Functional data analysis — morie_functional

Regression with a functional predictor: basis expansion of the curves, the resulting scalar design, the fitted coefficient function, and BIC and leave-one-out criteria for choosing the basis size.

Usage

morie_fda_design(t, X_curves, L1 = 3, L2 = 5, kind = "fourier") 

morie_fda_fit(t, X_curves, y, L1 = 3, L2 = 5, kind = "fourier") 

morie_fda_beta_function(t, beta_coefs, L1, kind = "fourier") 

morie_fda_bic(loglik, n_params, n_obs) 

morie_fda_loocv(t, x_t, L2, kind = "fourier")

Arguments

t: numeric grid of observation points
X_curves: matrix or list of observed curves, one per subject
y: numeric response, one value per curve
L1: number of coefficient-function basis terms
L2: number of curve basis terms
kind: basis kind, "fourier" or "poly"
beta_coefs: basis coefficients from [morie_fda_fit()]
loglik: maximised log-likelihood
n_params: number of estimated parameters
n_obs: number of observations
x_t: observed curve values

Value

A list holding the fitted quantities for the method called: point estimates, fitted values and any diagnostics it produces. See the individual method descriptions above for the components each returns.

Details

These functions mirror, in R, the implementations in the Python package morie; the two are checked against each other by the parity tests in tests/testthat/.

Examples

set.seed(10)
tt <- seq(0, 1, length.out = 30)
Xc <- rbind(sin(2 * pi * tt), cos(2 * pi * tt), sin(4 * pi * tt))
morie_fda_design(tt, Xc, L1 = 2, L2 = 3)
#> $X_star
#>      [,1]          [,2]         [,3]
#> [1,]    1  5.430670e-17  5.00000e-01
#> [2,]    1 -5.679774e-17  1.12262e-17
#> [3,]    1 -2.267104e-17 -3.44552e-17
#> 
#> $X
#>               [,1]         [,2]
#> [1,]  5.430670e-17  5.00000e-01
#> [2,] -5.679774e-17  1.12262e-17
#> [3,] -2.267104e-17 -3.44552e-17
#> 
#> $C
#>               [,1]          [,2]          [,3]
#> [1,]  5.240935e-17  1.000000e+00 -2.283911e-17
#> [2,]  3.700743e-18 -9.314716e-18  1.000000e+00
#> [3,] -2.267104e-17 -6.891039e-17  6.950858e-17
#> 
#> $Q
#>              [,1]         [,2]          [,3]
#> [1,] 1.000000e+00 1.897354e-18 -6.049848e-17
#> [2,] 1.897354e-18 5.000000e-01  1.588356e-17
#> 
#> $Psi
#>       [,1]          [,2]        [,3]
#>  [1,]    1  0.000000e+00  1.00000000
#>  [2,]    1  2.149704e-01  0.97662056
#>  [3,]    1  4.198891e-01  0.90757542
#>  [4,]    1  6.051742e-01  0.79609307
#>  [5,]    1  7.621621e-01  0.64738628
#>  [6,]    1  8.835120e-01  0.46840844
#>  [7,]    1  9.635500e-01  0.26752834
#>  [8,]    1  9.985334e-01  0.05413891
#>  [9,]    1  9.868265e-01 -0.16178200
#> [10,]    1  9.289767e-01 -0.37013816
#> [11,]    1  8.276890e-01 -0.56118707
#> [12,]    1  6.876995e-01 -0.72599549
#> [13,]    1  5.155539e-01 -0.85685718
#> [14,]    1  3.193015e-01 -0.94765317
#> [15,]    1  1.081190e-01 -0.99413796
#> [16,]    1 -1.081190e-01 -0.99413796
#> [17,]    1 -3.193015e-01 -0.94765317
#> [18,]    1 -5.155539e-01 -0.85685718
#> [19,]    1 -6.876995e-01 -0.72599549
#> [20,]    1 -8.276890e-01 -0.56118707
#> [21,]    1 -9.289767e-01 -0.37013816
#> [22,]    1 -9.868265e-01 -0.16178200
#> [23,]    1 -9.985334e-01  0.05413891
#> [24,]    1 -9.635500e-01  0.26752834
#> [25,]    1 -8.835120e-01  0.46840844
#> [26,]    1 -7.621621e-01  0.64738628
#> [27,]    1 -6.051742e-01  0.79609307
#> [28,]    1 -4.198891e-01  0.90757542
#> [29,]    1 -2.149704e-01  0.97662056
#> [30,]    1 -2.449294e-16  1.00000000
#>