fit_transformation: Fitting Bidimensional or Tridimensional Regression /...

In TriDimRegression: Bayesian Statistics for 2D/3D Transformations

Fitting Bidimensional or Tridimensional Regression / Geometric Transformation Models via Formula.

Description

Fits Bidimensional or Tridimensional regression / geometric transformation models using Stan engine. The formula described dependent and independent numeric variables in the data. See also fit_transformation_df.

For the 2D data, you can fit "translation" (2 parameters for translation only), "euclidean" (4 parameters: 2 for translation, 1 for scaling, and 1 for rotation), "affine" (6 parameters: 2 for translation and 4 that jointly describe scaling, rotation and sheer), or "projective" (8 parameters: affine plus 2 additional parameters to account for projection).

For 3D data, you can fit "translation" (3 for translation only), "euclidean_x", "euclidean_y", "euclidean_z" (5 parameters: 3 for translation scale, 1 for rotation, and 1 for scaling), "affine" (12 parameters: 3 for translation and 9 to account for scaling, rotation, and sheer), and "projective" (15 parameters: affine plus 3 additional parameters to account for projection). transformations.

For details on transformation matrices and computation of scale and rotation parameters please see vignette("transformation_matrices", package = "TriDimRegression")

Usage

## S3 method for class 'formula'
fit_transformation(
  formula,
  data,
  transformation,
  priors = NULL,
  chains = 1,
  cores = NULL,
  ...
)

Arguments

formula	a symbolic description of the model to be fitted in the format Xdep + Ydep ~ Xind + Yind, where Xdep and Ydep are dependent and Xind and Yind are independent variables
data	a data frame containing variables for the model.
transformation	the transformation to be used: "translation" (both 2D and 3D), "euclidean" (2D), "euclidean_x", "euclidean_y", "euclidean_z" (3D, rotation about, respectively, x, y, and z axis), "affine" (2D and 3D), or "projective" (2D and 3D).
priors	named list of parameters for prior distributions of parameters a (translation, normal distribution), b (all other parameters, normal distribution), and sigma (residual variance, exponential). E.g., list("a" = c(0, 10), "b"= c(0, 1), "sigma"=1). Default priors are "a" = c(0, max_absolute_difference_in_means(d, iv)) / 2), "b" = c(0, max_absolute_difference_in_means(d, iv)) / 2), "sigma" = 1 * sd(dv).
chains	Number of chains for sampling.
cores	Number of CPU cores to use for sampling. If omitted, all available cores are used.
...	Additional arguments passed to sampling function.

Value

A tridim_transformation object

See Also

fit_transformation_df

Examples

# Geometric transformations of 2D data
euc2 <- fit_transformation(depV1 + depV2 ~ indepV1 + indepV2,
                                     NakayaData, 'euclidean')
aff2 <- fit_transformation(depV1 + depV2 ~ indepV1 + indepV2,
                                     NakayaData, 'affine')
prj2 <- fit_transformation(depV1 + depV2 ~ indepV1 + indepV2,
                                     NakayaData, 'projective')

# summary of transformation coefficients
coef(euc2)

# statistical comparison via WAIC criterion
loo::loo_compare(waic(euc2), waic(aff2), waic(prj2))

TriDimRegression documentation built on Sept. 13, 2023, 5:07 p.m.