inferenceDataObject-class {fdaPDE}

Class for inference data

Description

A class that contains all possible information for inference over linear parameters and/or nonparametric field in spatial regression with differential regularization problem. This object can be used as parameter in smoothing function of the fdaPDE library smooth.FEM.

Details

At least one between test and interval must be nonzero. n_cov, coeff and beta0, if provided, need to be coherent. dim and locations, if provided, need to be coherent. The usage of inferenceDataObjectBuilder is recommended for the construction of an object of this class.

Slots

test

A vector of integers taking value 0, 1 or 2; if 0 no test is performed, if 1 one-at-the-time tests are performed, if 2 a simultaneous test is performed.

interval

A vector of integers taking value 0, 1, 2 or 3; if 0 no confidence interval is computed, if 1 one-at-the-time confidence intervals are computed, if 2 simultaneous confidence intervals are computed, if 3 Bonferroni confidence intervals are computed.

type

A vector of integers taking value 1, 2, 3, 4 or 5 corresponding to Wald, Speckman, Eigen-Sign-Flip, Enhanced-Eigen-Sign-Flip or Sign-Flip inferential approach.

component

A vector of integers taking value 1, 2 or 3, indicating whether the inferential analysis should be carried out respectively for the parametric, nonparametric or both the components.

exact

An integer taking value 1 or 2. If 1 an exact computation of the test statistics will be performed, whereas if 2 an approximated computation will be carried out (not implemented in this version).

dim

Dimension of the problem, it is equal to 2 in the 1.5D and 2D cases and equal to 3 in the 2.5D and 3D cases.

n_cov

Number of covariates taken into account in the linear part of the regression problem.

locations

A matrix of numeric coefficients with columns of dimension dim. When nonparametric inference is requested it represents the set of spatial locations for which the inferential analysis should be performed. The default values is a one-dimensional matrix of value 1 indicating that all the observed location points should be considered. In the sign-flip and eigen-sign-flip implementations only observed points are allowed.

locations_indices

A vector of indices indicating which spatial points have to be considered among the observed ones for nonparametric inference. If a vector of location indices is provided then the slot 'location' is discarded.

locations_are_nodes

An integer taking value 1 or 2; in the first case it indicates that the selected locations to perform inference on f are all coinciding with the nodes; otherwise it takes value 2;

coeff

A matrix of numeric coefficients with columns of dimension n_cov and each row represents a linear combination of the linear parameters to be tested and/or to be estimated via confidence interval.

beta0

Vector of null hypothesis values for the linear parameters of the model. Used only if test is not 0 and component is not 2.

f0

Function representing the expression of the nonparametric component f under the null hypothesis. Used only if component is not 1.

f0_eval

Vector of f0 evaluations at the chosen test locations. It will be eventually set later in checkInferenceParameters, if nonparametric inference is required.

f_var

An integer taking value 1 or 2. If 1 local variance estimates for the nonlinear part of the model will be computed, whereas if 2 they will not.

quantile

Vector of quantiles needed for confidence intervals, used only if interval is not 0.

alpha

1 minus confidence level vector of sign-flipping approaches confidence intervals. Used only if interval is not 0.

n_flip

An integer representing the number of sign-flips in the case of sign-flipping approaches.

tol_fspai

A real number greater than 0 specifying the tolerance for FSPAI algorithm, in case of non-exact inference (not implemented in this version).

definition

An integer taking value 0 or 1. If set to 1, the class will be considered as created by the function inferenceDataObjectBuilder, leading to avoid some of the checks that are performed on inference data within smoothing functions.