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Functional random-intercept (multilevel) model for waveforms

Source: R/stats-functional-mixed.R
functionalMixedModel.Rd

Fits the subject random-intercept model to a set of curves nested in subjects. It splits the pointwise variance into between- and within-subject components (a functional ICC curve) and, when group is given, tests the between-subject fixed effect on the subject-mean curves so strides are not treated as independent.

Usage

functionalMixedModel(
  curves,
  subject,
  group = NULL,
  n_perm = 1000L,
  seed = NULL
)

Arguments

curves

An N x P matrix of curves: N observations (e.g. strides pooled over subjects), P domain points.

subject

Length-N grouping identifying the random-intercept level (the subject each curve belongs to).

group

Optional between-subject fixed effect (length N), constant within each subject (e.g. a patient/control label).

n_perm

Permutations for the curve-wide fixed-effect p-value (default 1000; 0 to skip).

seed

Optional RNG seed for the permutation test.

Value

a functional_mixed object: mean_curve, var_between, var_within, icc (functional ICC curve), subject_means (one row per subject), n_subjects, and – when group is given – f_curve, p_pointwise, p_global (subject-level fixed-effect test) plus group_diff (the signed difference curve for two groups).

References

Morris JS (2015) Functional regression, Annu Rev Stat Appl; Pini & Vantini (2017) interval-wise testing.

See also

functionalRegression(), spmTTest()

Examples

set.seed(1)
P <- 101; t <- seq(0, 1, length.out = P)
make <- function(off) t(sapply(1:12, function(k) off + sin(2 * pi * t) + rnorm(P, 0, 0.1)))
ctrl <- do.call(rbind, lapply(rnorm(6, 0, 0.5), make))
pat  <- do.call(rbind, lapply(rnorm(6, 1.0, 0.5), make))   # shifted group
Y <- rbind(ctrl, pat)
subj <- rep(1:12, each = 12); grp <- rep(c("ctrl", "pat"), each = 72)
fm <- functionalMixedModel(Y, subj, grp, n_perm = 200)
fm$p_global                         # group difference, subject-level correct
#> [1] 0.0199005