# fanova.RPm: Functional ANOVA with Random Project. In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 fanova.RPm R Documentation

## 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

```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` codelogical. 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.

### 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

### 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.

### Note

anova.RPm deprecated.

If `hetero=TRUE` then all factors must be categorical.

### Author(s)

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

### 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 as: `fanova.onefactor`

### Examples

```## Not run:
# 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)

## End(Not run)

```

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.