README.md
In cmlopera/olsrr: Tools for Building OLS Regression Models
olsrr
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")
Articles
- Quick
Overview
- Variable Selection
Methods
- Residual
Diagnostics
- Heteroskedasticity
- Measures of
Influence
- Collinearity
Diagnostics
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 2.622
#> R-Squared 0.835 Coef. Var 13.051
#> Adj. R-Squared 0.811 MSE 6.875
#> Pred R-Squared 0.771 MAE 1.858
#> --------------------------------------------------------------
#> RMSE: Root Mean Square Error
#> MSE: Mean Square Error
#> MAE: Mean Absolute Error
#>
#> 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 Selection Method
#> ---------------------------
#>
#> Candidate Terms:
#>
#> 1. bcs
#> 2. pindex
#> 3. enzyme_test
#> 4. liver_test
#> 5. age
#> 6. gender
#> 7. alc_mod
#> 8. alc_heavy
#>
#> We are selecting variables based on p value...
#>
#> Variables Entered/Removed:
#>
#> - liver_test added
#> - alc_heavy added
#> - enzyme_test added
#> - pindex added
#> - bcs added
#>
#> No more variables to be added/removed.
#>
#>
#> Final Model Output
#> ------------------
#>
#> Model Summary
#> -----------------------------------------------------------------
#> R 0.884 RMSE 195.454
#> R-Squared 0.781 Coef. Var 27.839
#> Adj. R-Squared 0.758 MSE 38202.426
#> Pred R-Squared 0.700 MAE 137.656
#> -----------------------------------------------------------------
#> RMSE: Root Mean Square Error
#> MSE: Mean Square Error
#> MAE: Mean Absolute Error
#>
#> 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 Selection Summary
#> ------------------------------------------------------------------------------------------
#> Added/ Adj.
#> Step Variable Removed R-Square R-Square C(p) AIC RMSE
#> ------------------------------------------------------------------------------------------
#> 1 liver_test addition 0.455 0.444 62.5120 771.8753 296.2992
#> 2 alc_heavy addition 0.567 0.550 41.3680 761.4394 266.6484
#> 3 enzyme_test addition 0.659 0.639 24.3380 750.5089 238.9145
#> 4 pindex addition 0.750 0.730 7.5370 735.7146 206.5835
#> 5 bcs addition 0.781 0.758 3.1920 730.6204 195.4544
#> ------------------------------------------------------------------------------------------
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)
#> Backward Elimination Method
#> ---------------------------
#>
#> Candidate Terms:
#>
#> 1 . bcs
#> 2 . pindex
#> 3 . enzyme_test
#> 4 . liver_test
#> 5 . age
#> 6 . gender
#> 7 . alc_mod
#> 8 . alc_heavy
#>
#>
#> Variables Removed:
#>
#> - alc_mod
#> - gender
#> - age
#>
#> No more variables to be removed.
k
#>
#>
#> Backward Elimination Summary
#> ---------------------------------------------------------------------------
#> Variable AIC RSS Sum Sq R-Sq Adj. R-Sq
#> ---------------------------------------------------------------------------
#> Full Model 736.390 1825905.713 6543614.824 0.78184 0.74305
#> alc_mod 734.407 1826477.828 6543042.709 0.78177 0.74856
#> gender 732.494 1829435.617 6540084.920 0.78142 0.75351
#> age 730.620 1833716.447 6535804.090 0.78091 0.75808
#> ---------------------------------------------------------------------------
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 (\chi^{2}) 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 = 0.231818
Collinearity Diagnostics
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_coll_diag(model)
#> Tolerance and Variance Inflation Factor
#> ---------------------------------------
#> # A tibble: 4 x 3
#> Variables Tolerance VIF
#> <chr> <dbl> <dbl>
#> 1 disp 0.125 7.99
#> 2 hp 0.194 5.17
#> 3 wt 0.145 6.92
#> 4 qsec 0.319 3.13
#>
#>
#> Eigenvalue and Condition Index
#> ------------------------------
#> Eigenvalue Condition Index intercept disp hp
#> 1 4.721487187 1.000000 0.000123237 0.001132468 0.001413094
#> 2 0.216562203 4.669260 0.002617424 0.036811051 0.027751289
#> 3 0.050416837 9.677242 0.001656551 0.120881424 0.392366164
#> 4 0.010104757 21.616057 0.025805998 0.777260487 0.059594623
#> 5 0.001429017 57.480524 0.969796790 0.063914571 0.518874831
#> wt qsec
#> 1 0.0005253393 0.0001277169
#> 2 0.0002096014 0.0046789491
#> 3 0.0377028008 0.0001952599
#> 4 0.7017528428 0.0024577686
#> 5 0.2598094157 0.9925403056
Getting 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 this project is released with a Contributor Code of
Conduct. By participating in this project you agree to
abide by its terms.
