| Version: | 2.0.1 |
| Date: | 2022-02-17 |
| Title: | Calculates the Bidimensional Regression Between Two 2D Configurations |
| Imports: | Formula, methods |
| Depends: | R (≥ 4.1.0) |
| Description: | Calculates the bidimensional regression between two 2D configurations following the approach by Tobler (1965). |
| License: | GPL-3 |
| URL: | https://CRAN.R-project.org/package=BiDimRegression/, https://github.com/alexander-pastukhov/bidim-regression/, https://alexander-pastukhov.github.io/bidim-regression/ |
| BugReports: | https://github.com/alexander-pastukhov/bidim-regression/issues/ |
| Encoding: | UTF-8 |
| NeedsCompilation: | no |
| Repository: | CRAN |
| RoxygenNote: | 7.1.2 |
| LazyData: | true |
| Suggests: | testthat, knitr, rmarkdown, dplyr, ggplot2 |
| VignetteBuilder: | knitr |
| Packaged: | 2022-02-17 12:16:04 UTC; sasha |
| Author: | Claus-Christian Carbon
 [aut],
Alexander Pastukhov
[aut, cre] |
| Maintainer: | Alexander Pastukhov <pastukhov.alexander@gmail.com> |
| Date/Publication: | 2022-02-17 13:02:10 UTC |
Calculates the bidimensional regression between two 2D configurations
Description
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 re-implemented in a R-friendly style, see lm2 function.
Usage
BiDimRegression(coord)
Arguments
coord |
table that must contain two columns for dependent variables (named |
Value
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 t-tests regarding the model parameters (alphas and betas). -
euclidean.alpha1.*, euclidean.alpha2.*, affine.alpha1.*, affine.alpha2.*- intercept vectors, information includes.coefffor coefficient,.SEfor standard error,tValuefor t-statistics, andpValuefor significance. -
euclidean.beta1.*, euclidean.beta2.*, affine.beta1.*, affine.beta2.*, affine.beta3.*, affine.beta4.*- slope vectors, information includes.coefffor coefficient,.SEfor standard error,tValuefor t-statistics, andpValuefor significance. -
euclidean.fValue, affine.fValue- F-statistics, following the advice of Nakaya (1997). -
euclidean.df1, affine.df1- degrees of freedom of the nominator used for the F-statistics propagated by Nakaya (1997); df1 = p-2, 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 F-statistics propagated by Nakaya (1997); df2 = 2n-p, 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 F-statistics. -
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.fValuefor F-statistics,.df1and.df2for the degrees of freedom,.pValuefor the significance level, and.dAICfor AIC difference between two models.
See Also
Examples
resultingMeasures <- BiDimRegression(NakayaData)
print(resultingMeasures)
Data from Carbon, C. C. (2013). BiDimRegression: Bidimensional Regression Modeling Using R. \ Journal of Statistical Software, Code Snippets, 52(1), 1-11 (URL http://www.jstatsoft.org/v52/c01/)\
Description
Example 1 from the domain of aesthetics to show how the method can be utilized for assessing the similarity of two portrayed persons, actually the Mona Lisa in the world famous Louvre version and the only recently re-discovered Prado version
Usage
data(CarbonExample1Data)Format
A data frame with 36 observations on the following 4 variables.
depV1a numeric vector
depV2a numeric vector
indepV1a numeric vector
indepV2a numeric vector
Examples
data(CarbonExample1Data)
## maybe str(CarbonExample1Data) ; plot(CarbonExample1Data) ...
Data from Carbon, C. C. (2013). BiDimRegression: Bidimensional Regression Modeling Using R. \ Journal of Statistical Software, Code Snippets, 52(1), 1-11 (URL http://www.jstatsoft.org/v52/c01/)\
Description
Example 2 originates from the area of geography and inspects the accuracy of different maps of the city of Paris which were created over the last 350 years as compared to a recent map
Usage
data(CarbonExample2Data)Format
A data frame with 13 observations on the following 4 variables.
