Fits 2D and 3D geometric transformations. Provides posterior via Stan. Includes computation of LOO and WAIC information criteria, R-squared.
To fit transformation, call the main function either via a formula that specifies
dependent and independent variables with the data table or by supplying two tables
one containing all independent variables and one containing all dependent variables.
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")
Once the data is fitted, you can extract the transformation coefficients via coef function and the matrix
itself via transformation_matrix. Predicted data, either based on the original data or on the new data,
can be generated via predict. Bayesian R-squared can be computed with or without adjustment via
R2 function. In all three cases, you have choice between summary (mean + specified quantiles) or full
posterior samples. loo and waic provide corresponding measures that can be used for comparison
via loo::loo_compare() function.
References
Stan Development Team (2020). RStan: the R interface to Stan. R package version 2.19.3. https://mc-stan.org
Examples
# Fitting via formula
euc2 <- fit_transformation(depV1 + depV2 ~ indepV1 + indepV2,
NakayaData, 'euclidean')
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aff2 <- fit_transformation(depV1 + depV2 ~ indepV1 + indepV2,
NakayaData, 'affine')
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prj2 <- fit_transformation(depV1 + depV2 ~ indepV1 + indepV2,
NakayaData, 'projective')
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# summary of transformation coefficients
coef(euc2)
#> Coef Mean 5.5 94.5
#> 1 a1 0.1481502 -0.000752388 0.2930807
#> 2 a2 -0.0133224 -0.171476678 0.1414942
#> 3 b1 1.3442255 1.237738724 1.4508081
#> 4 b2 -0.5681462 -0.665426616 -0.4587525
# statistical comparison via WAIC criterion
loo::loo_compare(waic(euc2), waic(aff2), waic(prj2))
#> Warning:
#> 17 (89.5%) p_waic estimates greater than 0.4. We recommend trying loo instead.
#> Warning:
#> 18 (94.7%) p_waic estimates greater than 0.4. We recommend trying loo instead.
#> Warning:
#> 18 (94.7%) p_waic estimates greater than 0.4. We recommend trying loo instead.
#> elpd_diff se_diff
#> model1 0.0 0.0
#> model2 -4819.9 2557.8
#> model3 -5487.3 2917.7
# Fitting via two tables
euc2 <- fit_transformation_df(NakayaData[, 1:2], NakayaData[, 3:4],
'euclidean')
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tr3 <- fit_transformation_df(Face3D_W070, Face3D_W097, transformation ='translation')
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