# patsy API reference¶

This is a complete reference for everything you get when you import patsy.

## Basic API¶

patsy.dmatrix(formula_like, data={}, eval_env=0, NA_action='drop', return_type='matrix')

Construct a single design matrix given a formula_like and data.

Parameters: formula_like – An object that can be used to construct a design matrix. See below. data – A dict-like object that can be used to look up variables referenced in formula_like. eval_env – Either a EvalEnvironment which will be used to look up any variables referenced in formula_like that cannot be found in data, or else a depth represented as an integer which will be passed to EvalEnvironment.capture(). eval_env=0 means to use the context of the function calling dmatrix() for lookups. If calling this function from a library, you probably want eval_env=1, which means that variables should be resolved in your caller’s namespace. NA_action – What to do with rows that contain missing values. You can "drop" them, "raise" an error, or for customization, pass an NAAction object. See NAAction for details on what values count as ‘missing’ (and how to alter this). return_type – Either "matrix" or "dataframe". See below.

The formula_like can take a variety of forms. You can use any of the following:

Regardless of the input, the return type is always either:

The actual contents of the design matrix is identical in both cases, and in both cases a DesignInfo object will be available in a .design_info attribute on the return value. However, for return_type="dataframe", any pandas indexes on the input (either in data or directly passed through formula_like) will be preserved, which may be useful for e.g. time-series models.

New in version 0.2.0: The NA_action argument.

patsy.dmatrices(formula_like, data={}, eval_env=0, NA_action='drop', return_type='matrix')

Construct two design matrices given a formula_like and data.

This function is identical to dmatrix(), except that it requires (and returns) two matrices instead of one. By convention, the first matrix is the “outcome” or “y” data, and the second is the “predictor” or “x” data.

See dmatrix() for details.

patsy.incr_dbuilders(formula_like, data_iter_maker, eval_env=0, NA_action='drop')

Construct two design matrix builders incrementally from a large data set.

incr_dbuilders() is to incr_dbuilder() as dmatrices() is to dmatrix(). See incr_dbuilder() for details.

patsy.incr_dbuilder(formula_like, data_iter_maker, eval_env=0, NA_action='drop')

Construct a design matrix builder incrementally from a large data set.

Parameters: formula_like – Similar to dmatrix(), except that explicit matrices are not allowed. Must be a formula string, a ModelDesc, a DesignInfo, or an object with a __patsy_get_model_desc__ method. data_iter_maker – A zero-argument callable which returns an iterator over dict-like data objects. This must be a callable rather than a simple iterator because sufficiently complex formulas may require multiple passes over the data (e.g. if there are nested stateful transforms). eval_env – Either a EvalEnvironment which will be used to look up any variables referenced in formula_like that cannot be found in data, or else a depth represented as an integer which will be passed to EvalEnvironment.capture(). eval_env=0 means to use the context of the function calling incr_dbuilder() for lookups. If calling this function from a library, you probably want eval_env=1, which means that variables should be resolved in your caller’s namespace. NA_action – An NAAction object or string, used to determine what values count as ‘missing’ for purposes of determining the levels of categorical factors.

Tip: for data_iter_maker, write a generator like:

def iter_maker():
for data_chunk in my_data_store:
yield data_chunk


and pass iter_maker (not iter_maker()).

New in version 0.2.0: The NA_action argument.

exception patsy.PatsyError(message, origin=None)

This is the main error type raised by Patsy functions.

In addition to the usual Python exception features, you can pass a second argument to this function specifying the origin of the error; this is included in any error message, and used to help the user locate errors arising from malformed formulas. This second argument should be an Origin object, or else an arbitrary object with a .origin attribute. (If it is neither of these things, then it will simply be ignored.)

For ordinary display to the user with default formatting, use str(exc). If you want to do something cleverer, you can use the .message and .origin attributes directly. (The latter may be None.)

## Convenience utilities¶

patsy.balanced(factor_name=num_levels[, factor_name=num_levels, ..., repeat=1])

Create simple balanced factorial designs for testing.

Given some factor names and the number of desired levels for each, generates a balanced factorial design in the form of a data dictionary. For example:

In [1]: balanced(a=2, b=3)
Out[1]:
{'a': ['a1', 'a1', 'a1', 'a2', 'a2', 'a2'],
'b': ['b1', 'b2', 'b3', 'b1', 'b2', 'b3']}


By default it produces exactly one instance of each combination of levels, but if you want multiple replicates this can be accomplished via the repeat argument:

In [2]: balanced(a=2, b=2, repeat=2)
Out[2]:
{'a': ['a1', 'a1', 'a2', 'a2', 'a1', 'a1', 'a2', 'a2'],
'b': ['b1', 'b2', 'b1', 'b2', 'b1', 'b2', 'b1', 'b2']}

patsy.demo_data(*names, nlevels=2, min_rows=5)

Create simple categorical/numerical demo data.

Pass in a set of variable names, and this function will return a simple data set using those variable names.

Names whose first letter falls in the range “a” through “m” will be made categorical (with nlevels levels). Those that start with a “p” through “z” are numerical.

We attempt to produce a balanced design on the categorical variables, repeating as necessary to generate at least min_rows data points. Categorical variables are returned as a list of strings.

Numerical data is generated by sampling from a normal distribution. A fixed random seed is used, so that identical calls to demo_data() will produce identical results. Numerical data is returned in a numpy array.

Example:

class patsy.DesignInfo(column_names, factor_infos=None, term_codings=None)

This is the main object that Patsy uses to pass metadata about a design matrix to statistical libraries, in order to allow further downstream processing like intelligent tests, prediction on new data, etc. Usually encountered as the .design_info attribute on design matrices.

Here’s an example of the most common way to get a DesignInfo:

In [3]: mat = dmatrix("a + x", demo_data("a", "x", nlevels=3))

In [4]: di = mat.design_info

column_names

The names of each column, represented as a list of strings in the proper order. Guaranteed to exist.

In [5]: di.column_names
Out[5]: ['Intercept', 'a[T.a2]', 'a[T.a3]', 'x']

column_name_indexes

An OrderedDict mapping column names (as strings) to column indexes (as integers). Guaranteed to exist and to be sorted from low to high.

