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Functional ANOVA with Random Project.

Source: R/fanova.RPm.R, R/summary.anova.R
fanova.RPm.Rd

The procedure is based on the analysis of randomly chosen one-dimensional projections. The function tests ANOVA models for functional data with continuous covariates and perform special contrasts for the factors in the formula.

Usage

fanova.RPm(
  object,
  formula,
  data.fac,
  RP = min(30, ncol(object)),
  alpha = 0.95,
  zproj = NULL,
  par.zproj = list(norm = TRUE),
  hetero = TRUE,
  pr = FALSE,
  w = rep(1, ncol(object)),
  nboot = 0,
  contrast = NULL,
  ...
)

# S3 method for class 'fanova.RPm'
summary(object, ndec = NULL, ...)

Arguments

object

Functional response data. Object with class fdata with n curves discretizated in m points. For multivariate problems object can be a data.frame or a matrix

formula

as formula without response.

data.fac

Explanatory variables. Data frame with dimension (n x p), where p are the number of factors or covariates considered.

RP

Vector of number of random projections.

alpha

Confidence level, by default alpha=0.95.

zproj

Function for generating the projections or an object that contains that projections.

par.zproj

List of parameters for zproj function.

hetero

logical. If TRUE (by default) means heteroskedastic ANOVA.

pr

logical. If TRUE prints intermediate results.

w

Vector of weights (only for multivariate problems).

nboot

Number of bootstrap samples, by default no bootstrap computations, nboot=0.

contrast

List of special contrast to be used ; by default no special contrasts are used (contrast=NULL).

...

Further arguments passed to or from other methods.

ndec

Number of decimals.

Value

An object with the following components:

  • proj: The projection value of each point on the curves. Matrix with dimensions (RP x m), where RP is the number of projections and m is the number of points observed in each projection curve.

  • mins: Minimum number for each random projection.

  • result: p-value for each random projection.

  • test.Bonf: Significance (TRUE or FALSE) for vector of random projections RP in columns and factors (and special contrasts) in rows.

  • p.Bonf: p-value for vector of random projections RP in columns and factors (and special contrasts) in rows.

  • test.fdr: False Discovery Rate (TRUE or FALSE) for vector of random projections RP in columns and factors (and special contrasts) in rows.

  • p.fdr: p-value of False Discovery Rate for vector of random projections RP in columns and factors (and special contrasts) in rows.

  • test.Boot: False Discovery Rate (TRUE or FALSE) for vector of random projections RP in columns and factors (and special contrasts) in rows.

  • p.Boot: p-value of Bootstrap sample for vector of random projections RP in columns and factors (and special contrasts) in rows.

Details

zproj allows to change the generator process of the projections. This can be done through the inclusion of a function or a collection of projections generated outside the function. By default, for a functional problem, the function rproc2fdata is used. For multivariate problems, if no function is included, the projections are generated by a normalized gaussian process of the same dimension as object. Any user function can be included with the only limitation that the two first parameters are:

  • n: number of projections

  • t: discretization points for functional problems

  • m: number of columns for multivariate problems.

That functions must return a fdata or matrix object respectively.

The function allows user-defined contrasts. The list of contrast to be used for some of the factors in the formula. Each contrast matrix in the list has r rows, where r is the number of factor levels. The user can also request special predetermined contrasts, for example using the contr.helmert, contr.sum or contr.treatment functions.

The function returns (by default) the significance of the variables using the Bonferroni test and the False Discovery Rate test. Bootstrap procedure provides more precision

Note

anova.RPm deprecated.

If hetero=TRUE then all factors must be categorical.

References

Cuesta-Albertos, J.A., Febrero-Bande, M. A simple multiway ANOVA for functional data. TEST 2010, DOI 10.1007/s11749-010-0185-3.

See also

See Also as: fanova.onefactor

Author

Juan A. Cuesta-Albertos, Manuel Febrero-Bande, Manuel Oviedo de la Fuente
manuel.oviedo@udc.es

Examples

if (FALSE) { # \dontrun{
# ex fanova.hetero
data(phoneme)
names(phoneme)
# A MV matrix obtained from functional data
data=as.data.frame(phoneme$learn$data[,c(1,seq(0,150,10)[-1])]) 
group=phoneme$classlearn
n=nrow(data)
group.rand=as.factor(sample(rep(1:3,len=n),n))
RP=c(2,5,15,30)

#ex 1: real factor and random factor
m03=data.frame(group,group.rand)
resul1=fanova.RPm(phoneme$learn,~group+group.rand,m03,RP=c(5,30))
summary(resul1)

#ex 2: real factor with special contrast
m0=data.frame(group)
cr5=contr.sum(5)   #each level vs last level
resul03c1=fanova.RPm(data,~group,m0,contrast=list(group=cr5))
summary(resul03c1)

#ex 3: random factor with special contrast. Same projs as ex 2.
m0=data.frame(group.rand)
zz=resul03c1$proj
cr3=contr.sum(3)   #each level vs last level
resul03c1=fanova.RPm(data,~group.rand,m0,contrast=list(group.rand=cr3),zproj=zz)
summary(resul03c1)
} # }