Description Usage Arguments Value See Also Examples
View source: R/BiDimRegression.R
Calculates the bidimensional regression between two 2D configurations using both Euclidean and Affine transformations following the approach by Tobler (1965).
This function assumes strict data format and returns all coefficients and statistics in a single structure. Same functionality is now reimplemented in a Rfriendly style, see lm2
function.
1  BiDimRegression(coord)

coord 
table that must contain two columns for dependent variables (named 
an S3 class BiDimRegression
containing all essential measures of the bidimensional regression
euclidean.r, affine.r
 the regression coefficient, defined analogously to Pearson's r.
euclidean.rsqr, affine.rsqr
 the squared regression coefficient.
euclidean.diABSqr, affine.diABSqr
 the squared distortion index for dependent variables; following Waterman and Gordon's (1984) extension of the bidimensional regression, it provides a measure of comparison of distortions, but the range of values is 0 to 1 following Friedman and Kohler (2003).
euclidean.dMaxABSqr, affine.dMaxABSqr
 the maximal squared distortion index for dependent variables.
euclidean.diXYSqr, affine.diXYSqr
 the distortion index for independent variables.
euclidean.dMaxXYSqr, affine.dMaxXYSqr
 the maximal squared distortion index for independent variables.
euclidean.scaleFactorX, affine.scaleFactorX
 the scaling factor of the first dimension (1.0 means no scaling; values below 1.0 indicate a contraction, values above 1.0 indicate an expansion).
euclidean.scaleFactorY, affine.scaleFactorY
 the scaling factor of the second dimension.
euclidean.angleDEG, affine.angleDEG
 the rotation angle in degrees.
euclidean.shear, affine.shear
 shearing of the transformed configuration, always zero for the Euclidean transformation.
euclidean.ttestDF, affine.ttestDF
 degrees of freedom (DF) for the ttests regarding the model parameters (alphas and betas).
euclidean.alpha1.*, euclidean.alpha2.*, affine.alpha1.*, affine.alpha2.*
 intercept vectors, information includes .coeff
for coefficient, .SE
for standard error, tValue
for tstatistics, and pValue
for significance.
euclidean.beta1.*, euclidean.beta2.*, affine.beta1.*, affine.beta2.*, affine.beta3.*, affine.beta4.*
 slope vectors, information includes .coeff
for coefficient, .SE
for standard error, tValue
for tstatistics, and pValue
for significance.
euclidean.fValue, affine.fValue
 Fstatistics, following the advice of Nakaya (1997).
euclidean.df1, affine.df1
 degrees of freedom of the nominator used for the Fstatistics propagated by Nakaya (1997); df1 = p2, with p is the number of elements needed to calculate the referring model: p=4 for the Euclidean and p=6 for the affine geometry Nakaya, 1997, Table 1.
euclidean.df2, affine.df2
 degrees of freedom of the denominator used for the Fstatistics propagated by Nakaya (1997); df2 = 2np, with p is the number of elements needed to calculate the referring model (see df1) and n is the number of coordinate pairs.
euclidean.pValue, affine.pValue
 the significance level based on the preceding Fstatistics.
euclidean.dAICso, affine.dAICso
 the AIC difference between the regarding bidimensional regression model and the bidimensional null model (S0) according to Nakaya (1997), formula 56.
eucVSaff.*
 statistical comparison between Euclidean and Affine models, include .fValue
for Fstatistics, .df1
and .df2
for the degrees of freedom, .pValue
for the significance level, and .dAIC
for AIC difference between two models.
1 2  resultingMeasures < BiDimRegression(NakayaData)
print(resultingMeasures)

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