In [6]: di.column_name_indexes
Out[6]: OrderedDict([('Intercept', 0), ('a[T.a2]', 1), ('a[T.a3]', 2), ('x', 3)])

term_names

The names of each term, represented as a list of strings in the proper order. Guaranteed to exist. There is a one-to-many relationship between columns and terms – each term generates one or more columns.

In [7]: di.term_names
Out[7]: ['Intercept', 'a', 'x']

term_name_slices

An OrderedDict mapping term names (as strings) to Python slice() objects indicating which columns correspond to each term. Guaranteed to exist. The slices are guaranteed to be sorted from left to right and to cover the whole range of columns with no overlaps or gaps.

In [8]: di.term_name_slices
Out[8]:
OrderedDict([('Intercept', slice(0, 1, None)),
('a', slice(1, 3, None)),
('x', slice(3, 4, None))])

terms

A list of Term objects representing each term. May be None, for example if a user passed in a plain preassembled design matrix rather than using the Patsy machinery.

In [9]: di.terms
Out[9]: [Term([]), Term([EvalFactor('a')]), Term([EvalFactor('x')])]

In [10]: [term.name() for term in di.terms]
Out[10]: ['Intercept', 'a', 'x']

term_slices

An OrderedDict mapping Term objects to Python slice() objects indicating which columns correspond to which terms. Like terms, this may be None.

In [11]: di.term_slices
Out[11]:
OrderedDict([(Term([]), slice(0, 1, None)),
(Term([EvalFactor('a')]), slice(1, 3, None)),
(Term([EvalFactor('x')]), slice(3, 4, None))])

factor_infos

A dict mapping factor objects to FactorInfo objects providing information about each factor. Like terms, this may be None.

In [12]: di.factor_infos
Out[12]:
{EvalFactor('a'): FactorInfo(factor=EvalFactor('a'),
type='categorical',
state=<factor state>,
categories=('a1', 'a2', 'a3')),
EvalFactor('x'): FactorInfo(factor=EvalFactor('x'),
type='numerical',
state=<factor state>,
num_columns=1)}

term_codings

An OrderedDict mapping each Term object to a list of SubtermInfo objects which together describe how this term is encoded in the final design matrix. Like terms, this may be None.

In [13]: di.term_codings
Out[13]:
OrderedDict([(Term([]),
[SubtermInfo(factors=(), contrast_matrices={}, num_columns=1)]),
(Term([EvalFactor('a')]),
[SubtermInfo(factors=(EvalFactor('a'),),
contrast_matrices={EvalFactor('a'): ContrastMatrix(array([[ 0.,  0.],
[ 1.,  0.],
[ 0.,  1.]]),
['[T.a2]',
'[T.a3]'])},
num_columns=2)]),
(Term([EvalFactor('x')]),
[SubtermInfo(factors=(EvalFactor('x'),),
contrast_matrices={},
num_columns=1)])])

builder

In versions of patsy before 0.4.0, this returned a DesignMatrixBuilder object which could be passed to build_design_matrices(). Starting in 0.4.0, build_design_matrices() now accepts DesignInfo objects directly, and writing f(design_info.builder) is now a deprecated alias for simply writing f(design_info).

A number of convenience methods are also provided that take advantage of the above metadata:

describe()

Example:

In [1]: y, X = dmatrices("y ~ x1 + x2", demo_data("y", "x1", "x2"))

In [2]: y.design_info.describe()
Out[2]: 'y'

In [3]: X.design_info.describe()
Out[3]: '1 + x1 + x2'


Warning

There is no guarantee that the strings returned by this function can be parsed as formulas, or that if they can be parsed as a formula that they will produce a model equivalent to the one you started with. This function produces a best-effort description intended for humans to read.

linear_constraint(constraint_likes)

Construct a linear constraint in matrix form from a (possibly symbolic) description.

Possible inputs:

• A dictionary which is taken as a set of equality constraint. Keys can be either string column names, or integer column indexes.
• A string giving a arithmetic expression referring to the matrix columns by name.
• A list of such strings which are ANDed together.
• A tuple (A, b) where A and b are array_likes, and the constraint is Ax = b. If necessary, these will be coerced to the proper dimensionality by appending dimensions with size 1.

The string-based language has the standard arithmetic operators, / * + - and parentheses, plus “=” is used for equality and “,” is used to AND together multiple constraint equations within a string. You can If no = appears in some expression, then that expression is assumed to be equal to zero. Division is always float-based, even if __future__.true_division isn’t in effect.

Returns a LinearConstraint object.

Examples:

di = DesignInfo(["x1", "x2", "x3"])

# Equivalent ways to write x1 == 0:
di.linear_constraint({"x1": 0})  # by name
di.linear_constraint({0: 0})  # by index
di.linear_constraint("x1 = 0")  # string based
di.linear_constraint("x1")  # can leave out "= 0"
di.linear_constraint("2 * x1 = (x1 + 2 * x1) / 3")
di.linear_constraint(([1, 0, 0], 0))  # constraint matrices

# Equivalent ways to write x1 == 0 and x3 == 10
di.linear_constraint({"x1": 0, "x3": 10})
di.linear_constraint({0: 0, 2: 10})
di.linear_constraint({0: 0, "x3": 10})
di.linear_constraint("x1 = 0, x3 = 10")
di.linear_constraint("x1, x3 = 10")
di.linear_constraint(["x1", "x3 = 0"])  # list of strings
di.linear_constraint("x1 = 0, x3 - 10 = x1")
di.linear_constraint([[1, 0, 0], [0, 0, 1]], [0, 10])

# You can also chain together equalities, just like Python:
di.linear_constraint("x1 = x2 = 3")

slice(columns_specifier)

Locate a subset of design matrix columns, specified symbolically.

A patsy design matrix has two levels of structure: the individual columns (which are named), and the terms in the formula that generated those columns. This is a one-to-many relationship: a single term may span several columns. This method provides a user-friendly API for locating those columns.

(While we talk about columns here, this is probably most useful for indexing into other arrays that are derived from the design matrix, such as regression coefficients or covariance matrices.)

The columns_specifier argument can take a number of forms:

• A term name
• A column name
• A Term object
• An integer giving a raw index
• A raw slice object

In all cases, a Python slice() object is returned, which can be used directly for indexing.

