Breusch Pagan Test

Test for constant variance. It assumes that the error terms are normally distributed.

bp_test(model, fitted.values = TRUE, rhs = FALSE, multiple = FALSE,
  p.adj = c("none", "bonferroni", "sidak", "holm"), vars = NA)

Arguments

model

an object of class lm

fitted.values

logical; if TRUE, use fitted values of regression model

rhs

logical; if TRUE, specifies that tests for heteroskedasticity be performed for the right-hand-side (explanatory) variables of the fitted regression model

multiple

logical; if TRUE, specifies that multiple testing be performed

p.adj

p value adjustment, following options are available: bonferroni, holm, sidak and none

vars

variables to be used for for heteroskedasticity test

Value

bp_test returns an object of class "bp_test". An object of class "bp_test" is a list containing the following components:

References

T.S. Breusch & A.R. Pagan (1979), A Simple Test for Heteroscedasticity and Random Coefficient Variation. Econometrica 47, 1287�1294

Cook, R. D.; Weisberg, S. (1983). "Diagnostics for Heteroskedasticity in Regression". Biometrika. 70 (1): 1�10.

Examples

# Use fitted values of the model
model <- lm(mpg ~ disp + hp + wt + drat, data = mtcars)
bp_test(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          =    1.4297 
#>  Prob > Chi2   =    0.2318 

# Use independent variables of the model
model <- lm(mpg ~ disp + hp + wt + drat, data = mtcars)
bp_test(model, rhs = TRUE)
#> 
#>  Breusch Pagan Test for Heteroskedasticity
#>  -----------------------------------------
#>  Ho: the variance is constant            
#>  Ha: the variance is not constant        
#> 
#>            Data            
#>  --------------------------
#>  Response : mpg 
#>  Variables: disp hp wt drat 
#> 
#>       Test Summary        
#>  -------------------------
#>  DF            =    4 
#>  Chi2          =    1.5138 
#>  Prob > Chi2   =    0.8242 

# Use independent variables of the model and perform multiple tests
model <- lm(mpg ~ disp + hp + wt + drat, data = mtcars)
bp_test(model, rhs = TRUE, multiple = TRUE)
#> 
#>  Breusch Pagan Test for Heteroskedasticity
#>  -----------------------------------------
#>  Ho: the variance is constant            
#>  Ha: the variance is not constant        
#> 
#>            Data            
#>  --------------------------
#>  Response : mpg 
#>  Variables: disp hp wt drat 
#> 
#>      Test Summary (Unadjusted p values)    
#>  ----------------------------------------
#>   Variable          chi2     df      p    
#>  ----------------------------------------
#>   disp             1.2355     1    0.2663 
#>   hp               0.9210     1    0.3372 
#>   wt               1.2530     1    0.2630 
#>   drat             1.1668     1    0.2800 
#>  ----------------------------------------
#>   simultaneous     1.5138     4    0.8242 
#>  ----------------------------------------

# Bonferroni p value Adjustment
model <- lm(mpg ~ disp + hp + wt + drat, data = mtcars)
bp_test(model, rhs = TRUE, multiple = TRUE, p.adj = 'bonferroni')
#> 
#>  Breusch Pagan Test for Heteroskedasticity
#>  -----------------------------------------
#>  Ho: the variance is constant            
#>  Ha: the variance is not constant        
#> 
#>            Data            
#>  --------------------------
#>  Response : mpg 
#>  Variables: disp hp wt drat 
#> 
#>      Test Summary (Bonferroni p values)    
#>  ----------------------------------------
#>   Variable          chi2     df      p    
#>  ----------------------------------------
#>   disp             1.2355     1    1.0000 
#>   hp               0.9210     1    1.0000 
#>   wt               1.2530     1    1.0000 
#>   drat             1.1668     1    1.0000 
#>  ----------------------------------------
#>   simultaneous     1.5138     4    0.8242 
#>  ----------------------------------------

# Sidak p value Adjustment
model <- lm(mpg ~ disp + hp + wt + drat, data = mtcars)
bp_test(model, rhs = TRUE, multiple = TRUE, p.adj = 'sidak')
#> 
#>  Breusch Pagan Test for Heteroskedasticity
#>  -----------------------------------------
#>  Ho: the variance is constant            
#>  Ha: the variance is not constant        
#> 
#>            Data            
#>  --------------------------
#>  Response : mpg 
#>  Variables: disp hp wt drat 
#> 
#>        Test Summary (Sidak p values)       
#>  ----------------------------------------
#>   Variable          chi2     df      p    
#>  ----------------------------------------
#>   disp             1.2355     1    0.7103 
#>   hp               0.9210     1    0.8070 
#>   wt               1.2530     1    0.7049 
#>   drat             1.1668     1    0.7313 
#>  ----------------------------------------
#>   simultaneous     1.5138     4    0.8242 
#>  ----------------------------------------

# Holm's p value Adjustment
model <- lm(mpg ~ disp + hp + wt + drat, data = mtcars)
bp_test(model, rhs = TRUE, multiple = TRUE, p.adj = 'holm')
#> 
#>  Breusch Pagan Test for Heteroskedasticity
#>  -----------------------------------------
#>  Ho: the variance is constant            
#>  Ha: the variance is not constant        
#> 
#>            Data            
#>  --------------------------
#>  Response : mpg 
#>  Variables: disp hp wt drat 
#> 
#>        Test Summary (Holm's p values)      
#>  ----------------------------------------
#>   Variable          chi2     df      p    
#>  ----------------------------------------
#>   disp             1.2355     1    0.7990 
#>   hp               0.9210     1    0.3372 
#>   wt               1.2530     1    1.0000 
#>   drat             1.1668     1    0.5601 
#>  ----------------------------------------
#>   simultaneous     1.5138     4    0.8242 
#>  ----------------------------------------