anova.RPm: Functional ANOVA with Random Project.

Description

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




# S3 method for RPm
anova(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,…)

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.

Vector of number of random projections.

alpha

Alpha value, by defalult 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

=TRUE/FALSE. TRUE (by default) means heteroskedastic ANOVA.

If TRUE, prints intermediate results.

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.

Value

An object with the following components:

proj

The projection value of each point on the curves. Matrix with dimension (RP x m), where RP is the number of projection and m are the 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 factor (and special contrast) by rows.

p.Bonf

p-value for vector of random projections RP in columns and factor (and special contrast) by rows.

test.fdr

False Discovery Rate (TRUE or FALSE) for vector of random projections RP in columns and factor (and special contrast) by rows.

p.fdr

p-value of False Discovery Rate for vector of random projections RP in columns and factor (and special contrast) by rows.

test.Boot

False Discovery Rate (TRUE or FALSE) for vector of random projections RP in columns and factor (and special contrast) by rows.

p.Boot

p-value of Bootstrap sambple for vector of random projections RP in columns and factor (and special contrast) by 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 and t,m:discretization points,number of columns, respectively for functional and 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

References

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

Examples

Run this code

# NOT RUN {
# ex anova.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=anova.RPm(phoneme$learn,~group+group.rand,m03,RP=c(5,30))
summary.anova(resul1)

#ex 2: real factor with special contrast
m0=data.frame(group)
cr5=contr.sum(5)   #each level vs last level
resul03c1=anova.RPm(data,~group,m0,contrast=list(group=cr5))
summary.anova(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=anova.RPm(data,~group.rand,m0,contrast=list(group.rand=cr3),zproj=zz)
summary.anova(resul03c1)
# }

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