MRIaggr (version 1.1.5)

simul_fMM: Simulation under the mixture model

Description

Simulation of a sample following a distribution issue from a non-spatial mixture model.

Usage

simul_fMM(n, G, Ydist="gaussian", Y_mu, Y_sd, nclass = "auto",
    beta=FALSE, Xdist=NULL, X_mu=NULL, X_sd=NULL,
    n.Id=NULL, Id_sd=NULL, noise_sd=NULL,
    display_Y=TRUE, display_X=TRUE, window=FALSE,
	filename="calc-echantillon", width=1000, height=700, path=NULL, unit="px", res=NA)

Arguments

n

The number of observation to simulate. interger.

G

The number of groups to be considered for the mixture. integer.

Ydist

The distribution of the observations. character vector[G]. Must contains only : "unif", "unif_segment", "gaussian", "Gamma" or "Beta".

Y_mu

The expected value of each group. numeric vector[G].

Y_sd

The standard deviation of each group. numeric vector[G].

nclass

The number of observation by class for the histogram. integer.

beta

Should a concomitant model be considered ? logical.

Xdist

The distribution of the concomitant variable. character vector[G]. Must contains only : "unif", "gaussian", "Gamma".

X_mu

The expected value of the concomitant varible for each group. numeric vector[G].

n.Id

The number of patient to be considered. numeric.

Id_sd

The standard deviation of the random effect. numeric.

X_sd

The standard deviation of the concomitant varible for each group. numeric vector[G].

noise_sd

The standard deviation of the noise. numeric. NULL indicates no noise.

display_Y

Should the graphics representing the Y distribution be displayed. logical.

display_X

Should the graphics representing the X distribution be displayed. logical.

window

Display the graphics in the current graphics device (F), in a new device (T), save it in a png/eps/svg file ("png" / "esp" / "png"). NULL indicates no display.

filename

Name of the file (without the extension) where the plot should be saved. character. Ignored if window is not png/eps/svg.

width

the width of the device. numeric. Ignored if window is not png/eps/svg.

height

the width of the device. numeric. Ignored if window is not png/eps/svg.

path

the directory where the plot file will be created. character. Default is NULL corresponding to the current working directory.

unit

the units in which height and width are given. Can be "px", "in", "cm" or "mm". Default is "px".

res

the nominal resolution in ppi which will be recorded in the bitmap file, if a positive integer. numeric. Default is NA.

Value

• A list containing :
• Y
  a vector containing the simulated response variables.
• X
  a vector containing the simulated concomitant variables.
• moy
  a numeric containing the empirical mean of the response variable.
• var
  a numeric containing the empirical standard deviation of the response variable.
• Y_g
  a list containing the simulated response variables for each group.
• X_g
  a list containing the simulated concomitant variables for each group.
• moy_g
  a vector containing the empirical mean of the response variable for each group.
• var_g
  a vector containing the empirical standard deviation of the response variable for each group.
• Ydist
  a list containing the family used to simulate the response variables.
• Y_mu
  a vector containing the simulated mean of the response variable for each group (without possible addition of noise).
• Y_sd
  a vector containing the simulated standard deviation of the response variable for each group (without possible addition of noise).
• beta
  a vector containing the theorical parameters of the concomitant model for each group.
• Xdist
  a vector containing the family used to simulate the concomitant variables.
• X_mu
  a vector containing the empirical expected value of the concomitant variable for each group.
• X_sd
  a vector containing the empirical standard deviation of the concomitant variable for each group.
• group
  a matrix indicating the group membership of the observations.
• prior
  a matrix indicating the prior probabilities associated to the concomitant model.

Examples

# settings 
G <- 3 # nb of groups
n_px <- 30 # width of the area
n <- (n_px*G)^2 # total number of pixel
mu <- c(-3,0,4) # mean values of the groups
sigma <- c(sqrt(3),1,sqrt(3)) # sd values of the groups
Ydist <- c("gaussian","gaussian","gaussian") # distribution of the groups

# simulation 
set.seed(10)
simulation <- simul_fMM(n=rep(n/3,G),
                          G=G,                          
                          Ydist=Ydist,
                          Y_mu=mu,
                          Y_sd=sigma,
                          display_Y=TRUE)
                          
if(try(require(fields))){
image.plot(x=1:sqrt(n),y=1:sqrt(n),xlab="",ylab="",axes=FALSE,
           z=matrix(simulation$Y,sqrt(n),sqrt(n)),
           main="Groups")
}