lmridge | R Documentation |

Fits a linear ridge regression model after scaling regressors and returns an object of class "lmridge" (by calling `lmridgeEst`

function) designed to be used in plotting method, testing of ridge coefficients and for computation of different ridge related statistics. The ridge biasing parameter *K* can be a scalar or a vector. See Hoerl et al., 1975 <doi: 10.1080/03610927508827232>, Horel and Kennard, 1970 <doi: 10.1080/00401706.1970.10488634>.

lmridge(formula, data, K = 0, scaling=c("sc", "scaled", "non", "centered"), ...) lmridgeEst(formula, data, K=0, scaling=c("sc", "scaled", "non", "centered"), ...) ## Default S3 method: lmridge(formula, data, K = 0, scaling=c("sc", "scaled", "non", "centered"), ...) ## S3 method for class 'lmridge' coef(object, ...) ## S3 method for class 'lmridge' print(x, digits = max(5,getOption("digits") - 5), ...) ## S3 method for class 'lmridge' fitted(object, ...)

`formula` |
Standard R formula expression, that is, a symbolic representation of the model to be fitted and has form |

`data` |
An optional data frame containing the variables in the model. If not found in data, the variables are taken from |

`K` |
Ridge biasing parameter (may be a vector). |

`scaling` |
The method to be used to scale the predictors. The scaling option |

`object` |
A lmridge object, typically generated by a call to |

`x` |
An object of class |

`digits` |
Minimum number of significant digits to be used. |

`...` |
Additional arguments to be passed to or from other methods. |

`lmridge`

or `lmridgeEst`

function fits in linear ridge regression after scaling the regressors and centering the response. The `lmridge`

is default a function that calls `lmridgeEst`

for computation of ridge coefficients and returns an object of class "lmridge" designed to be used in plotting method, testing of ridge coefficients and for computation of different ridge related statistics. If intercept is present in the model, its coefficient is not penalized. However, intercept is estimated from the relation *y=\overline{y}-β \overline{X}*. `print.lmridge`

tries to be smart about formatting of ridge coefficients.

`lmridge`

function returns an object of class "lmridge" after calling list of named objects from `lmridgeEst`

function:

`coef` |
A named vector of fitted coefficients. |

`call` |
The matched call. |

`Inter` |
Was an intercept included? |

`scaling` |
The scaling method used. |

`mf` |
Actual data used. |

`y` |
The response variable. |

`xs` |
The scaled matrix of predictors. |

`xm` |
The vector of means of the predictors. |

`terms` |
The |

`xscale` |
Square root of sum of squared deviation from mean regarding the scaling option used in |

`rfit` |
The fitted value of ridge regression for given biasing parameter |

`K` |
The ridge regression biasing parameter |

`d` |
A vector of singular values of scaled |

`div` |
Eigenvalues of scaled regressors. |

`Z` |
A list of matrix |

The function at the current form cannot handle missing values. The user has to take prior action with missing values before using this function.

Muhammad Imdad Ullah, Muhammad Aslam

Hoerl, A. E., Kennard, R. W., and Baldwin, K. F. (1975). Ridge Regression: Some Simulation. *Communication in Statistics*, **4**, 105-123. doi: 10.1080/03610927508827232.

Hoerl, A. E. and Kennard, R. W., (1970). Ridge Regression: Biased Estimation of Nonorthogonal Problems. *Technometrics*, **12**, 55-67. doi: 10.2307/1267351.

Imdad, M. U. *Addressing Linear Regression Models with Correlated Regressors: Some Package Development in R* (Doctoral Thesis, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan), 2017.

Testing of ridge coefficient `summary.lmridge`

data(Hald) mod <- lmridge(y~., data = as.data.frame(Hald), K = seq(0, 0.1, 0.01), scaling = "sc") ## Scaled Coefficients mod$coef ## Re-Scaled Coefficients coef(mod) ## ridge predicted values predict(mod) ## ridge residuals residuals(mod) ##ridge and VIF trace plot(mod) ## ridge VIF values vif(mod) ## ridge Var-Cov matrix vcov(mod) ## ridge biasing parameter by researchers kest(mod) ## ridge fitted values fitted(mod) ## ridge statistics 1 rstats1(mod) ## ridge statistics 2 rstats2(mod) ## list of objects from lmridgeEst function lmridgeEst(y~., data = as.data.frame(Hald), K = seq(0, 0.1, 0.01), scaling = "sc") lmridgeEst(y~., data = as.data.frame(Hald), K = seq(0, 0.1, 0.01), scaling = "non")

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