Test for constant variance. It assumes that the error terms are normally distributed.
ols_bp_test(model, fitted.values = TRUE, rhs = FALSE, multiple = FALSE, p.adj = c("none", "bonferroni", "sidak", "holm"), vars = NA)
| model | An object of class |
|---|---|
| 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 | Adjustment for p value, the following options are available: bonferroni, holm, sidak and none. |
| vars | Variables to be used for heteroskedasticity test. |
ols_bp_test returns an object of class "ols_bp_test".
An object of class "ols_bp_test" is a list containing the
following components:
breusch pagan statistic
p-value of bp
fitted values of the regression model
names of explanatory variables of fitted regression model
logical value indicating if multiple tests should be performed
adjusted p values
variables to be used for heteroskedasticity test
response variable
predictors
Breusch Pagan Test was introduced by Trevor Breusch and Adrian Pagan in 1979. It is used to test for heteroskedasticity in a linear regression model. It test whether variance of errors from a regression is dependent on the values of a independent variable.
Null Hypothesis: Equal/constant variances
Alternative Hypothesis: Unequal/non-constant variances
Computation
Fit a regression model
Regress the squared residuals from the above model on the independent variables
Compute nR2. It follows a chi square distribution with p -1 degrees of freedom, where p is the number of independent variables, n is the sample size and R2 is the coefficient of determination from the regression in step 2.
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.
Other heteroskedasticity tests: ols_f_test,
ols_score_test,
ols_test_bartlett
# model model <- lm(mpg ~ disp + hp + wt + drat, data = mtcars) # use fitted values of the model ols_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 = 1.429672 #> Prob > Chi2 = 0.231818# use independent variables of the model ols_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 = 1.513808 #> Prob > Chi2 = 0.8241927# use independent variables of the model and perform multiple tests ols_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 1.2355345 1 0.2663334 #> hp 0.9209878 1 0.3372157 #> wt 1.2529988 1 0.2629805 #> drat 1.1668486 1 0.2800497 #> ---------------------------------------------- #> simultaneous 1.5138083 4 0.8241927 #> ----------------------------------------------# bonferroni p value adjustment ols_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 1.2355345 1 1.0000000 #> hp 0.9209878 1 1.0000000 #> wt 1.2529988 1 1.0000000 #> drat 1.1668486 1 1.0000000 #> ---------------------------------------------- #> simultaneous 1.5138083 4 0.8241927 #> ----------------------------------------------# sidak p value adjustment ols_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 1.2355345 1 0.7102690 #> hp 0.9209878 1 0.8070305 #> wt 1.2529988 1 0.7049362 #> drat 1.1668486 1 0.7313356 #> ---------------------------------------------- #> simultaneous 1.5138083 4 0.8241927 #> ----------------------------------------------# holm's p value adjustment ols_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 1.2355345 1 0.7990002 #> hp 0.9209878 1 0.3372157 #> wt 1.2529988 1 1.0000000 #> drat 1.1668486 1 0.5600994 #> ---------------------------------------------- #> simultaneous 1.5138083 4 0.8241927 #> ----------------------------------------------