Example:

y, X = dmatrices("y ~ a", demo_data("y", "a", nlevels=3))
betas = np.linalg.lstsq(X, y)[0]
a_betas = betas[X.design_info.slice("a")]


(If you want to look up a single individual column by name, use design_info.column_name_indexes[name].)

subset(which_terms)

Create a new DesignInfo for design matrices that contain a subset of the terms that the current DesignInfo does.

For example, if design_info has terms x, y, and z, then:

design_info2 = design_info.subset(["x", "z"])


will return a new DesignInfo that can be used to construct design matrices with only the columns corresponding to the terms x and z. After we do this, then in general these two expressions will return the same thing (here we assume that x, y, and z each generate a single column of the output):

build_design_matrix([design_info], data)[0][:, [0, 2]]
build_design_matrix([design_info2], data)[0]


However, a critical difference is that in the second case, data need not contain any values for y. This is very useful when doing prediction using a subset of a model, in which situation R usually forces you to specify dummy values for y.

If using a formula to specify the terms to include, remember that like any formula, the intercept term will be included by default, so use 0 or -1 in your formula if you want to avoid this.

This method can also be used to reorder the terms in your design matrix, in case you want to do that for some reason. I can’t think of any.

Note that this method will generally not produce the same result as creating a new model directly. Consider these DesignInfo objects:

design1 = dmatrix("1 + C(a)", data)
design2 = design1.subset("0 + C(a)")
design3 = dmatrix("0 + C(a)", data)


Here design2 and design3 will both produce design matrices that contain an encoding of C(a) without any intercept term. But design3 uses a full-rank encoding for the categorical term C(a), while design2 uses the same reduced-rank encoding as design1.

Parameters: which_terms – The terms which should be kept in the new DesignMatrixBuilder. If this is a string, then it is parsed as a formula, and then the names of the resulting terms are taken as the terms to keep. If it is a list, then it can contain a mixture of term names (as strings) and Term objects.
classmethod from_array(array_like, default_column_prefix='column')

Find or construct a DesignInfo appropriate for a given array_like.

If the input array_like already has a .design_info attribute, then it will be returned. Otherwise, a new DesignInfo object will be constructed, using names either taken from the array_like (e.g., for a pandas DataFrame with named columns), or constructed using default_column_prefix.

This is how dmatrix() (for example) creates a DesignInfo object if an arbitrary matrix is passed in.

Parameters: array_like – An ndarray or pandas container. default_column_prefix – If it’s necessary to invent column names, then this will be used to construct them. a DesignInfo object
class patsy.FactorInfo(factor, type, state, num_columns=None, categories=None)

A FactorInfo object is a simple class that provides some metadata about the role of a factor within a model. DesignInfo.factor_infos is a dictionary which maps factor objects to FactorInfo objects for each factor in the model.

New in version 0.4.0.

Attributes:

factor

The factor object being described.

type

The type of the factor – either the string "numerical" or the string "categorical".

state

An opaque object which holds the state needed to evaluate this factor on new data (e.g., for prediction). See factor_protocol.eval().

num_columns

For numerical factors, the number of columns this factor produces. For categorical factors, this attribute will always be None.

categories

For categorical factors, a tuple of the possible categories this factor takes on, in order. For numerical factors, this attribute will always be None.

class patsy.SubtermInfo(factors, contrast_matrices, num_columns)

A SubtermInfo object is a simple metadata container describing a single primitive interaction and how it is coded in our design matrix. Our final design matrix is produced by coding each primitive interaction in order from left to right, and then stacking the resulting columns. For each Term, we have one or more of these objects which describe how that term is encoded. DesignInfo.term_codings is a dictionary which maps term objects to lists of SubtermInfo objects.

To code a primitive interaction, the following steps are performed:

• Evaluate each factor on the provided data.
• Encode each factor into one or more proto-columns. For numerical factors, these proto-columns are identical to whatever the factor evaluates to; for categorical factors, they are encoded using a specified contrast matrix.
• Form all pairwise, elementwise products between proto-columns generated by different factors. (For example, if factor 1 generated proto-columns A and B, and factor 2 generated proto-columns C and D, then our final columns are A * C, B * C, A * D, B * D.)
• The resulting columns are stored directly into the final design matrix.

Sometimes multiple primitive interactions are needed to encode a single term; this occurs, for example, in the formula "1 + a:b" when a and b are categorical. See From terms to matrices for full details.

New in version 0.4.0.

Attributes:

factors

The factors which appear in this subterm’s interaction.

contrast_matrices

A dict mapping factor objects to ContrastMatrix objects, describing how each categorical factor in this interaction is coded.

num_columns

The number of design matrix columns which this interaction generates.

class patsy.DesignMatrix

A simple numpy array subclass that carries design matrix metadata.

design_info

A DesignInfo object containing metadata about this design matrix.

This class also defines a fancy __repr__ method with labeled columns. Otherwise it is identical to a regular numpy ndarray.

Warning

You should never check for this class using isinstance(). Limitations of the numpy API mean that it is impossible to prevent the creation of numpy arrays that have type DesignMatrix, but that are not actually design matrices (and such objects will behave like regular ndarrays in every way). Instead, check for the presence of a .design_info attribute – this will be present only on “real” DesignMatrix objects.

Create a DesignMatrix, or cast an existing matrix to a DesignMatrix.

A call like:

DesignMatrix(my_array)


will convert an arbitrary array_like object into a DesignMatrix.

The return from this function is guaranteed to be a two-dimensional ndarray with a real-valued floating point dtype, and a .design_info attribute which matches its shape. If the design_info argument is not given, then one is created via DesignInfo.from_array() using the given default_column_prefix.

Depending on the input array, it is possible this will pass through its input unchanged, or create a view.

static __new__(cls, input_array, design_info=None, default_column_prefix='column')

Create a DesignMatrix, or cast an existing matrix to a DesignMatrix.

A call like:

DesignMatrix(my_array)


will convert an arbitrary array_like object into a DesignMatrix.

The return from this function is guaranteed to be a two-dimensional ndarray with a real-valued floating point dtype, and a .design_info attribute which matches its shape. If the design_info argument is not given, then one is created via DesignInfo.from_array() using the given default_column_prefix.

