Coeficientes de uma Regressão

Diferenças entre Coeficientes Padronizados vs Brutos

Jose Storopoli https://scholar.google.com/citations?user=xGU7H1QAAAAJ&hl=en (UNINOVE)https://www.uninove.br
August 1, 2021

Em tabelas de regressão temos geralmente temos duas opções de como reportar os coeficientes:

Simulação

Para explicar melhor esses conceitos, simularemos alguns dados:

N <- 1000
x <- rnorm(N, 1, 0.1)
error <- rnorm(N, 0, 1)
y <- rep(10, N) + (100 * x) + error

df <- data.frame(x, y)

Observem os dados com o pacote skimr (Waring et al., 2021) usando a função skim():

Table 1: Data summary
Name df
Number of rows 1000
Number of columns 2
_______________________
Column type frequency:
numeric 2
________________________
Group variables None

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
x 0 1 1 0.1 0.72 0.94 1 1.1 1.3 ▁▅▇▃▁
y 0 1 110 10.1 79.76 103.59 110 116.8 142.3 ▁▅▇▃▁

Média e Desvio Padrões

Prestem atenção:

Coeficientes Brutos vs Padronizados

Agora vamos executar uma regressão1 e mostrar coeficientes tanto como brutos, assim como padronizados:

library(lm.beta)
model <- lm.beta(lm(y ~ x, df))
summary(model)

Call:
lm(formula = y ~ x, data = df)

Residuals:
   Min     1Q Median     3Q    Max 
-3.028 -0.691  0.004  0.709  3.291 

Coefficients:
            Estimate Standardized Std. Error t value
(Intercept)    9.161        0.000      0.323    28.4
x            100.880        0.995      0.321   314.2
                       Pr(>|t|)    
(Intercept) <0.0000000000000002 ***
x           <0.0000000000000002 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1 on 998 degrees of freedom
Multiple R-squared:  0.99,  Adjusted R-squared:  0.99 
F-statistic: 9.87e+04 on 1 and 998 DF,  p-value: <0.0000000000000002

Ambas colunas o output de summary() mostram a mesma coisa:

Ambiente

R version 4.1.0 (2021-05-18)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur 10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods  
[7] base     

other attached packages:
 [1] lm.beta_1.5-1        loo_2.4.1            DescTools_0.99.41   
 [4] gapminder_0.3.0      ggExtra_0.9          dplyr_1.0.6         
 [7] rstan_2.21.2         StanHeaders_2.21.0-7 MASS_7.3-54         
[10] ggforce_0.3.3        gganimate_1.0.7      plotly_4.9.3        
[13] carData_3.0-4        DiagrammeR_1.0.6.1   brms_2.15.0         
[16] rstanarm_2.21.1      Rcpp_1.0.6           skimr_2.1.3         
[19] readr_1.4.0          readxl_1.3.1         tibble_3.1.2        
[22] ggplot2_3.3.3        patchwork_1.1.1      cowplot_1.1.1       