cmlopera/olsrr documentation built on May 26, 2019, 10:34 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
olsrr
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")
Articles
- Quick Overview
- Variable Selection Methods
- Residual Diagnostics
- Heteroskedasticity
- Measures of Influence
- Collinearity Diagnostics
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 2.622
#> R-Squared 0.835 Coef. Var 13.051
#> Adj. R-Squared 0.811 MSE 6.875
#> Pred R-Squared 0.771 MAE 1.858
#> --------------------------------------------------------------
#> RMSE: Root Mean Square Error
#> MSE: Mean Square Error
#> MAE: Mean Absolute Error
#>
#> 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 Selection Method
#> ---------------------------
#>
#> Candidate Terms:
#>
#> 1. bcs
#> 2. pindex
#> 3. enzyme_test
#> 4. liver_test
#> 5. age
#> 6. gender
#> 7. alc_mod
#> 8. alc_heavy
#>
#> We are selecting variables based on p value...
#>
#> Variables Entered/Removed:
#>
#> - liver_test added
#> - alc_heavy added
#> - enzyme_test added
#> - pindex added
#> - bcs added
#>
#> No more variables to be added/removed.
#>
#>
#> Final Model Output
#> ------------------
#>
#> Model Summary
#> -----------------------------------------------------------------
#> R 0.884 RMSE 195.454
#> R-Squared 0.781 Coef. Var 27.839
#> Adj. R-Squared 0.758 MSE 38202.426
#> Pred R-Squared 0.700 MAE 137.656
#> -----------------------------------------------------------------
#> RMSE: Root Mean Square Error
#> MSE: Mean Square Error
#> MAE: Mean Absolute Error
#>
#> 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 Selection Summary
#> ------------------------------------------------------------------------------------------
#> Added/ Adj.
#> Step Variable Removed R-Square R-Square C(p) AIC RMSE
#> ------------------------------------------------------------------------------------------
#> 1 liver_test addition 0.455 0.444 62.5120 771.8753 296.2992
#> 2 alc_heavy addition 0.567 0.550 41.3680 761.4394 266.6484
#> 3 enzyme_test addition 0.659 0.639 24.3380 750.5089 238.9145
#> 4 pindex addition 0.750 0.730 7.5370 735.7146 206.5835
#> 5 bcs addition 0.781 0.758 3.1920 730.6204 195.4544
#> ------------------------------------------------------------------------------------------
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)
#> Backward Elimination Method
#> ---------------------------
#>
#> Candidate Terms:
#>
#> 1 . bcs
#> 2 . pindex
#> 3 . enzyme_test
#> 4 . liver_test
#> 5 . age
#> 6 . gender
#> 7 . alc_mod
#> 8 . alc_heavy
#>
#>
#> Variables Removed:
#>
#> - alc_mod
#> - gender
#> - age
#>
#> No more variables to be removed.
k
#>
#>
#> Backward Elimination Summary
#> ---------------------------------------------------------------------------
#> Variable AIC RSS Sum Sq R-Sq Adj. R-Sq
#> ---------------------------------------------------------------------------
#> Full Model 736.390 1825905.713 6543614.824 0.78184 0.74305
#> alc_mod 734.407 1826477.828 6543042.709 0.78177 0.74856
#> gender 732.494 1829435.617 6540084.920 0.78142 0.75351
#> age 730.620 1833716.447 6535804.090 0.78091 0.75808
#> ---------------------------------------------------------------------------
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 (\chi^{2}) 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 = 0.231818
Collinearity Diagnostics
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols_coll_diag(model)
#> Tolerance and Variance Inflation Factor
#> ---------------------------------------
#> # A tibble: 4 x 3
#> Variables Tolerance VIF
#> <chr> <dbl> <dbl>
#> 1 disp 0.125 7.99
#> 2 hp 0.194 5.17
#> 3 wt 0.145 6.92
#> 4 qsec 0.319 3.13
#>
#>
#> Eigenvalue and Condition Index
#> ------------------------------
#> Eigenvalue Condition Index intercept disp hp
#> 1 4.721487187 1.000000 0.000123237 0.001132468 0.001413094
#> 2 0.216562203 4.669260 0.002617424 0.036811051 0.027751289
#> 3 0.050416837 9.677242 0.001656551 0.120881424 0.392366164
#> 4 0.010104757 21.616057 0.025805998 0.777260487 0.059594623
#> 5 0.001429017 57.480524 0.969796790 0.063914571 0.518874831
#> wt qsec
#> 1 0.0005253393 0.0001277169
#> 2 0.0002096014 0.0046789491
#> 3 0.0377028008 0.0001952599
#> 4 0.7017528428 0.0024577686
#> 5 0.2598094157 0.9925403056
Getting 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 this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.