Depending on the input array, it is possible this will pass through its input unchanged, or create a view.

## Stateful transforms¶

Patsy comes with a number of stateful transforms built in:

patsy.center(x)

A stateful transform that centers input data, i.e., subtracts the mean.

If input has multiple columns, centers each column separately.

Equivalent to standardize(x, rescale=False)

patsy.standardize(x, center=True, rescale=True, ddof=0)

A stateful transform that standardizes input data, i.e. it subtracts the mean and divides by the sample standard deviation.

Either centering or rescaling or both can be disabled by use of keyword arguments. The ddof argument controls the delta degrees of freedom when computing the standard deviation (cf. numpy.std()). The default of ddof=0 produces the maximum likelihood estimate; use ddof=1 if you prefer the square root of the unbiased estimate of the variance.

If input has multiple columns, standardizes each column separately.

Note

This function computes the mean and standard deviation using a memory-efficient online algorithm, making it suitable for use with large incrementally processed data-sets.

patsy.scale(x, center=True, rescale=True, ddof=0)

An alias for standardize(), for R compatibility.

Finally, this is not itself a stateful transform, but it’s useful if you want to define your own:

patsy.stateful_transform(class_)

Create a stateful transform callable object from a class that fulfills the stateful transform protocol.

## Handling categorical data¶

class patsy.Treatment(reference=None)

Treatment coding (also known as dummy coding).

This is the default coding.

For reduced-rank coding, one level is chosen as the “reference”, and its mean behaviour is represented by the intercept. Each column of the resulting matrix represents the difference between the mean of one level and this reference level.

For full-rank coding, classic “dummy” coding is used, and each column of the resulting matrix represents the mean of the corresponding level.

The reference level defaults to the first level, or can be specified explicitly.

# reduced rank
In [1]: dmatrix("C(a, Treatment)", balanced(a=3))
Out[1]:
DesignMatrix with shape (3, 3)
Intercept  C(a, Treatment)[T.a2]  C(a, Treatment)[T.a3]
1                      0                      0
1                      1                      0
1                      0                      1
Terms:
'Intercept' (column 0)
'C(a, Treatment)' (columns 1:3)

# full rank
In [2]: dmatrix("0 + C(a, Treatment)", balanced(a=3))
Out[2]:
DesignMatrix with shape (3, 3)
C(a, Treatment)[a1]  C(a, Treatment)[a2]  C(a, Treatment)[a3]
1                    0                    0
0                    1                    0
0                    0                    1
Terms:
'C(a, Treatment)' (columns 0:3)

# Setting a reference level
In [3]: dmatrix("C(a, Treatment(1))", balanced(a=3))
Out[3]:
DesignMatrix with shape (3, 3)
Intercept  C(a, Treatment(1))[T.a1]  C(a, Treatment(1))[T.a3]
1                         1                         0
1                         0                         0
1                         0                         1
Terms:
'Intercept' (column 0)
'C(a, Treatment(1))' (columns 1:3)

In [4]: dmatrix("C(a, Treatment('a2'))", balanced(a=3))
Out[4]:
DesignMatrix with shape (3, 3)
Intercept  C(a, Treatment('a2'))[T.a1]  C(a, Treatment('a2'))[T.a3]
1                            1                            0
1                            0                            0
1                            0                            1
Terms:
'Intercept' (column 0)
"C(a, Treatment('a2'))" (columns 1:3)


Equivalent to R contr.treatment. The R documentation suggests that using Treatment(reference=-1) will produce contrasts that are “equivalent to those produced by many (but not all) SAS procedures”.

class patsy.Diff

Backward difference coding.

This coding scheme is useful for ordered factors, and compares the mean of each level with the preceding level. So you get the second level minus the first, the third level minus the second, etc.

For full-rank coding, a standard intercept term is added (which gives the mean value for the first level).

Examples:

# Reduced rank
In [1]: dmatrix("C(a, Diff)", balanced(a=3))
Out[1]:
DesignMatrix with shape (3, 3)
Intercept  C(a, Diff)[D.a1]  C(a, Diff)[D.a2]
1          -0.66667          -0.33333
1           0.33333          -0.33333
1           0.33333           0.66667
Terms:
'Intercept' (column 0)
'C(a, Diff)' (columns 1:3)

# Full rank
In [2]: dmatrix("0 + C(a, Diff)", balanced(a=3))
Out[2]:
DesignMatrix with shape (3, 3)
C(a, Diff)[D.a1]  C(a, Diff)[D.a2]  C(a, Diff)[D.a3]
1          -0.66667          -0.33333
1           0.33333          -0.33333
1           0.33333           0.66667
Terms:
'C(a, Diff)' (columns 0:3)

class patsy.Poly(scores=None)

Orthogonal polynomial contrast coding.

This coding scheme treats the levels as ordered samples from an underlying continuous scale, whose effect takes an unknown functional form which is Taylor-decomposed into the sum of a linear, quadratic, etc. components.

For reduced-rank coding, you get a linear column, a quadratic column, etc., up to the number of levels provided.

For full-rank coding, the same scheme is used, except that the zero-order constant polynomial is also included. I.e., you get an intercept column included as part of your categorical term.

By default the levels are treated as equally spaced, but you can override this by providing a value for the scores argument.

