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MFQPCA (Multilevel Functional Quantile Principal Component Analysis)

Source: R/mfqpca.R
mfqpca.Rd

Solves the multilevel functional quantile principal component analysis methodology

Usage

mfqpca(
  data,
  group,
  colname = NULL,
  npc.between = 2,
  npc.within = 2,
  quantile.value = 0.5,
  periodic = TRUE,
  splines.df = 10,
  splines.method = "conquer",
  tol = 0.01,
  max.iters = 10,
  verbose = FALSE,
  seed = NULL
)

Arguments

data

An \((N \times T)\) matrix, a tf object from the tidyfun package or a data.frame containing the functional data as a tf column.

group

Either a string or an array. If it is a string, it must point to the grouping variable in data only if data is a dataframe. If an array, it must be the N dimensional array indicating the hierarchical structure of the data. Elements in the array with the same value indicate they are repeated measures of the same individual.

colname

The name of the column containing the functional data. Use only if data is a dataframe and colname is a column in the dataframe.

npc.between

The number of estimated between level components.

npc.within

The number of estimated within level components.

quantile.value

The quantile considered.

periodic

Boolean indicating if the data is expected to be periodic (start coincides with end) or not.

splines.df

Degrees of freedom for the splines.

splines.method

Method used in the resolution of the splines quantile regression model. It currently accepts the methods c('conquer', 'quantreg').

tol

Tolerance on the convergence of the algorithm.

max.iters

Maximum number of iterations.

verbose

Boolean indicating the verbosity.

seed

Seed for the random generator number.

Value

mfqpca_object

Examples


n.individuals <- 20
n.repeated <- 10
n.time = 144
N <- n.repeated * n.individuals

group <- rep(1:n.individuals, each=n.repeated)

# Define score values using a normal distribution
c1.vals <- rnorm(n.individuals)
c1.vals <- c1.vals[match(group, unique(group))]
c2.vals <- rnorm(N)

# Define principal components
pcb <- sin(seq(0, 2*pi, length.out = n.time))
pcw <- cos(seq(0, 2*pi, length.out = n.time))

# Generate a data matrix and add missing observations
Y <- c1.vals * matrix(pcb, nrow = N, ncol=n.time, byrow = TRUE) +
c2.vals * matrix(pcw, nrow = N, ncol=n.time, byrow = TRUE)

# Add noise
Y <- Y + matrix(rnorm(N*n.time, 0, 0.4), nrow = N)
Y[sample(N*n.time, as.integer(0.2*N))] <- NA

results <- mfqpca(data = Y, group = group, npc.between = 1, npc.within=1, quantile.value = 0.5)