Description Usage Arguments Details Value Note See Also Examples

Model selection by exhaustive search, forward or backward stepwise, or sequential replacement

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ```
regsubsets(x=, ...)
## S3 method for class 'formula'
regsubsets(x=, data=, weights=NULL, nbest=1, nvmax=8,
force.in=NULL, force.out=NULL, intercept=TRUE,
method=c("exhaustive", "backward", "forward", "seqrep"),
really.big=FALSE,
nested=(nbest==1),...)
## Default S3 method:
regsubsets(x=, y=, weights=rep(1, length(y)), nbest=1, nvmax=8,
force.in=NULL, force.out=NULL, intercept=TRUE,
method=c("exhaustive","backward", "forward", "seqrep"),
really.big=FALSE,nested=(nbest==1),...)
## S3 method for class 'biglm'
regsubsets(x,nbest=1,nvmax=8,force.in=NULL,
method=c("exhaustive","backward", "forward", "seqrep"),
really.big=FALSE,nested=(nbest==1),...)
## S3 method for class 'regsubsets'
summary(object,all.best=TRUE,matrix=TRUE,matrix.logical=FALSE,df=NULL,...)
## S3 method for class 'regsubsets'
coef(object,id,vcov=FALSE,...)
## S3 method for class 'regsubsets'
vcov(object,id,...)
``` |

`x` |
design matrix or model formula for full model, or |

`data` |
Optional data frame |

`y` |
response vector |

`weights` |
weight vector |

`nbest` |
number of subsets of each size to record |

`nvmax` |
maximum size of subsets to examine |

`force.in` |
index to columns of design matrix that should be in all models |

`force.out` |
index to columns of design matrix that should be in no models |

`intercept` |
Add an intercept? |

`method` |
Use exhaustive search, forward selection, backward selection or sequential replacement to search. |

`really.big` |
Must be TRUE to perform exhaustive search on more than 50 variables. |

`nested` |
See the Note below: if |

`object` |
regsubsets object |

`all.best` |
Show all the best subsets or just one of each size |

`matrix` |
Show a matrix of the variables in each model or just summary statistics |

`matrix.logical` |
With |

`df` |
Specify a number of degrees of freedom for the summary
statistics. The default is |

`id` |
Which model or models (ordered as in the summary output) to return coefficients and variance matrix for |

`vcov` |
If |

`...` |
Other arguments for future methods |

Since this function returns separate best models of all sizes up to
`nvmax`

and since different model selection criteria such as AIC,
BIC, CIC, DIC, ... differ only in how models of different sizes are compared, the
results do not depend on the choice of cost-complexity tradeoff.

When `x`

is a `biglm`

object it is assumed to be the full
model, so `force.out`

is not relevant. If there is an intercept it
is forced in by default; specify a `force.in`

as a logical vector
with `FALSE`

as the first element to allow the intercept to be
dropped.

The model search does not actually fit each model, so the returned
object does not contain coefficients or standard errors. Coefficients
and the variance-covariance matrix for one or model models can be
obtained with the `coef`

and `vcov`

methods.

`regsubsets`

returns an object of class "regsubsets" containing no
user-serviceable parts. It is designed to be processed by
`summary.regsubsets`

.

`summary.regsubsets`

returns an object with elements

`which` |
A logical matrix indicating which elements are in each model |

`rsq` |
The r-squared for each model |

`rss` |
Residual sum of squares for each model |

`adjr2` |
Adjusted r-squared |

`cp` |
Mallows' Cp |

`bic` |
Schwartz's information criterion, BIC |

`outmat` |
A version of the |

`obj` |
A copy of the |

The `coef`

method returns a coefficient vector or list of vectors,
the `vcov`

method returns a matrix or list of matrices.

As part of the setup process, the code initially fits models with the
first variable in `x`

, the first two, the first three, and so on.
For forward and backward selection it is possible that the model with the `k`

first variables will be better than the model with `k`

variables from the selection algorithm. If it is, the model with the
first `k`

variables will be returned, with a warning. This can
happen for forward and backward selection. It (obviously) can't for
exhaustive search.

With `nbest=1`

you can avoid these extra models with
`nested=TRUE`

, which is the default.

1 2 3 4 5 6 7 8 |

```
Subset selection object
5 Variables (and intercept)
Forced in Forced out
Agriculture FALSE FALSE
Examination FALSE FALSE
Education FALSE FALSE
Catholic FALSE FALSE
Infant.Mortality FALSE FALSE
1 subsets of each size up to 5
Selection Algorithm: exhaustive
Agriculture Examination Education Catholic Infant.Mortality
1 ( 1 ) " " " " "*" " " " "
2 ( 1 ) " " " " "*" "*" " "
3 ( 1 ) " " " " "*" "*" "*"
4 ( 1 ) "*" " " "*" "*" "*"
5 ( 1 ) "*" "*" "*" "*" "*"
Subset selection object
Call: regsubsets.formula(Fertility ~ ., data = swiss, nbest = 2)
5 Variables (and intercept)
Forced in Forced out
Agriculture FALSE FALSE
Examination FALSE FALSE
Education FALSE FALSE
Catholic FALSE FALSE
Infant.Mortality FALSE FALSE
2 subsets of each size up to 5
Selection Algorithm: exhaustive
Agriculture Examination Education Catholic Infant.Mortality
1 ( 1 ) " " " " "*" " " " "
1 ( 2 ) " " "*" " " " " " "
2 ( 1 ) " " " " "*" "*" " "
2 ( 2 ) " " " " "*" " " "*"
3 ( 1 ) " " " " "*" "*" "*"
3 ( 2 ) "*" " " "*" "*" " "
4 ( 1 ) "*" " " "*" "*" "*"
4 ( 2 ) " " "*" "*" "*" "*"
5 ( 1 ) "*" "*" "*" "*" "*"
[[1]]
(Intercept) Education
79.6100585 -0.8623503
[[2]]
(Intercept) Education Catholic
74.2336892 -0.7883293 0.1109210
[[3]]
(Intercept) Education Catholic Infant.Mortality
48.67707330 -0.75924577 0.09606607 1.29614813
(Intercept) Education Catholic Infant.Mortality
(Intercept) 62.711883147 -0.2349982009 -0.0011120059 -2.952862263
Education -0.234998201 0.0136416868 0.0004427309 0.003360365
Catholic -0.001112006 0.0004427309 0.0007408169 -0.001716363
Infant.Mortality -2.952862263 0.0033603646 -0.0017163629 0.149759535
```

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