Formula

java.lang.Object
- smile.data.formula.Formula

All Implemented Interfaces:

java.io.Serializable
```
public class Formula
extends java.lang.Object
implements java.io.Serializable
```
The model fitting formula in a compact symbolic form. An expression of the form y ~ model is interpreted as a specification that the response y is modelled by a linear predictor specified symbolically by model. Such a model consists of a series of terms separated by + operators. The terms themselves consist of variable and factor names separated by :: operators. Such a term is interpreted as the interaction of all the variables and factors appearing in the term. The special term "." means all columns not otherwise in the formula in the context of a data frame.
In addition to + and ::, a number of other operators are useful in model formulae. The && operator denotes factor crossing: a && b interpreted as a+b+a::b. The ^ operator indicates crossing to the specified degree. For example (a+b+c)^2 is identical to (a+b+c)*(a+b+c) which in turn expands to a formula containing the main effects for a, b and c together with their second-order interactions. The - operator removes the specified terms, so that (a+b+c)^2 - a::b is identical to a + b + c + b::c + a::c. It can also used to remove the intercept term: when fitting a linear model y ~ x - 1 specifies a line through the origin. A model with no intercept can be also specified as y ~ x + 0 or y ~ 0 + x.
While formulae usually involve just variable and factor names, they can also involve arithmetic expressions. The formula log(y) ~ a + log(x) is quite legal.
Note that the operators ~, +, ::, ^ are only available in Scala API.

See Also:

Serialized Form

Constructor Summary

Constructors
Constructor and Description

Formula(Term response, Term... predictors)
Constructor.

Constructors
Constructor and Description
`Formula(Term response, Term... predictors)` Constructor.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Tuple`	`apply(Tuple t)` Apply the formula on a tuple to generate the model data.
`StructType`	`bind(StructType inputSchema)` Binds the formula to a schema and returns the schema of predictors.
`boolean`	`equals(java.lang.Object o)`
`Formula`	`expand(StructType inputSchema)` Expands the Dot and FactorCrossing terms on the given schema.
`DataFrame`	`frame(DataFrame df)` Returns a data frame of predictors and optionally response variable (if input data frame has the related variable(s)).
`static Formula`	`lhs(java.lang.String lhs)` Factory method.
`static Formula`	`lhs(Term lhs)` Factory method.
`Matrix`	`matrix(DataFrame df)` Returns the design matrix of predictors.
`Matrix`	`matrix(DataFrame df, boolean bias)` Returns the design matrix of predictors.
`static Formula`	`of(java.lang.String response, java.lang.String... predictors)` Factory method.
`static Formula`	`of(java.lang.String response, Term... predictors)` Factory method.
`static Formula`	`of(Term response, Term... predictors)` Factory method.
`Term[]`	`predictors()` Returns the predictors.
`Term`	`response()` Returns the response term.
`static Formula`	`rhs(java.lang.String... predictors)` Factory method.
`static Formula`	`rhs(Term... predictors)` Factory method.
`java.lang.String`	`toString()`
`DataFrame`	`x(DataFrame df)` Returns a data frame of predictors.
`Tuple`	`x(Tuple t)` Apply the formula on a tuple to generate the predictors data.
`BaseVector`	`y(DataFrame df)` Returns the response vector.
`double`	`y(Tuple t)` Returns the real-valued response value.
`int`	`yint(Tuple t)` Returns the integer-valued response value.

Methods inherited from class java.lang.Object
clone, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - Formula
```
public Formula(Term response,
               Term... predictors)
```
    Constructor.
    
    Parameters:
    
    response - the left-hand side of formula, i.e. dependent variable.
    
    predictors - the right-hand side of formula, i.e. independent/predictor variables.
- Method Detail
  - predictors
```
public Term[] predictors()
```
    Returns the predictors.
  - response
```
public Term response()
```
    Returns the response term.
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object
  - equals
```
public boolean equals(java.lang.Object o)
```
    Overrides:
    
    equals in class java.lang.Object
  - lhs
```
public static Formula lhs(java.lang.String lhs)
```
    Factory method. The predictors will be all the columns not otherwise in the formula in the context of a data frame.
    