Examples:

# Reduced rank
In [1]: dmatrix("C(a, Poly)", balanced(a=4))
Out[1]:
DesignMatrix with shape (4, 4)
Intercept  C(a, Poly).Linear  C(a, Poly).Quadratic  C(a, Poly).Cubic
1           -0.67082                   0.5          -0.22361
1           -0.22361                  -0.5           0.67082
1            0.22361                  -0.5          -0.67082
1            0.67082                   0.5           0.22361
Terms:
'Intercept' (column 0)
'C(a, Poly)' (columns 1:4)

# Full rank
In [2]: dmatrix("0 + C(a, Poly)", balanced(a=3))
Out[2]:
DesignMatrix with shape (3, 3)
C(a, Poly).Constant  C(a, Poly).Linear  C(a, Poly).Quadratic
1           -0.70711               0.40825
1           -0.00000              -0.81650
1            0.70711               0.40825
Terms:
'C(a, Poly)' (columns 0:3)

# Explicit scores
In [3]: dmatrix("C(a, Poly([1, 2, 10]))", balanced(a=3))
Out[3]:
DesignMatrix with shape (3, 3)
Intercept  C(a, Poly([1, 2, 10])).Linear  C(a, Poly([1, 2, 10])).Quadratic
1                       -0.47782                           0.66208
1                       -0.33447                          -0.74485
1                        0.81229                           0.08276
Terms:
'Intercept' (column 0)
'C(a, Poly([1, 2, 10]))' (columns 1:3)


This is equivalent to R’s contr.poly. (But note that in R, reduced rank encodings are always dummy-coded, regardless of what contrast you have set.)

class patsy.Sum(omit=None)

Deviation coding (also known as sum-to-zero coding).

Compares the mean of each level to the mean-of-means. (In a balanced design, compares the mean of each level to the overall mean.)

For full-rank coding, a standard intercept term is added.

One level must be omitted to avoid redundancy; by default this is the last level, but this can be adjusted via the omit argument.

Warning

There are multiple definitions of ‘deviation coding’ in use. Make sure this is the one you expect before trying to interpret your results!

Examples:

# Reduced rank
In [1]: dmatrix("C(a, Sum)", balanced(a=4))
Out[1]:
DesignMatrix with shape (4, 4)
Intercept  C(a, Sum)[S.a1]  C(a, Sum)[S.a2]  C(a, Sum)[S.a3]
1                1                0                0
1                0                1                0
1                0                0                1
1               -1               -1               -1
Terms:
'Intercept' (column 0)
'C(a, Sum)' (columns 1:4)

# Full rank
In [2]: dmatrix("0 + C(a, Sum)", balanced(a=4))
Out[2]:
DesignMatrix with shape (4, 4)
C(a, Sum)[mean]  C(a, Sum)[S.a1]  C(a, Sum)[S.a2]  C(a, Sum)[S.a3]
1                1                0                0
1                0                1                0
1                0                0                1
1               -1               -1               -1
Terms:
'C(a, Sum)' (columns 0:4)

# Omit a different level
In [3]: dmatrix("C(a, Sum(1))", balanced(a=3))
Out[3]:
DesignMatrix with shape (3, 3)
Intercept  C(a, Sum(1))[S.a1]  C(a, Sum(1))[S.a3]
1                   1                   0
1                  -1                  -1
1                   0                   1
Terms:
'Intercept' (column 0)
'C(a, Sum(1))' (columns 1:3)

In [4]: dmatrix("C(a, Sum('a1'))", balanced(a=3))
Out[4]:
DesignMatrix with shape (3, 3)
Intercept  C(a, Sum('a1'))[S.a2]  C(a, Sum('a1'))[S.a3]
1                     -1                     -1
1                      1                      0
1                      0                      1
Terms:
'Intercept' (column 0)
"C(a, Sum('a1'))" (columns 1:3)


This is equivalent to R’s contr.sum.

class patsy.Helmert

Helmert contrasts.

Compares the second level with the first, the third with the average of the first two, and so on.

For full-rank coding, a standard intercept term is added.

Warning

There are multiple definitions of ‘Helmert coding’ in use. Make sure this is the one you expect before trying to interpret your results!

Examples:

# Reduced rank
In [1]: dmatrix("C(a, Helmert)", balanced(a=4))
Out[1]:
DesignMatrix with shape (4, 4)
Intercept  C(a, Helmert)[H.a2]  C(a, Helmert)[H.a3]  C(a, Helmert)[H.a4]
1                   -1                   -1                   -1
1                    1                   -1                   -1
1                    0                    2                   -1
1                    0                    0                    3
Terms:
'Intercept' (column 0)
'C(a, Helmert)' (columns 1:4)

# Full rank
In [2]: dmatrix("0 + C(a, Helmert)", balanced(a=4))
Out[2]:
DesignMatrix with shape (4, 4)
Columns:
['C(a, Helmert)[H.intercept]',
'C(a, Helmert)[H.a2]',
'C(a, Helmert)[H.a3]',
'C(a, Helmert)[H.a4]']
Terms:
'C(a, Helmert)' (columns 0:4)
(to view full data, use np.asarray(this_obj))


This is equivalent to R’s contr.helmert.

class patsy.ContrastMatrix(matrix, column_suffixes)

A simple container for a matrix used for coding categorical factors.

Attributes:

matrix

A 2d ndarray, where each column corresponds to one column of the resulting design matrix, and each row contains the entries for a single categorical variable level. Usually n-by-n for a full rank coding or n-by-(n-1) for a reduced rank coding, though other options are possible.

column_suffixes

A list of strings to be appended to the factor name, to produce the final column names. E.g. for treatment coding the entries will look like "[T.level1]".

## Spline regression¶

patsy.bs(x, df=None, knots=None, degree=3, include_intercept=False, lower_bound=None, upper_bound=None)

Generates a B-spline basis for x, allowing non-linear fits. The usual usage is something like:

y ~ 1 + bs(x, 4)


to fit y as a smooth function of x, with 4 degrees of freedom given to the smooth.

Parameters: df – The number of degrees of freedom to use for this spline. The return value will have this many columns. You must specify at least one of df and knots. knots – The interior knots to use for the spline. If unspecified, then equally spaced quantiles of the input data are used. You must specify at least one of df and knots. degree – The degree of the spline to use. include_intercept – If True, then the resulting spline basis will span the intercept term (i.e., the constant function). If False (the default) then this will not be the case, which is useful for avoiding overspecification in models that include multiple spline terms and/or an intercept term. lower_bound – The lower exterior knot location. upper_bound – The upper exterior knot location.

A spline with degree=0 is piecewise constant with breakpoints at each knot, and the default knot positions are quantiles of the input. So if you find yourself in the situation of wanting to quantize a continuous variable into num_bins equal-sized bins with a constant effect across each bin, you can use bs(x, num_bins - 1, degree=0). (The - 1 is because one degree of freedom will be taken by the intercept; alternatively, you could leave the intercept term out of your model and use bs(x, num_bins, degree=0, include_intercept=True).

