Overview
The olsrr package provides following tools for building OLS regression models using R:
- Comprehensive Regression Output
- Variable Selection Procedures
- Heteroskedasticity Tests
- Collinearity Diagnostics
- Model Fit Assessment
- Measures of Influence
- Residual Diagnostics
- Variable Contribution Assessment
Installation
# Install release version from CRAN
install.packages("olsrr")
# Install development version from GitHub
# install.packages("devtools")
devtools::install_github("rsquaredacademy/olsrr")Usage
olsrr uses consistent prefix ols_ for easy tab completion.
olsrr is built with the aim of helping those users who are new to the R language. If you know how to write a formula or build models using lm, you will find olsrr very useful. Most of the functions use an object of class lm as input. So you just need to build a model using lm and then pass it onto the functions in olsrr. Below is a quick demo:
Regression
ols_regress(mpg ~ disp + hp + wt + qsec, data = mtcars)
#> Model Summary
#> ---------------------------------------------------------------
#> R 0.914 RMSE 2.409
#> R-Squared 0.835 MSE 6.875
#> Adj. R-Squared 0.811 Coef. Var 13.051
#> Pred R-Squared 0.771 AIC 159.070
#> MAE 1.858 SBC 167.864
#> ---------------------------------------------------------------
#> RMSE: Root Mean Square Error
#> MSE: Mean Square Error
#> MAE: Mean Absolute Error
#> AIC: Akaike Information Criteria
#> SBC: Schwarz Bayesian Criteria
#>
#> ANOVA
#> --------------------------------------------------------------------
#> Sum of
#> Squares DF Mean Square F Sig.
#> --------------------------------------------------------------------
#> Regression 940.412 4 235.103 34.195 0.0000
#> Residual 185.635 27 6.875
#> Total 1126.047 31
#> --------------------------------------------------------------------
#>
#> Parameter Estimates
#> ----------------------------------------------------------------------------------------
#> model Beta Std. Error Std. Beta t Sig lower upper
#> ----------------------------------------------------------------------------------------
#> (Intercept) 27.330 8.639 3.164 0.004 9.604 45.055
#> disp 0.003 0.011 0.055 0.248 0.806 -0.019 0.025
#> hp -0.019 0.016 -0.212 -1.196 0.242 -0.051 0.013
#> wt -4.609 1.266 -0.748 -3.641 0.001 -7.206 -2.012
#> qsec 0.544 0.466 0.161 1.166 0.254 -0.413 1.501
#> ----------------------------------------------------------------------------------------Stepwise Regression
Build regression model from a set of candidate predictor variables by entering and removing predictors based on p values, in a stepwise manner until there is no variable left to enter or remove any more.
Variable Selection
# stepwise regression
model <- lm(y ~ ., data = surgical)
ols_step_both_p(model)
#>
#>
#> Stepwise Summary
#> ------------------------------------------------------------------------------
#> Step Variable AIC SBC SBIC R2 Adj. R2
#> ------------------------------------------------------------------------------
#> 0 Base Model 802.606 806.584 646.794 0.00000 0.00000
#> 1 liver_test (+) 771.875 777.842 616.009 0.45454 0.44405
#> 2 alc_heavy (+) 761.439 769.395 605.506 0.56674 0.54975
#> 3 enzyme_test (+) 750.509 760.454 595.297 0.65900 0.63854
#> 4 pindex (+) 735.715 747.649 582.943 0.75015 0.72975
#> 5 bcs (+) 730.620 744.543 579.638 0.78091 0.75808
#> ------------------------------------------------------------------------------
#>
#> Final Model Output
#> ------------------
#>
#> Model Summary
#> -------------------------------------------------------------------
#> R 0.884 RMSE 184.276
#> R-Squared 0.781 MSE 38202.426
#> Adj. R-Squared 0.758 Coef. Var 27.839
#> Pred R-Squared 0.700 AIC 730.620
#> MAE 137.656 SBC 744.543
#> -------------------------------------------------------------------
#> RMSE: Root Mean Square Error
#> MSE: Mean Square Error
#> MAE: Mean Absolute Error
#> AIC: Akaike Information Criteria
#> SBC: Schwarz Bayesian Criteria
#>
#> ANOVA
#> -----------------------------------------------------------------------
#> Sum of
#> Squares DF Mean Square F Sig.
#> -----------------------------------------------------------------------
#> Regression 6535804.090 5 1307160.818 34.217 0.0000
#> Residual 1833716.447 48 38202.426
#> Total 8369520.537 53
#> -----------------------------------------------------------------------
#>
#> Parameter Estimates
#> ------------------------------------------------------------------------------------------------
#> model Beta Std. Error Std. Beta t Sig lower upper
#> ------------------------------------------------------------------------------------------------
#> (Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
#> liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
#> alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
#> enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
#> pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
#> bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
#> ------------------------------------------------------------------------------------------------Stepwise AIC Backward Regression
Build regression model from a set of candidate predictor variables by removing predictors based on Akaike Information Criteria, in a stepwise manner until there is no variable left to remove any more.
