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Estimation of functional regression models for partially observed bidimensional functional data

po_2d_fit.Rd

The po_2d_fit function fits functional regression models for partially observed bidimensional functional data, where each surface is only observed over part of the common domain.

Usage

po_2d_fit(formula, data, family = stats::gaussian(), offset = NULL)

Arguments

formula

a formula object with at least one ffpo_2d term.

data

a list object containing the response variable and the covariates as the components of the list.

family

a family object specifying the distribution from which the data originates. The default distribution is gaussian.

offset

an offset vector. The default value is NULL.

Value

An object of class po_2d_fit. It is a list containing the following items:

  • An item named fit of class sop. See sop.fit.

  • An item named Beta which is a list with one entry per functional term, each containing the estimated coefficient surface (beta), its standard error (se), the lower and upper pointwise confidence limits (lower, upper) and the grids (x, y).

  • An item named intercept which is the estimated intercept of the model.

  • An item named theta which is the basis coefficient vector of the estimated bidimensional functional coefficient.

  • An item named covar_theta which is the covariance matrix of the basis coefficients, used to build the pointwise confidence intervals.

  • An item named M which holds the observed domain information for each functional term.

  • An item named ffpo_2d_evals which is the result of the evaluations of the ffpo_2d terms in the formula.

See also

ffpo_2d

Examples

# PARTIALLY OBSERVED BIDIMENSIONAL FUNCTIONAL DATA EXAMPLE
# \donttest{
# set seed for reproducibility
set.seed(123)

# generate example data with partially observed surfaces
sim  <- data_generator_po_2d(n = 30, grid_x = 8, grid_y = 8)
X    <- sim$noisy_surfaces_miss
y    <- sim$response
mp   <- sim$missing_points
mpts <- sim$miss_points

# Fit the model using an 'ffpo_2d' term for the partially observed surfaces.
# 'miss_points' and 'missing_points' describe the missing observations in the
# two complementary formats expected by 'ffpo_2d'.
fit  <- po_2d_fit(
  response ~ ffpo_2d(
    X = X, miss_points = mpts, missing_points = mp, nbasis = rep(5, 4)
  ),
  data = list(response = y, X = X)
)

# Inspect the structure of the returned object
str(fit, max.level = 1)
#> List of 7
#>  $ fit          :List of 15
#>   ..- attr(*, "class")= chr "sop"
#>  $ Beta         :List of 1
#>  $ intercept    : num 5.59
#>  $ theta        : num [1:25, 1] 2.78 -5.55 -13.88 -22.21 -30.54 ...
#>  $ covar_theta  : num [1:25, 1:25] 1191.1 622.7 54.2 -514.2 -1082.6 ...
#>  $ M            :List of 1
#>  $ ffpo_2d_evals:List of 1
#>  - attr(*, "class")= chr "po_2d_fit"
#>  - attr(*, "N")= int 30

# The basis coefficients of the functional coefficient can be accessed directly
fit$theta
#>              [,1]
#>  [1,]   2.7805011
#>  [2,]  -5.5501206
#>  [3,] -13.8806992
#>  [4,] -22.2111548
#>  [5,] -30.5415919
#>  [6,]   0.2185780
#>  [7,]  -4.0049825
#>  [8,]  -8.2285046
#>  [9,] -12.4519279
#> [10,] -16.6753384
#> [11,]  -2.3433450
#> [12,]  -2.4598444
#> [13,]  -2.5763101
#> [14,]  -2.6927011
#> [15,]  -2.8090850
#> [16,]  -4.9052681
#> [17,]  -0.9147063
#> [18,]   3.0758845
#> [19,]   7.0665258
#> [20,]  11.0571685
#> [21,]  -7.4671911
#> [22,]   0.6304318
#> [23,]   8.7280791
#> [24,]  16.8257526
#> [25,]  24.9234219

# A summary of the underlying fit can be obtained using the summary function
summary(fit)
#> 
#> Family: gaussian 
#> Link function: identity 
#> 
#> 
#> Formula:
#> NULL
#> 
#> 
#> Fixed terms: 
#> [1]   5.587516 -18.085605  29.066274 -11.723970  46.274761
#> 
#> 
#> Estimated degrees of freedom:
#>       t_1       t_2 Total edf     Total 
#>         0         0         0         5 
#> 
#> R-sq.(adj) =  -0.284   Deviance explained = 11.4%  n = 30
#> 
#> Number of iterations: 1
# }