FANOVA {FuzzySTs}

Computes a FANOVA model by a convenient metric, an exact calculation or an approximation

Description

Computes a FANOVA model by a convenient metric, an exact calculation or an approximation

Usage

FANOVA(
  formula,
  dataset,
  data.fuzzified,
  sig,
  method,
  distance.type = "DSGD",
  i = 1,
  j = 1,
  theta = 1/3,
  thetas = 1,
  p = 2,
  q = 0.5,
  breakpoints = 100,
  int.method = "int.simpson",
  plot = TRUE
)

Arguments

formula

a description of the model to be fitted.

dataset

the data frame containing all the variables of the model.

data.fuzzified

the fuzzified data set constructed by a call to the function FUZZ or the function GFUZZ, or a similar matrix.

sig

a numerical value representing the significance level of the test.

method

the choices are the following: "distance", "exact", "approximation".

distance.type

type of distance chosen from the family of distances. The different choices are given by: "Rho1", "Rho2", "Bertoluzza", "Rhop", "Delta.pq", "Mid/Spr", "wabl", "DSGD", "DSGD.G", "GSGD".

i

parameter of the density function of the Beta distribution, fixed by default to i = 1.

j

parameter of the density function of the Beta distribution, fixed by default to j = 1.

theta

a numerical value between 0 and 1, representing a weighting parameter. By default, theta is fixed to 1/3 referring to the Lebesgue space. This measure is used in the calculations of the following distances: d_Bertoluzza, d_mid/spr and d_phi-wabl/ldev/rdev.

thetas

a decimal value between 0 and 1, representing the weight given to the shape of the fuzzy number. By default, thetas is fixed to 1. This parameter is used in the calculations of the d_theta star and the d_GSGD distances.

p

a positive integer such that 1 \le p < infinity, referring to the parameter of the Rho_p and Delta_pq. By default, p is fixed to 2.

q

a decimal value between 0 and 1, referring to the parameter of the metric Delta_pq. By default, p is fixed to 0.5.

breakpoints

a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default.

int.method

the method of numerical integration. It is set by default to the Simpson method, i.e. int.method="int.simpson".

plot

fixed by default to "TRUE". plot="FALSE" if a plot of the fuzzy number is not required.

Value

Returns a list of all the arguments of the function, the total, treatment and residuals sums of squares, the coefficients of the model, the test statistics with the corresponding p-values, and the decision made.

Examples

mat <- matrix(c(1,1,1,1,1,1,1,2,2,2,2,3,2,3,4,2,3,3,2,4), ncol = 2)
data <- data.frame(mat)
data$X1 <- factor(data$X1)
MF121 <- TrapezoidalFuzzyNumber(0,1,1,2.2)
MF122 <- TrapezoidalFuzzyNumber(1.8,1.9,2.2,2.8)
MF123 <- TrapezoidalFuzzyNumber(1.9,2.3,3.1,3.3)
MF124 <- TrapezoidalFuzzyNumber(3.1,3.4,4.1,4.2)
PA12 <- c(1,2,3,4)
data.fuzzified <- GFUZZ(data, 1, 2, PA12, "Identical")
formula = X2 ~ X1
res <- FANOVA(formula, dataset = data, method ="distance", data.fuzzified = data.fuzzified, 
sig = 0.05, distance.type = "wabl")