A spline with degree=1 is piecewise linear with breakpoints at each knot.

The default is degree=3, which gives a cubic b-spline.

This is a stateful transform (for details see Stateful transforms). If knots, lower_bound, or upper_bound are not specified, they will be calculated from the data and then the chosen values will be remembered and re-used for prediction from the fitted model.

Using this function requires scipy be installed.

Note

This function is very similar to the R function of the same name. In cases where both return output at all (e.g., R’s bs will raise an error if degree=0, while patsy’s will not), they should produce identical output given identical input and parameter settings.

Warning

I’m not sure on what the proper handling of points outside the lower/upper bounds is, so for now attempting to evaluate a spline basis at such points produces an error. Patches gratefully accepted.

New in version 0.2.0.

patsy.cr(x, df=None, knots=None, lower_bound=None, upper_bound=None, constraints=None)

Generates a natural cubic spline basis for x (with the option of absorbing centering or more general parameters constraints), allowing non-linear fits. The usual usage is something like:

y ~ 1 + cr(x, df=5, constraints='center')


to fit y as a smooth function of x, with 5 degrees of freedom given to the smooth, and centering constraint absorbed in the resulting design matrix. Note that in this example, due to the centering constraint, 6 knots will get computed from the input data x to achieve 5 degrees of freedom.

Note

This function reproduce the cubic regression splines ‘cr’ and ‘cs’ as implemented in the R package ‘mgcv’ (GAM modelling).

Parameters: df – The number of degrees of freedom to use for this spline. The return value will have this many columns. You must specify at least one of df and knots. knots – The interior knots to use for the spline. If unspecified, then equally spaced quantiles of the input data are used. You must specify at least one of df and knots. lower_bound – The lower exterior knot location. upper_bound – The upper exterior knot location. constraints – Either a 2-d array defining general linear constraints (that is np.dot(constraints, betas) is zero, where betas denotes the array of initial parameters, corresponding to the initial unconstrained design matrix), or the string 'center' indicating that we should apply a centering constraint (this constraint will be computed from the input data, remembered and re-used for prediction from the fitted model). The constraints are absorbed in the resulting design matrix which means that the model is actually rewritten in terms of unconstrained parameters. For more details see Spline regression.

This is a stateful transforms (for details see Stateful transforms). If knots, lower_bound, or upper_bound are not specified, they will be calculated from the data and then the chosen values will be remembered and re-used for prediction from the fitted model.

Using this function requires scipy be installed.

New in version 0.3.0.

patsy.cc(x, df=None, knots=None, lower_bound=None, upper_bound=None, constraints=None)

Generates a cyclic cubic spline basis for x (with the option of absorbing centering or more general parameters constraints), allowing non-linear fits. The usual usage is something like:

y ~ 1 + cc(x, df=7, constraints='center')


to fit y as a smooth function of x, with 7 degrees of freedom given to the smooth, and centering constraint absorbed in the resulting design matrix. Note that in this example, due to the centering and cyclic constraints, 9 knots will get computed from the input data x to achieve 7 degrees of freedom.

Note

This function reproduce the cubic regression splines ‘cc’ as implemented in the R package ‘mgcv’ (GAM modelling).

Parameters: df – The number of degrees of freedom to use for this spline. The return value will have this many columns. You must specify at least one of df and knots. knots – The interior knots to use for the spline. If unspecified, then equally spaced quantiles of the input data are used. You must specify at least one of df and knots. lower_bound – The lower exterior knot location. upper_bound – The upper exterior knot location. constraints – Either a 2-d array defining general linear constraints (that is np.dot(constraints, betas) is zero, where betas denotes the array of initial parameters, corresponding to the initial unconstrained design matrix), or the string 'center' indicating that we should apply a centering constraint (this constraint will be computed from the input data, remembered and re-used for prediction from the fitted model). The constraints are absorbed in the resulting design matrix which means that the model is actually rewritten in terms of unconstrained parameters. For more details see Spline regression.

This is a stateful transforms (for details see Stateful transforms). If knots, lower_bound, or upper_bound are not specified, they will be calculated from the data and then the chosen values will be remembered and re-used for prediction from the fitted model.

Using this function requires scipy be installed.

New in version 0.3.0.

patsy.te(s1, .., sn, constraints=None)

Generates smooth of several covariates as a tensor product of the bases of marginal univariate smooths s1, .., sn. The marginal smooths are required to transform input univariate data into some kind of smooth functions basis producing a 2-d array output with the (i, j) element corresponding to the value of the j th basis function at the i th data point. The resulting basis dimension is the product of the basis dimensions of the marginal smooths. The usual usage is something like:

y ~ 1 + te(cr(x1, df=5), cc(x2, df=6), constraints='center')


to fit y as a smooth function of both x1 and x2, with a natural cubic spline for x1 marginal smooth and a cyclic cubic spline for x2 (and centering constraint absorbed in the resulting design matrix).

Parameters: constraints – Either a 2-d array defining general linear constraints (that is np.dot(constraints, betas) is zero, where betas denotes the array of initial parameters, corresponding to the initial unconstrained design matrix), or the string 'center' indicating that we should apply a centering constraint (this constraint will be computed from the input data, remembered and re-used for prediction from the fitted model). The constraints are absorbed in the resulting design matrix which means that the model is actually rewritten in terms of unconstrained parameters. For more details see Spline regression.

Using this function requires scipy be installed.

Note

This function reproduce the tensor product smooth ‘te’ as implemented in the R package ‘mgcv’ (GAM modelling). See also ‘Generalized Additive Models’, Simon N. Wood, 2006, pp 158-163

New in version 0.3.0.

## Working with formulas programmatically¶

class patsy.Term(factors)

The interaction between a collection of factor objects.

This is one of the basic types used in representing formulas, and corresponds to an expression like "a:b:c" in a formula string. For details, see How formulas work and Model specification for experts and computers.

Terms are hashable and compare by value.

Attributes:

factors

A tuple of factor objects.

patsy.INTERCEPT

This is a pre-instantiated zero-factors Term object representing the intercept, useful for making your code clearer. Do remember though that this is not a singleton object, i.e., you should compare against it using ==, not is.

class patsy.LookupFactor(varname, force_categorical=False, contrast=None, levels=None, origin=None)

A simple factor class that simply looks up a named entry in the given data.