Variable Selection
# stepwise aic backward regression
model <- lm(y ~ ., data = surgical)
k <- ols_step_backward_aic(model)
k
#>
#>
#> Stepwise Summary
#> -------------------------------------------------------------------------
#> Step Variable AIC SBC SBIC R2 Adj. R2
#> -------------------------------------------------------------------------
#> 0 Full Model 736.390 756.280 586.665 0.78184 0.74305
#> 1 alc_mod 734.407 752.308 583.884 0.78177 0.74856
#> 2 gender 732.494 748.406 581.290 0.78142 0.75351
#> 3 age 730.620 744.543 578.844 0.78091 0.75808
#> -------------------------------------------------------------------------
#>
#> Final Model Output
#> ------------------
#>
#> Model Summary
#> -------------------------------------------------------------------
#> R 0.884 RMSE 184.276
#> R-Squared 0.781 MSE 38202.426
#> Adj. R-Squared 0.758 Coef. Var 27.839
#> Pred R-Squared 0.700 AIC 730.620
#> MAE 137.656 SBC 744.543
#> -------------------------------------------------------------------
#> RMSE: Root Mean Square Error
#> MSE: Mean Square Error
#> MAE: Mean Absolute Error
#> AIC: Akaike Information Criteria
#> SBC: Schwarz Bayesian Criteria
#>
#> ANOVA
#> -----------------------------------------------------------------------
#> Sum of
#> Squares DF Mean Square F Sig.
#> -----------------------------------------------------------------------
#> Regression 6535804.090 5 1307160.818 34.217 0.0000
#> Residual 1833716.447 48 38202.426
#> Total 8369520.537 53
#> -----------------------------------------------------------------------
#>
#> Parameter Estimates
#> ------------------------------------------------------------------------------------------------
#> model Beta Std. Error Std. Beta t Sig lower upper
#> ------------------------------------------------------------------------------------------------
#> (Intercept) -1178.330 208.682 -5.647 0.000 -1597.914 -758.746
#> bcs 59.864 23.060 0.241 2.596 0.012 13.498 106.230
#> pindex 8.924 1.808 0.380 4.935 0.000 5.288 12.559
#> enzyme_test 9.748 1.656 0.521 5.887 0.000 6.419 13.077
#> liver_test 58.064 40.144 0.156 1.446 0.155 -22.652 138.779
#> alc_heavy 317.848 71.634 0.314 4.437 0.000 173.818 461.878
#> ------------------------------------------------------------------------------------------------Breusch Pagan Test
Breusch Pagan test is used to test for herteroskedasticity (non-constant error variance). It tests whether the variance of the errors from a regression is dependent on the values of the independent variables. It is a χ2 test.
model <- lm(mpg ~ disp + hp + wt + drat, data = mtcars)
ols_test_breusch_pagan(model)
#>
#> Breusch Pagan Test for Heteroskedasticity
#> -----------------------------------------
#> Ho: the variance is constant
#> Ha: the variance is not constant
#>
#> Data
#> -------------------------------
#> Response : mpg
#> Variables: fitted values of mpg
#>
#> Test Summary
#> ---------------------------
#> DF = 1
#> Chi2 = 1.429672
#> Prob > Chi2 = 0.231818Collinearity Diagnostics
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_coll_diag(model)
#> Tolerance and Variance Inflation Factor
#> ---------------------------------------
#> Variables Tolerance VIF
#> 1 disp 0.1252279 7.985439
#> 2 hp 0.1935450 5.166758
#> 3 wt 0.1445726 6.916942
#> 4 qsec 0.3191708 3.133119
#>
#>
#> Eigenvalue and Condition Index
#> ------------------------------
#> Eigenvalue Condition Index intercept disp hp wt
#> 1 4.721487187 1.000000 0.000123237 0.001132468 0.001413094 0.0005253393
#> 2 0.216562203 4.669260 0.002617424 0.036811051 0.027751289 0.0002096014
#> 3 0.050416837 9.677242 0.001656551 0.120881424 0.392366164 0.0377028008
#> 4 0.010104757 21.616057 0.025805998 0.777260487 0.059594623 0.7017528428
#> 5 0.001429017 57.480524 0.969796790 0.063914571 0.518874831 0.2598094157
#> qsec
#> 1 0.0001277169
#> 2 0.0046789491
#> 3 0.0001952599
#> 4 0.0024577686
#> 5 0.9925403056Getting Help
If you encounter a bug, please file a minimal reproducible example using reprex on github. For questions and clarifications, use StackOverflow.
Code of Conduct
Please note that the olsrr project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.