depV1a numeric vector
depV2a numeric vector
indepV1a numeric vector
indepV2a numeric vector
Examples
data(CarbonExample2Data)
## maybe str(CarbonExample2Data) ; plot(CarbonExample2Data) ...
Data from Carbon, C. C. (2013). BiDimRegression: Bidimensional Regression Modeling Using R. \ Journal of Statistical Software, Code Snippets, 52(1), 1-11 (URL http://www.jstatsoft.org/v52/c01/)\
Description
Example 3 focuses on demonstrating how good a cognitive map recalculated from averaged cognitive distance data fits with a related real map
Usage
data(CarbonExample3Data)Format
A data frame with 10 observations on the following 4 variables.
depV1a numeric vector
depV2a numeric vector
indepV1a numeric vector
indepV2a numeric vector
Examples
data(CarbonExample3Data)
## maybe str(CarbonExample3Data) ; plot(CarbonExample3Data) ...
Eye gaze calibration data
Description
A dataset containing a monocular eye gaze recording with calibration sequence. Courtesy of Bamberger Baby Institut (BamBI).
Usage
EyegazeData
Format
A data frame with 365 rows and 6 variables:
- time
sample timestamp, in milliseconds
- x, y
recorded gaze, in internal eye tracker units
- target_x, target_y
location of the calibration target on the screen, in pixels
- target
index of the target within the sequence
...
Data from Friedman, A., & Kohler, B. (2003). Bidimensional regression: Assessing the configural similarity and accuracy of cognitive maps and other two-dimensional data sets. Psychological Methods, 8(4), 468-491.
Description
Data from Friedman, A., & Kohler, B. (2003). Bidimensional regression: Assessing the configural similarity and accuracy of cognitive maps and other two-dimensional data sets. Psychological Methods, 8(4), 468-491.
Usage
data(FriedmanKohlerData1)Format
A data frame with 4 observations on the following 4 variables.
depV1a numeric vector
depV2a numeric vector
indepV1a numeric vector
indepV2a numeric vector
Examples
data(FriedmanKohlerData1)
## maybe str(FriedmanKohlerData1) ; plot(FriedmanKohlerData1) ...
Data from Friedman, A., & Kohler, B. (2003). Bidimensional regression: Assessing the configural similarity and accuracy of cognitive maps and other two-dimensional data sets. Psychological Methods, 8(4), 468-491.
Description
Data from Friedman, A., & Kohler, B. (2003). Bidimensional regression: Assessing the configural similarity and accuracy of cognitive maps and other two-dimensional data sets. Psychological Methods, 8(4), 468-491.
Usage
data(FriedmanKohlerData2)Format
A data frame with 4 observations on the following 4 variables.
depV1a numeric vector
depV2a numeric vector
indepV1a numeric vector
indepV2a numeric vector
Examples
data(FriedmanKohlerData2)
## maybe str(FriedmanKohlerData2) ; plot(FriedmanKohlerData2) ...
Data from Nakaya, T. (1997). Statistical inferences in bidimensional regression models. Geographical Analysis, 29(2), 169-186.
Description
Data from Nakaya, T. (1997). Statistical inferences in bidimensional regression models. Geographical Analysis, 29(2), 169-186.
Usage
data(NakayaData)Format
A data frame with 19 observations on the following 4 variables.
depV1a numeric vector
depV2a numeric vector
indepV1a numeric vector
indepV2a numeric vector
Examples
data(NakayaData)
## maybe str(NakayaData) ; plot(NakayaData) ...
Anova for lm2 objects
Description
Anova for lm2 objects, returns a table with pairwise comparisons between models or, if only one model was supplied, with the null model.
Usage
## S3 method for class 'lm2'
anova(object, ...)