Useful for programatically constructing formulas, and as a simple example of the factor protocol. For details see Model specification for experts and computers.

Example:

dmatrix(ModelDesc([], [Term([LookupFactor("x")])]), {"x": [1, 2, 3]})

Parameters: varname – The name of this variable; used as a lookup key in the passed in data dictionary/DataFrame/whatever. force_categorical – If True, then treat this factor as categorical. (Equivalent to using C() in a regular formula, but of course you can’t do that with a LookupFactor. contrast – If given, the contrast to use; see C(). (Requires force_categorical=True.) levels – If given, the categorical levels; see C(). (Requires force_categorical=True.) origin – Either None, or the Origin of this factor for use in error reporting.

New in version 0.2.0: The force_categorical and related arguments.

class patsy.EvalFactor(code, origin=None)

A factor class that executes arbitrary Python code and supports stateful transforms.

Parameters: code – A string containing a Python expression, that will be evaluated to produce this factor’s value.

This is the standard factor class that is used when parsing formula strings and implements the standard stateful transform processing. See Stateful transforms and Model specification for experts and computers.

Two EvalFactor’s are considered equal (e.g., for purposes of redundancy detection) if they contain the same token stream. Basically this means that the source code must be identical except for whitespace:

assert EvalFactor("a + b") == EvalFactor("a+b")
assert EvalFactor("a + b") != EvalFactor("b + a")

class patsy.ModelDesc(lhs_termlist, rhs_termlist)

A simple container representing the termlists parsed from a formula.

This is a simple container object which has exactly the same representational power as a formula string, but is a Python object instead. You can construct one by hand, and pass it to functions like dmatrix() or incr_dbuilder() that are expecting a formula string, but without having to do any messy string manipulation. For details see Model specification for experts and computers.

Attributes:

lhs_termlist
rhs_termlist

Two termlists representing the left- and right-hand sides of a formula, suitable for passing to design_matrix_builders().

## Working with the Python execution environment¶

class patsy.EvalEnvironment(namespaces, flags=0)

Represents a Python execution environment.

Encapsulates a namespace for variable lookup and set of __future__ flags.

classmethod capture(eval_env=0, reference=0)

Capture an execution environment from the stack.

If eval_env is already an EvalEnvironment, it is returned unchanged. Otherwise, we walk up the stack by eval_env + reference steps and capture that function’s evaluation environment.

For eval_env=0 and reference=0, the default, this captures the stack frame of the function that calls capture(). If eval_env + reference is 1, then we capture that function’s caller, etc.

This somewhat complicated calling convention is designed to be convenient for functions which want to capture their caller’s environment by default, but also allow explicit environments to be specified. See the second example.

Example:

x = 1
this_env = EvalEnvironment.capture()
assert this_env.namespace["x"] == 1
def child_func():
return EvalEnvironment.capture(1)
this_env_from_child = child_func()
assert this_env_from_child.namespace["x"] == 1


Example:

# This function can be used like:
#   my_model(formula_like, data)
#     -> evaluates formula_like in caller's environment
#   my_model(formula_like, data, eval_env=1)
#     -> evaluates formula_like in caller's caller's environment
#   my_model(formula_like, data, eval_env=my_env)
#     -> evaluates formula_like in environment 'my_env'
def my_model(formula_like, data, eval_env=0):
eval_env = EvalEnvironment.capture(eval_env, reference=1)
return model_setup_helper(formula_like, data, eval_env)


This is how dmatrix() works.

eval(expr, source_name='<string>', inner_namespace={})

Evaluate some Python code in the encapsulated environment.

Parameters: expr – A string containing a Python expression. source_name – A name for this string, for use in tracebacks. inner_namespace – A dict-like object that will be checked first when expr attempts to access any variables. The value of expr.
namespace

A dict-like object that can be used to look up variables accessible from the encapsulated environment.

subset(names)

Creates a new, flat EvalEnvironment that contains only the variables specified.

with_outer_namespace(outer_namespace)

Return a new EvalEnvironment with an extra namespace added.

This namespace will be used only for variables that are not found in any existing namespace, i.e., it is “outside” them all.

## Building design matrices¶

patsy.design_matrix_builders(termlists, data_iter_maker, eval_env, NA_action='drop')

Construct several DesignInfo objects from termlists.

This is one of Patsy’s fundamental functions. This function and build_design_matrices() together form the API to the core formula interpretation machinery.

Parameters: termlists – A list of termlists, where each termlist is a list of Term objects which together specify a design matrix. data_iter_maker – A zero-argument callable which returns an iterator over dict-like data objects. This must be a callable rather than a simple iterator because sufficiently complex formulas may require multiple passes over the data (e.g. if there are nested stateful transforms). eval_env – Either a EvalEnvironment which will be used to look up any variables referenced in termlists that cannot be found in data_iter_maker, or else a depth represented as an integer which will be passed to EvalEnvironment.capture(). eval_env=0 means to use the context of the function calling design_matrix_builders() for lookups. If calling this function from a library, you probably want eval_env=1, which means that variables should be resolved in your caller’s namespace. NA_action – An NAAction object or string, used to determine what values count as ‘missing’ for purposes of determining the levels of categorical factors. A list of DesignInfo objects, one for each termlist passed in.

This function performs zero or more iterations over the data in order to sniff out any necessary information about factor types, set up stateful transforms, pick column names, etc.

See How formulas work for details.

New in version 0.2.0: The NA_action argument.

New in version 0.4.0: The eval_env argument.

patsy.build_design_matrices(design_infos, data, NA_action='drop', return_type='matrix', dtype=dtype('float64'))

Construct several design matrices from DesignMatrixBuilder objects.

This is one of Patsy’s fundamental functions. This function and design_matrix_builders() together form the API to the core formula interpretation machinery.

Parameters: design_infos – A list of DesignInfo objects describing the design matrices to be built. data – A dict-like object which will be used to look up data. NA_action – What to do with rows that contain missing values. You can "drop" them, "raise" an error, or for customization, pass an NAAction object. See NAAction for details on what values count as ‘missing’ (and how to alter this). return_type – Either "matrix" or "dataframe". See below. dtype – The dtype of the returned matrix. Useful if you want to use single-precision or extended-precision.

