Psychology,10, 2767.https://doi.org/10.3389/fpsyg.2019.02767
Rafi, Z., & Greenland, S. (2020). Semantic and cognitive tools to aidstatistical science: Replace confidence and significance bycompatibility and surprise.BMC Medical Research Methodology,20(1),244.https://doi.org/10.1186/s12874-020-01105-9
Schweder, T. (2018). Confidence is epistemic probability for empiricalscience.Journal of Statistical Planning and Inference,195,116–125.https://doi.org/10.1016/j.jspi.2017.09.016
Schweder, T., & Hjort, N. L. (2003). Frequentist Analogues of Priors andPosteriors. In B. Stigum (Ed.),Econometrics and the Philosophy ofEconomics: Theory-Data Confrontations in Economics (pp. 285–217).Retrieved fromhttps://www.duo.uio.no/handle/10852/10425
Vos, P., & Holbert, D. (2022). Frequentist statistical inference withoutrepeated sampling.Synthese,200(2), 89.https://doi.org/10.1007/s11229-022-03560-x
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📊 Computation and processing of models' parameters