Arguments
object |
an object of class "lm2" |
... |
further objects of class "lm2" |
Value
an anova data frame
See Also
Examples
lm2euc <- lm2(depV1+depV2~indepV1+indepV2, NakayaData, transformation = 'Euclidean')
lm2aff <- lm2(depV1+depV2~indepV1+indepV2, NakayaData, transformation = 'Affine')
anova(lm2euc, lm2aff)
Fitting Bidimensional Regression Models
Description
lm2 is used to fit bidimensional linear regression models using Euclidean and Affine transformations following the approach by Tobler (1965).
Usage
lm2(formula, data, transformation)
Arguments
formula |
a symbolic description of the model to be fitted in the format |
data |
a data frame containing variables for the model. |
transformation |
the transformation to be used, either |
Value
lm2 returns an object of class "lm2". An object of class "lm" is a list containing at least the following components:
transformation |
string with the transformation type ( |
npredictors |
number of predictors used in the model: 4 for euclidean, 6 for affine, 8 for projective. |
df_model, df_residual |
degrees of freedom for the model and for the residuals |
transformation_matrix |
|
coeff |
transformation coefficients, with |
transformed_coeff |
|
fitted_values |
data frame containing fitted values for the original data set |
residuals |
data frame containing residuals for the original fit |
r.squared, adj.r.squared |
R-squared and adjusted R-squared. |
F, p.value |
F-statistics and the corresponding p-value, given the |
dAIC |
Akaike Information Criterion (AIC) difference between the regression model and the null model. A negative values indicates that the regression model is better. See Nakaya (1997). |
distortion_index |
Distortion index following Waterman and Gordon (1984), as adjusted by Friedman and Kohler (2003) |
lm |
an underlying linear model for |
formula |
formula, describing input and output columns |
data |
data used to fit the model |
Call |
function call information, incorporates the |
See Also
Examples
lm2euc <- lm2(depV1 + depV2 ~ indepV1 + indepV2, NakayaData, 'euclidean')
lm2aff <- lm2(depV1 + depV2 ~ indepV1 + indepV2, NakayaData, 'affine')
lm2prj <- lm2(depV1 + depV2 ~ indepV1 + indepV2, NakayaData, 'projective')
anova(lm2euc, lm2aff, lm2prj)
predict(lm2euc)
summary(lm2euc)
Computes model for the affine transformation
Description
Computes model for the affine transformation
Usage
lm2affine(data)
Arguments
data |
the preprocessed data frame from |
Value
object with transformation specific data to be supplemented with further stats
Computes model for the euclidean transformation
Description
Computes model for the euclidean transformation
Usage
lm2euclidean(data)
Arguments
data |
the preprocessed data frame from |
Value
object with transformation specific data to be supplemented with further stats
Fits the specified model and computes stats
Description
Calls a specific transformation model function and then computes statistics
that is common across all transformations.
This function should not be called directly, please use lm2.
Usage
lm2fit(data, transformation)
Arguments
data |
the preprocessed data frame from |
transformation |
the transformation to be used, either |
Value
returns an object of class "lm2", see lm2
for the description.
Computes model for the projective transformation
Description
Computes model for the projective transformation
Usage
lm2projective(data)
Arguments
data |
the preprocessed data frame from |
Value
object with transformation specific data to be supplemented with further stats
Predict method for Bidimensional Regression Model Fits
Description
Predicted values based on the bidimensional regressional model object.
Usage
## S3 method for class 'lm2'
predict(object, newdata, ...)
Arguments
object |
an object of class "lm2" |
newdata |
An optional two column data frame with independent variables. If omitted, the fitted values are used. |
... |
optional arguments |
Value
a two column data frame with predicted values for dependent variables.
See Also
Examples
lm2euc <- lm2(depV1+depV2~indepV1+indepV2, NakayaData, transformation = 'Euclidean')
predict(lm2euc, NakayaData[, 3:4])
Makes a lightweight summary lm2 object
Description
Drops heavy bits, like the data frame with predicted values or the lm object. However, the print tells more! :)
Usage
## S3 method for class 'lm2'
summary(object, ...)
Arguments
object |
an object of class "lm2", see |