This function returns either a list of DesignMatrix objects (for return_type="matrix") or a list of pandas.DataFrame objects (for return_type="dataframe"). In both cases, all returned design matrices will have .design_info attributes containing the appropriate DesignInfo objects.

Note that unlike design_matrix_builders(), this function takes only a simple data argument, not any kind of iterator. That’s because this function doesn’t need a global view of the data – everything that depends on the whole data set is already encapsulated in the design_infos. If you are incrementally processing a large data set, simply call this function for each chunk.

Index handling: This function always checks for indexes in the following places:

If multiple indexes are found, they must be identical (same values in the same order). If no indexes are found, then a default index is generated using np.arange(num_rows). One way or another, we end up with a single index for all the data. If return_type="dataframe", then this index is used as the index of the returned DataFrame objects. Examining this index makes it possible to determine which rows were removed due to NAs.

Determining the number of rows in design matrices: This is not as obvious as it might seem, because it’s possible to have a formula like “~ 1” that doesn’t depend on the data (it has no factors). For this formula, it’s obvious what every row in the design matrix should look like (just the value 1); but, how many rows like this should there be? To determine the number of rows in a design matrix, this function always checks in the following places:

• If data is a pandas.DataFrame, then its number of rows.
• The number of entries in any factors present in any of the design
• matrices being built.

All these values much match. In particular, if this function is called to generate multiple design matrices at once, then they must all have the same number of rows.

New in version 0.2.0: The NA_action argument.

## Missing values¶

class patsy.NAAction(on_NA='drop', NA_types=['None', 'NaN'])

An NAAction object defines a strategy for handling missing data.

“NA” is short for “Not Available”, and is used to refer to any value which is somehow unmeasured or unavailable. In the long run, it is devoutly hoped that numpy will gain first-class missing value support. Until then, we work around this lack as best we’re able.

There are two parts to this: First, we have to determine what counts as missing data. For numerical data, the default is to treat NaN values (e.g., numpy.nan) as missing. For categorical data, the default is to treat NaN values, and also the Python object None, as missing. (This is consistent with how pandas does things, so if you’re already using None/NaN to mark missing data in your pandas DataFrames, you’re good to go.)

Second, we have to decide what to do with any missing data when we encounter it. One option is to simply discard any rows which contain missing data from our design matrices (drop). Another option is to raise an error (raise). A third option would be to simply let the missing values pass through into the returned design matrices. However, this last option is not yet implemented, because of the lack of any standard way to represent missing values in arbitrary numpy matrices; we’re hoping numpy will get this sorted out before we standardize on anything ourselves.

You can control how patsy handles missing data through the NA_action= argument to functions like build_design_matrices() and dmatrix(). If all you want to do is to choose between drop and raise behaviour, you can pass one of those strings as the NA_action= argument directly. If you want more fine-grained control over how missing values are detected and handled, then you can create an instance of this class, or your own object that implements the same interface, and pass that as the NA_action= argument instead.

The NAAction constructor takes the following arguments:

Parameters: on_NA – How to handle missing values. The default is "drop", which removes all rows from all matrices which contain any missing values. Also available is "raise", which raises an exception when any missing values are encountered. NA_types – Which rules are used to identify missing values, as a list of strings. Allowed values are: "None": treat the None object as missing in categorical data. "NaN": treat floating point NaN values as missing in categorical and numerical data.

New in version 0.2.0.

handle_NA(values, is_NAs, origins)

Takes a set of factor values that may have NAs, and handles them appropriately.

Parameters: values – A list of ndarray objects representing the data. These may be 1- or 2-dimensional, and may be of varying dtype. All will have the same number of rows (or entries, for 1-d arrays). is_NAs – A list with the same number of entries as values, containing boolean ndarray objects that indicate which rows contain NAs in the corresponding entry in values. origins – A list with the same number of entries as values, containing information on the origin of each value. If we encounter a problem with some particular value, we use the corresponding entry in origins as the origin argument when raising a PatsyError. A list of new values (which may have a differing number of rows.)
is_categorical_NA(obj)

Return True if obj is a categorical NA value.

Note that here obj is a single scalar value.

is_numerical_NA(arr)

Returns a 1-d mask array indicating which rows in an array of numerical values contain at least one NA value.

Note that here arr is a numpy array or pandas DataFrame.

## Linear constraints¶

class patsy.LinearConstraint(variable_names, coefs, constants=None)

A linear constraint in matrix form.

This object represents a linear constraint of the form Ax = b.

Usually you won’t be constructing these by hand, but instead get them as the return value from DesignInfo.linear_constraint().

coefs

A 2-dimensional ndarray with float dtype, representing A.

constants

A 2-dimensional single-column ndarray with float dtype, representing b.

variable_names

A list of strings giving the names of the variables being constrained. (Used only for consistency checking.)

## Origin tracking¶

class patsy.Origin(code, start, end)

This represents the origin of some object in some string.

For example, if we have an object x1_obj that was produced by parsing the x1 in the formula "y ~ x1:x2", then we conventionally keep track of that relationship by doing:

x1_obj.origin = Origin("y ~ x1:x2", 4, 6)


Then later if we run into a problem, we can do:

raise PatsyError("invalid factor", x1_obj)


and we’ll produce a nice error message like:

PatsyError: invalid factor
y ~ x1:x2
^^


Origins are compared by value, and hashable.

caretize(indent=0)

Produces a user-readable two line string indicating the origin of some code. Example:

y ~ x1:x2
^^


If optional argument ‘indent’ is given, then both lines will be indented by this much. The returned string does not have a trailing newline.

classmethod combine(origin_objs)

Class method for combining a set of Origins into one large Origin that spans them.

Example usage: if we wanted to represent the origin of the “x1:x2” term, we could do Origin.combine([x1_obj, x2_obj]).

Single argument is an iterable, and each element in the iterable should be either:

• An Origin object
• None
• An object that has a .origin attribute which fulfills the above criteria.

Returns either an Origin object, or None.

relevant_code()

Extracts and returns the span of the original code represented by this Origin. Example: x1.