Description Usage Arguments Details Value Author(s) See Also Examples

This function implements forward stepwise regression, for use in the selectiveInference package

1 |

`x` |
Matrix of predictors (n by p) |

`y` |
Vector of outcomes (length n) |

`maxsteps` |
Maximum number of steps to take |

`intercept` |
Should an intercept be included on the model? Default is TRUE |

`normalize` |
Should the predictors be normalized? Default is TRUE. (Note:
this argument has no real effect on model selection since forward stepwise is
scale invariant already; however, it is included for completeness, and to match
the interface for the |

`verbose` |
Print out progress along the way? Default is FALSE |

This function implements forward stepwise regression, adding the predictor at each
step that maximizes the absolute correlation between the predictorsâ€”once
orthogonalized with respect to the current modelâ€”and the residual. This entry
criterion is standard, and is equivalent to choosing the variable that achieves
the biggest drop in RSS at each step; it is used, e.g., by the `step`

function
in R. Note that, for example, the `lars`

package implements a stepwise option
(with type="step"), but uses a (mildly) different entry criterion, based on maximal
absolute correlation between the original (non-orthogonalized) predictors and the
residual.

`action` |
Vector of predictors in order of entry |

`sign` |
Signs of coefficients of predictors, upon entry |

`df` |
Degrees of freedom of each active model |

`beta` |
Matrix of regression coefficients for each model along the path, one column per model |

`completepath` |
Was the complete stepwise path computed? |

`bls` |
If completepath is TRUE, the full least squares coefficients |

`Gamma` |
Matrix that captures the polyhedral selection at each step |

`nk` |
Number of polyhedral constraints at each step in path |

`vreg` |
Matrix of linear contrasts that gives coefficients of variables to enter along the path |

`x` |
Matrix of predictors used |

`y` |
Vector of outcomes used |

`bx` |
Vector of column means of original x |

`by` |
Mean of original y |

`sx` |
Norm of each column of original x |

`intercept` |
Was an intercept included? |

`normalize` |
Were the predictors normalized? |

`call` |
The call to fs |

Ryan Tibshirani, Rob Tibshirani, Jonathan Taylor, Joshua Loftus, Stephen Reid

`fsInf`

, `predict.fs`

,`coef.fs`

, `plot.fs`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 |

```
Loading required package: glmnet
Loading required package: Matrix
Loading required package: foreach
Loaded glmnet 2.0-16
Loading required package: intervals
Attaching package: 'intervals'
The following object is masked from 'package:Matrix':
expand
Loading required package: survival
Call:
fsInf(obj = fsfit)
Standard deviation of noise (specified or estimated) sigma = 1.027
Sequential testing results with alpha = 0.100
Step Var Coef Z-score P-value LowConfPt UpConfPt LowTailArea UpTailArea
1 1 2.317 13.406 0.000 2.019 2.605 0.049 0.048
2 2 1.703 12.996 0.000 1.486 1.922 0.048 0.050
3 9 -0.265 -1.683 0.487 -0.782 1.152 0.050 0.050
4 8 -0.175 -1.156 0.260 -4.764 1.532 0.050 0.050
5 10 0.173 1.075 0.755 -12.195 3.056 0.050 0.050
6 4 -0.178 -1.140 0.407 -11.057 7.428 0.050 0.050
7 7 0.158 0.979 0.763 -9.225 2.137 0.050 0.050
8 5 0.128 0.896 0.838 -6.737 0.737 0.050 0.050
9 6 -0.036 -0.225 0.303 -Inf Inf 0.000 0.000
10 3 0.037 0.255 0.121 -1.478 Inf 0.050 0.000
Estimated stopping point from ForwardStop rule = 2
```

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