View source: R/rk.model.matrix.R

rk.model.matrix | R Documentation |

Creates a design (or model) matrix using the `rk`

function to expand variables via a reproducing kernel basis.

```
rk.model.matrix(object, data = environment(object), ...)
```

`object` |
a |

`data` |
a data frame containing the variables referenced in |

`...` |
additional arguments passed to the |

Designed to be a more flexible alternative to the `model.matrix`

function. The `rk`

function is used to construct a marginal basis for each variable that appears in the input `object`

. Tensor product interactions are formed by taking a `row.kronecker`

product of marginal basis matrices. Interactions of any order are supported using standard formulaic conventions, see Note.

The design matrix corresponding to the input formula and data, which has the following attributes:

`assign` |
an integer vector with an entry for each column in the matrix giving the term in the formula which gave rise to the column |

`term.labels` |
a character vector containing the labels for each of the terms in the model |

`knots` |
a named list giving the knots used for each variable in the formula |

`m` |
a named list giving the penalty order used for each variable in the formula |

`periodic` |
a named list giving the periodicity used for each variable in the formula |

`xlev` |
a named list giving the factor levels used for each variable in the formula |

For formulas of the form `y ~ x + z`

, the constructed model matrix has the form `cbind(rk(x), rk(z))`

, which simply concatenates the two marginal basis matrices. For formulas of the form `y ~ x : z`

, the constructed model matrix has the form `row.kronecker(rk(x), rk(z))`

, where `row.kronecker`

denotes the row-wise kronecker product. The formula `y ~ x * z`

is a shorthand for `y ~ x + z + x : z`

, which concatenates the two previous results. Unless it is suppressed (using `0+`

), the first column of the basis will be a column of ones named `(Intercept)`

.

Nathaniel E. Helwig <helwig@umn.edu>

Helwig, N. E. (2017). Regression with ordered predictors via ordinal smoothing splines. Frontiers in Applied Mathematics and Statistics, 3(15), 1-13. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3389/fams.2017.00015")}

Helwig, N. E. (2021). Spectrally sparse nonparametric regression via elastic net regularized smoothers. Journal of Computational and Graphical Statistics, 30(1), 182-191. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10618600.2020.1806855")}

Helwig, N. E. (2024). Precise tensor product smoothing via spectral splines. Stats, 7(1), 34-53. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3390/stats7010003")}

See `rk`

for details on the reproducing kernel basis

```
# load auto data
data(auto)
# additive effects
x <- rk.model.matrix(mpg ~ ., data = auto)
dim(x) # check dimensions
attr(x, "assign") # check group assignments
attr(x, "term.labels") # check term labels
# two-way interactions
x <- rk.model.matrix(mpg ~ . * ., data = auto)
dim(x) # check dimensions
attr(x, "assign") # check group assignments
attr(x, "term.labels") # check term labels
# specify df for horsepower, weight, and acceleration
# note: default df = 5 is used for displacement and model.year
df <- list(horsepower = 6, weight = 7, acceleration = 8)
x <- rk.model.matrix(mpg ~ ., data = auto, df = df)
sapply(attr(x, "knots"), length) # check df
# specify knots for model.year
# note: default knots are selected for other variables
knots <- list(model.year = c(1970, 1974, 1978, 1982))
x <- rk.model.matrix(mpg ~ ., data = auto, knots = knots)
sapply(attr(x, "knots"), length) # check df
```

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