TFixed {demest} | R Documentation

## Specify a model based on a Student's t distribution with known location, scale, and degrees of freedom.

### Description

Specify a model of the form

y_i = t(location[i], scale[i], df)

or

y_i = t(exposure[i] * location[i], scale[i], df)

.

### Usage

    TFixed(location, scale, df = 7, useExpose = TRUE)

### Arguments

`location` | An object of class `Values` specifying the center of the distribution.
`scale` | Parameter governing dispersion. Can be an object of class `Values`, or a single number, a single number, in which case it is applied to all elements of `location`.
`df` | A positive number. Defaults to 7.
`useExpose` | Whether the model includes an exposure term. Defaults to `TRUE`.

### Details

The model is useful as a data model where a few cells have much larger errors than the rest. Smaller values for `df` lead to thicker tails (ie larger probabilities of extreme values.) Subscript i denotes a cell within a classification defined by variables such as age, sex, and time. For instance cell i might be 30-34 year old females in 2020.

### Value

An object of class `SpecLikelihoodTFixed`.

### See Also

`TFixed` is typically used as part of a call to function `Model`. Similar data models that do not allow for the possibility of occasional large errors can be specified using `Normal` (though setting `df` to a value greater than 30 in `TFixed` will have much the same effect.) Flexible normal models can be specified using `Normal`.

### Examples

    location <- Values(array(c(0.95, 0.96, 0.95, 0.94),
                         dim = c(2, 2),
                         dimnames = list(age = c("0-39", "40+"),
                                         sex = c("Female", "Male"))))
    scale <- Values(array(c(0.05, 0.08, 0.05, 0.04),
                       dim = c(2, 2),
                       dimnames = list(age = c("0-39", "40+"),
                                       sex = c("Female", "Male"))))
    TFixed(location = location, scale = scale)
    TFixed(location = location, scale = 0.1, df = 1)
    TFixed(location = location, scale = 0.1, useExpose = FALSE)

    ## indistinguishable from normal distribution:
    TFixed(location = location, scale = scale, df = 30)

    ## Cauchy distribution (very heavy tails):
    TFixed(location = location, scale = scale, df = 1)

[Package demest version 0.0.0.3.1 Index]