| boxcoxfr {AID} | R Documentation |
Box-Cox Transformation for One-Way ANOVA
Description
boxcoxfr performs Box-Cox transformation for one-way ANOVA. It is useful to use if the normality or/and the homogenity of variance is/are not satisfied while comparing two or more groups.
Usage
boxcoxfr(y, x, option = "both", lambda = seq(-3, 3, 0.01), lambda2 = NULL,
tau = 0.05, alpha = 0.05, verbose = TRUE)Arguments
y |
a numeric vector of data values. |
x |
a vector or factor object which gives the group for the corresponding elements of y. |
option |
a character string to select the desired option for the objective of transformation. "nor" and "var" are the options which search for a transformation to satisfy the normality of groups and the homogenity of variances, respectively. "both" is the option which searches for a transformation to satisfy both the normality of groups and the homogenity of variances. Default is set to "both". |
lambda |
a vector which includes the sequence of feasible lambda values. Default is set to (-3, 3) with increment 0.01. |
lambda2 |
a numeric for an additional shifting parameter. Default is set to lambda2 = 0. |
tau |
the feasible region parameter for the construction of feasible region. Default is set to 0.05. If tau = 0, it returns the MLE of transformation parameter. |
alpha |
the level of significance to check the normality and variance homogenity after transformation. Default is set to alpha = 0.05. |
verbose |
a logical for printing output to R console. |
Details
Denote y the variable at the original scale and y' the transformed variable. The Box-Cox power transformation is defined by:
y' = \left\{ \begin{array}{ll}
\frac{y^\lambda - 1}{\lambda} \mbox{ , if $\lambda \neq 0$} \cr
log(y) \mbox{ , if $\lambda = 0$}
\end{array} \right.
If the data include any nonpositive observations, a shifting parameter \lambda_2 can be included in the transformation given by:
y' = \left\{ \begin{array}{ll}
\frac{(y + \lambda_2)^\lambda - 1}{\lambda} \mbox{ , if $\lambda \neq 0$} \cr
log(y + \lambda_2) \mbox{ , if $\lambda = 0$}
\end{array} \right.
Maximum likelihood estimation in feasible region (MLEFR) is used while estimating transformation parameter. MLEFR maximizes the likehood function in feasible region constructed by Shapiro-Wilk test and Bartlett's test. After transformation, normality of the data in each group and homogeneity of variance are assessed by Shapiro-Wilk test and Bartlett's test, respectively.
Value
A list with class "boxcoxfr" containing the following elements:
method |
method applied in the algorithm |
lambda.hat |
the estimated lambda |
lambda2 |
additional shifting parameter |
shapiro |
a data frame which gives the test results for the normality of groups via Shapiro-Wilk test |
bartlett |
a matrix which returns the test result for the homogenity of variance via Bartlett's test |
alpha |
the level of significance to assess the assumptions. |
tf.data |
transformed data set |
x |
a factor object which gives the group for the corresponding elements of y |
y.name |
variable name of y |
x.name |
variable name of x |
Author(s)
Osman Dag, Ozlem Ilk
References
Dag, O., Ilk, O. (2017). An Algorithm for Estimating Box-Cox Transformation Parameter in ANOVA. Communications in Statistics - Simulation and Computation, 46:8, 6424–6435.
Examples
######
# Communication between AID and onewaytests packages
library(AID)
library(onewaytests)
# Average Annual Daily Traffic Data (AID)
data(AADT)
# to obtain descriptive statistics by groups (onewaytests)
describe(aadt ~ class, data = AADT)
# to check normality of data in each group (onewaytests)
nor.test(aadt ~ class, data = AADT)
# to check variance homogeneity (onewaytests)
homog.test(aadt ~ class, data = AADT, method = "Bartlett")
# to apply Box-Cox transformation (AID)
out <- boxcoxfr(AADT$aadt, AADT$class)
# to obtain transformed data
AADT$tf.aadt <- out$tf.data
# to conduct one-way ANOVA with transformed data (onewaytests)
result<-aov.test(tf.aadt ~ class, data = AADT)
# to make pairwise comparison (onewaytests)
paircomp(result)
# to convert the statistics into the original scale (AID)
confInt(out, level = 0.95)
######
library(AID)
data <- rnorm(120, 10, 1)
factor <- rep(c("X", "Y", "Z"), each = 40)
out <- boxcoxfr(data, factor, lambda = seq(-5, 5, 0.01), tau = 0.01, alpha = 0.01)
confInt(out, level = 0.95)
######