# cor.fd: Correlation matrix from functional data object(s) In fda: Functional Data Analysis

 cor.fd R Documentation

## Correlation matrix from functional data object(s)

### Description

Compute a correlation matrix for one or two functional data objects.

### Usage

```cor.fd(evalarg1, fdobj1, evalarg2=evalarg1, fdobj2=fdobj1)
```

### Arguments

 `evalarg1` a vector of argument values for fdobj1. `evalarg2` a vector of argument values for fdobj2. `fdobj1, fdobj2` functional data objects

### Details

1. var1 <- var.fd(fdobj1)

2. evalVar1 <- eval.bifd(evalarg1, evalarg1, var1)

3. if(missing(fdobj2)) Convert evalVar1 to correlations

4. else:

4.1. var2 <- var.fd(fdobj2)

4.2. evalVar2 <- eval.bifd(evalarg2, evalarg2, var2)

4.3. var12 <- var.df(fdobj1, fdobj2)

4.4. evalVar12 <- eval.bifd(evalarg1, evalarg2, var12)

4.5. Convert evalVar12 to correlations

### Value

A matrix or array:

With one or two functional data objects, fdobj1 and possibly fdobj2, the value is a matrix of dimensions length(evalarg1) by length(evalarg2) giving the correlations at those points of fdobj1 if missing(fdobj2) or of correlations between eval.fd(evalarg1, fdobj1) and eval.fd(evalarg2, fdobj2).

With a single multivariate data object with k variables, the value is a 4-dimensional array of dim = c(nPts, nPts, 1, choose(k+1, 2)), where nPts = length(evalarg1).

`mean.fd`, `sd.fd`, `std.fd` `stdev.fd` `var.fd`

### Examples

```daybasis3 <- create.fourier.basis(c(0, 365))
daybasis5 <- create.fourier.basis(c(0, 365), 5)
tempfd3 <- with(CanadianWeather, smooth.basis(
day.5, dailyAv[,,"Temperature.C"],
daybasis3, fdnames=list("Day", "Station", "Deg C"))\$fd )
precfd5 <- with(CanadianWeather, smooth.basis(
day.5, dailyAv[,,"log10precip"],
daybasis5, fdnames=list("Day", "Station", "Deg C"))\$fd )

# Correlation matrix for a single functional data object
(tempCor3 <- cor.fd(seq(0, 356, length=4), tempfd3))

# Cross correlation matrix between two functional data objects
# Compare with structure described above under 'value':
(tempPrecCor3.5 <- cor.fd(seq(0, 365, length=4), tempfd3,
seq(0, 356, length=6), precfd5))

# The following produces contour and perspective plots

daybasis65 <- create.fourier.basis(rangeval=c(0, 365), nbasis=65)
daytempfd <- with(CanadianWeather, smooth.basis(
day.5, dailyAv[,,"Temperature.C"],
daybasis65, fdnames=list("Day", "Station", "Deg C"))\$fd )
dayprecfd <- with(CanadianWeather, smooth.basis(
day.5, dailyAv[,,"log10precip"],
daybasis65, fdnames=list("Day", "Station", "log10(mm)"))\$fd )

str(tempPrecCor <- cor.fd(weeks, daytempfd, weeks, dayprecfd))
# dim(tempPrecCor)= c(53, 53)

op <- par(mfrow=c(1,2), pty="s")
contour(weeks, weeks, tempPrecCor,
xlab="Average Daily Temperature",
ylab="Average Daily log10(precipitation)",
main=paste("Correlation function across locations\n",
"for Canadian Anual Temperature Cycle"),
cex.main=0.8, axes=FALSE)
axisIntervals(1, atTick1=seq(0, 365, length=5), atTick2=NA,
atLabels=seq(1/8, 1, 1/4)*365,
labels=paste("Q", 1:4) )
axisIntervals(2, atTick1=seq(0, 365, length=5), atTick2=NA,
atLabels=seq(1/8, 1, 1/4)*365,
labels=paste("Q", 1:4) )
persp(weeks, weeks, tempPrecCor,
xlab="Days", ylab="Days", zlab="Correlation")
mtext("Temperature-Precipitation Correlations", line=-4, outer=TRUE)
par(op)

# Correlations and cross correlations
# in a bivariate functional data object
gaittime   <- (1:20)/21
gaitbasis5 <- create.fourier.basis(c(0,1),nbasis=5)
gaitfd5    <- smooth.basis(gaittime, gait, gaitbasis5)\$fd

gait.t3 <- (0:2)/2
(gaitCor3.5 <- cor.fd(gait.t3, gaitfd5))
# Check the answers with manual computations
gait3.5 <- eval.fd(gait.t3, gaitfd5)
all.equal(cor(t(gait3.5[,,1])), gaitCor3.5[,,,1])
# TRUE
all.equal(cor(t(gait3.5[,,2])), gaitCor3.5[,,,3])
# TRUE
all.equal(cor(t(gait3.5[,,2]), t(gait3.5[,,1])),
gaitCor3.5[,,,2])
# TRUE

# NOTE:
dimnames(gaitCor3.5)[[4]]
# [1] Hip-Hip
# [2] Knee-Hip
# [3] Knee-Knee
# If [2] were "Hip-Knee", then
# gaitCor3.5[,,,2] would match
# cor(t(gait3.5[,,1]), t(gait3.5[,,2]))
# *** It does NOT.  Instead, it matches:
# cor(t(gait3.5[,,2]), t(gait3.5[,,1]))

```

fda documentation built on April 27, 2022, 1:07 a.m.