loaded via a namespace (and not attached):
  [1] utf8_1.2.1           tidyselect_1.1.1     lme4_1.1-27         
  [4] htmlwidgets_1.5.3    grid_4.1.0           munsell_0.5.0       
  [7] codetools_0.2-18     ragg_1.1.2           distill_1.2         
 [10] DT_0.18              gifski_1.4.3-1       miniUI_0.1.1.1      
 [13] withr_2.4.2          Brobdingnag_1.2-6    colorspace_2.0-1    
 [16] highr_0.9            knitr_1.33           rstudioapi_0.13     
 [19] stats4_4.1.0         bayesplot_1.8.0      labeling_0.4.2      
 [22] repr_1.1.3           mnormt_2.0.2         polyclip_1.10-0     
 [25] farver_2.1.0         bridgesampling_1.1-2 rprojroot_2.0.2     
 [28] coda_0.19-4          vctrs_0.3.8          generics_0.1.0      
 [31] xfun_0.23            R6_2.5.0             markdown_1.1        
 [34] isoband_0.2.4        gamm4_0.2-6          projpred_2.0.2      
 [37] assertthat_0.2.1     promises_1.2.0.1     scales_1.1.1        
 [40] rootSolve_1.8.2.1    gtable_0.3.0         downlit_0.2.1       
 [43] processx_3.5.2       lmom_2.8             rlang_0.4.11        
 [46] systemfonts_1.0.2    splines_4.1.0        lazyeval_0.2.2      
 [49] checkmate_2.0.0      inline_0.3.19        yaml_2.2.1          
 [52] reshape2_1.4.4       abind_1.4-5          threejs_0.3.3       
 [55] crosstalk_1.1.1      backports_1.2.1      httpuv_1.6.1        
 [58] rsconnect_0.8.18     tools_4.1.0          bookdown_0.22       
 [61] ellipsis_0.3.2       jquerylib_0.1.4      RColorBrewer_1.1-2  
 [64] proxy_0.4-25         ggridges_0.5.3       plyr_1.8.6          
 [67] base64enc_0.1-3      visNetwork_2.0.9     progress_1.2.2      
 [70] purrr_0.3.4          ps_1.6.0             prettyunits_1.1.1   
 [73] zoo_1.8-9            here_1.0.1           magrittr_2.0.1      
 [76] data.table_1.14.0    magick_2.7.2         colourpicker_1.1.0  
 [79] tmvnsim_1.0-2        mvtnorm_1.1-1        matrixStats_0.59.0  
 [82] hms_1.1.0            shinyjs_2.0.0        mime_0.10           
 [85] evaluate_0.14        xtable_1.8-4         shinystan_2.5.0     
 [88] gridExtra_2.3        rstantools_2.1.1     compiler_4.1.0      
 [91] V8_3.4.2             crayon_1.4.1         minqa_1.2.4         
 [94] htmltools_0.5.1.1    mgcv_1.8-35          later_1.2.0         
 [97] tidyr_1.1.3          expm_0.999-6         Exact_2.1           
[100] RcppParallel_5.1.4   lubridate_1.7.10     DBI_1.1.1           
[103] tweenr_1.0.2         boot_1.3-28          Matrix_1.3-3        
[106] cli_2.5.0            parallel_4.1.0       igraph_1.2.6        
[109] pkgconfig_2.0.3      xml2_1.3.2           dygraphs_1.1.1.6    
[112] bslib_0.2.5.1        stringr_1.4.0        callr_3.7.0         
[115] digest_0.6.27        rmarkdown_2.8        cellranger_1.1.0    
[118] gld_2.6.2            curl_4.3.1           shiny_1.6.0         
[121] gtools_3.8.2         nloptr_1.2.2.2       lifecycle_1.0.0     
[124] nlme_3.1-152         jsonlite_1.7.2       viridisLite_0.4.0   
[127] fansi_0.5.0          pillar_1.6.1         lattice_0.20-44     
[130] fastmap_1.1.0        httr_1.4.2           pkgbuild_1.2.0      
[133] survival_3.2-11      glue_1.4.2           xts_0.12.1          
[136] png_0.1-7            shinythemes_1.2.0    class_7.3-19        
[139] stringi_1.6.2        sass_0.4.0           textshaping_0.3.4   
[142] e1071_1.7-7         
Waring, E., Quinn, M., McNamara, A., Arino de la Rubia, E., Zhu, H., & Ellis, S. (2021). Skimr: Compact and flexible summaries of data. Retrieved from https://CRAN.R-project.org/package=skimr

  1. estou rodando uma regressão simples frequentista pois o foco não é a robustez da inferência mas apenas uma mera exemplificação de como interpretar coeficientes.↩︎

References

Corrections

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Reuse

Text and figures are licensed under Creative Commons Attribution CC BY-SA 4.0. Source code is available at https://github.com/storopoli/Estatistica-Bayesiana, unless otherwise noted. The figures that have been reused from other sources don't fall under this license and can be recognized by a note in their caption: "Figure from ...".

Citation

For attribution, please cite this work as

Storopoli (2021, Aug. 1). Estatística Bayesiana com R e Stan: Coeficientes de uma Regressão. Retrieved from https://storopoli.io/Estatistica-Bayesiana/aux-Regressao_Coeficientes.html

BibTeX citation

@misc{storopoli2021regressaocoeficientesR,
  author = {Storopoli, Jose},
  title = {Estatística Bayesiana com R e Stan: Coeficientes de uma Regressão},
  url = {https://storopoli.io/Estatistica-Bayesiana/aux-Regressao_Coeficientes.html},
  year = {2021}
}