# Class "semi-continuous" and Inherited Classes

### Description

The `semi-continuous`

class inherits from the `continuous-class`

and is the parent of the `nonnegative-continuous`

class, which in turn is the parent of the `SC_proportion class`

for semi-continuous variables. A semi-continuous variable has support on one or more point
masses and a continuous interval. The `semi-continuous`

class differs from the `censored-continuous-class`

and
the `truncated-continuous-class`

in that observations that fall on the point masses are bonafide data, rather than
indicators of censoring or truncation. If there are no observations that fall on a point mass, then either the
`continuous-class`

or one of its other subclasses should be used. Aside from these facts, the rest of the
documentation here is primarily directed toward developers.

### Objects from the Classes

Objects can be created that are of `semi-continuous`

, `nonnegative-continuous`

, or
`SC_proportion`

class via the `missing_variable`

generic function by specifying `type = "semi-continuous"`

`type = "nonnegative-continuous"`

, `type = "SC_proportion"`

.

### Slots

The semi-continuous class inherits from the continuous class and is intended for variables that, for example have a point mass at certain points and are continuous in between. Thus, its default transformation is the identity transformation, which is to say no transformation in practice. It has one additional slot.

- indicator
Object of class

`"ordered-categorical"`

that indicates whether an observed value falls on a point mass or the continuous interval in between. By convention, zero signifies an observation that falls within the continuous interval

At the moment, there are no methods for the semi-continuous class. However, the basic approach to modeling a semi-continuous
variable has two steps. First, the **indicator** is modeled using the methods that are defined for it and its missing values
are imputed. Second, the continuous part of the semi-continuous variable is modeled using the same techniques that are used
when modeling continuous variables. Note that in the second step, only a subset of the observations are modeled, although this
subset possibly includes values that were originally missing in which case they are imputed.

The nonnegative-continuous class inherits from the semi-continuous class, which has its point mass at zero and
is continuous over the positive real line. By default, the transformation for the positive part of a
nonnegative-continuuos variable is `log(y + a)`

, where `a`

is a small constant determined by the
observed data. If a variable is strictly positive, the `positive-continuous-class`

should be used instead.

The SC_proportion class inherits from the nonnegative-continuous class. It has no additional slots, and the only supported
transformation function is the `(y * (n - 1) + .5) / n`

function. Its default `fit_model`

method is a
wrapper for the `betareg`

function in the betareg package. Its **family** must be
`binomial`

so that its `link`

function can be passed to `betareg`

If the observed values fall strictly on the open unit interval, the `proportion-class`

should be used instead.

### Author(s)

Ben Goodrich and Jonathan Kropko, for this version, based on earlier versions written by Yu-Sung Su, Masanao Yajima, Maria Grazia Pittau, Jennifer Hill, and Andrew Gelman.

### See Also

`missing_variable`

, `continuous-class`

, `positive-continuous-class`

,
`proportion-class`

### Examples

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