lm2 {BiDimRegression} R Documentation

## 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 `A + B ~ C + D`, where `A` and `B` are dependent and `C` and `D` are independent variables `data` a data frame containing variables for the model. `transformation` the transformation to be used, either `'euclidean'`, `'affine'`, or `'projective'`.

### 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 (`euclidean`, `affine`, or `projective`) `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` `3x3` transformation matrix `coeff` transformation coefficients, with `a` denoting the intercept terms. `transformed_coeff` `scale`, `angle`, and `sheer` coefficients, depends on transformation. `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 `df_model` and `df_residual` degrees of freedom. `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 `Euclidean` and `affine` transformations. `formula` formula, describing input and output columns `data` data used to fit the model `Call` function call information, incorporates the `formula`, `transformation`, and `data`.

`anova.lm2` `BiDimRegression`

### 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)
```

[Package BiDimRegression version 2.0.0 Index]