    Parameters:
    
    lhs - the left-hand side of formula, i.e. dependent variable.
  - lhs
```
public static Formula lhs(Term lhs)
```
    Factory method. The predictors will be all the columns not otherwise in the formula in the context of a data frame.
    
    Parameters:
    
    lhs - the left-hand side of formula, i.e. dependent variable.
  - rhs
```
public static Formula rhs(java.lang.String... predictors)
```
    Factory method. No response variable.
    
    Parameters:
    
    predictors - the right-hand side of formula, i.e. independent/predictor variables.
  - rhs
```
public static Formula rhs(Term... predictors)
```
    Factory method. No response variable.
    
    Parameters:
    
    predictors - the right-hand side of formula, i.e. independent/predictor variables.
  - of
```
public static Formula of(java.lang.String response,
                         java.lang.String... predictors)
```
    Factory method.
    
    Parameters:
    
    response - the left-hand side of formula, i.e. dependent variable.
    
    predictors - the right-hand side of formula, i.e. independent/predictor variables.
  - of
```
public static Formula of(java.lang.String response,
                         Term... predictors)
```
    Factory method.
    
    Parameters:
    
    response - the left-hand side of formula, i.e. dependent variable.
    
    predictors - the right-hand side of formula, i.e. independent/predictor variables.
  - of
```
public static Formula of(Term response,
                         Term... predictors)
```
    Factory method.
    
    Parameters:
    
    response - the left-hand side of formula, i.e. dependent variable.
    
    predictors - the right-hand side of formula, i.e. independent/predictor variables.
  - expand
```
public Formula expand(StructType inputSchema)
```
    Expands the Dot and FactorCrossing terms on the given schema.
    
    Parameters:
    
    inputSchema - the schema to expand on
  - bind
```
public StructType bind(StructType inputSchema)
```
    Binds the formula to a schema and returns the schema of predictors.
    
    Parameters:
    
    inputSchema - the schema to bind with
  - apply
```
public Tuple apply(Tuple t)
```
    Apply the formula on a tuple to generate the model data.
  - x
```
public Tuple x(Tuple t)
```
    Apply the formula on a tuple to generate the predictors data.
  - frame
```
public DataFrame frame(DataFrame df)
```
    Returns a data frame of predictors and optionally response variable (if input data frame has the related variable(s)).
    
    Parameters:
    
    df - The input DataFrame.
  - x
```
public DataFrame x(DataFrame df)
```
    Returns a data frame of predictors.
    
    Parameters:
    
    df - The input DataFrame.
  - matrix
```
public Matrix matrix(DataFrame df)
```
    Returns the design matrix of predictors. All categorical variables will be dummy encoded. If the formula doesn't has an Intercept term, the bias column will be included. Otherwise, it is based on the setting of Intercept term.
    
    Parameters:
    
    df - The input DataFrame.
  - matrix
```
public Matrix matrix(DataFrame df,
                     boolean bias)
```
    Returns the design matrix of predictors. All categorical variables will be dummy encoded.
    
    Parameters:
    
    df - The input DataFrame.
    
    bias - If true, include the bias column.
  - y
```
public BaseVector y(DataFrame df)
```
    Returns the response vector.
    
    Parameters:
    
    df - The input DataFrame.
  - y
```
public double y(Tuple t)
```
    Returns the real-valued response value.
  - yint
```
public int yint(Tuple t)
```
    Returns the integer-valued response value.

Class Formula

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Formula

Method Detail

predictors

response

toString

equals

lhs

lhs

rhs

rhs

of

of

of

expand

bind

apply

x

frame

x

matrix

matrix

y

y

yint