API Reference

This reference provides detailed documentation for all modules, classes, and methods in the current release of Bambi.

bambi.models

class bambi.models.Model(formula=None, data=None, family='gaussian', priors=None, link=None, categorical=None, potentials=None, dropna=False, auto_scale=True, automatic_priors='default', noncentered=True, priors_cor=None, taylor=None)

Specification of model class.

Parameters

• formula (str) – A model description written using the formula syntax from the formulae library.

• data (pandas.DataFrame or str) – The dataset to use. Either a pandas DataFrame, or the name of the file containing the data, which will be passed to pd.read_csv().

• family (str or bambi.families.Family) – A specification of the model family (analogous to the family object in R). Either a string, or an instance of class bambi.families.Family. If a string is passed, a family with the corresponding name must be defined in the defaults loaded at Model initialization. Valid pre-defined families are "bernoulli", "beta", "binomial", "gamma", "gaussian", "negativebinomial", "poisson", "t", and "wald". Defaults to "gaussian".

• priors (dict) – Optional specification of priors for one or more terms. A dictionary where the keys are the names of terms in the model, “common” or “group_specific” and the values are instances of class Prior when automatic_priors is "default", or either Prior, int, float, or str when automatic_priors is "mle".

• link (str) – The name of the link function to use. Valid names are "cloglog", "identity", "inverse_squared", "inverse", "log", "logit", and "probit". Not all the link functions can be used with all the families. See TODO.

• categorical (str or list) – The names of any variables to treat as categorical. Can be either a single variable name, or a list of names. If categorical is None, the data type of the columns in the data will be used to infer handling. In cases where numeric columns are to be treated as categoricals (e.g., group specific factors coded as numerical IDs), explicitly passing variable names via this argument is recommended.

• potentials (A list of 2-tuples.) – Optional specification of potentials. A potential is an arbitrary expression added to the likelihood, this is generally useful to add constrains to models, that are difficult to express otherwise. The first term of a 2-tuple is the name of a variable in the model, the second a lambda function expressing the desired constraint. If a constraint involves n variables, you can pass n 2-tuples or pass a tuple which first element is a n-tuple and second element is a lambda function with n arguments. The number and order of the lambda function has to match the number and order of the variables names.

• dropna (bool) – When True, rows with any missing values in either the predictors or outcome are automatically dropped from the dataset in a listwise manner.

• auto_scale (bool) – If True (default), priors are automatically rescaled to the data (to be weakly informative) any time default priors are used. Note that any priors explicitly set by the user will always take precedence over default priors.

• automatic_priors (str) – An optional specification to compute/scale automatic priors. "default" means to use a method inspired on the R rstanarm library. "mle" means to use old default priors in Bambi that rely on maximum likelihood estimations obtained via the statsmodels library.

• noncentered (bool) – If True (default), uses a non-centered parameterization for normal hyperpriors on grouped parameters. If False, naive (centered) parameterization is used.

• priors_cor (dict) – An optional value for eta in the LKJ prior for the correlation matrix of group-specific terms. Keys in the dictionary indicate the groups, and values indicate the value of eta. This is a very experimental feature. Defaults to None, which means priors for the group-specific terms are independent.

• taylor (int) – Order of Taylor expansion to use in approximate variance when constructing the default priors when automatic_priors is "mle". Should be between 1 and 13. Lower values are less accurate, tending to undershoot the correct prior width, but are faster to compute and more stable. Odd-numbered values tend to work better. Defaults to 5 for Normal models and 1 for non-Normal models. Values higher than the defaults are generally not recommended as they can be unstable.

build()

Set up the model for sampling/fitting.

Performs any steps that require access to all model terms (e.g., scaling priors on each term), then calls the backend’s build() method.

property common_terms

Return dict of all and only common effects in model.

fit(draws=1000, tune=1000, discard_tuned_samples=True, omit_offsets=True, method='mcmc', init='auto', n_init=50000, chains=None, cores=None, random_seed=None, **kwargs)

Fit the model using PyMC3.

Parameters

• draws (int) – The number of samples to draw from the posterior distribution. Defaults to 1000.

• tune (int) – Number of iterations to tune. Defaults to 1000. Samplers adjust the step sizes, scalings or similar during tuning. These tuning samples are be drawn in addition to the number specified in the draws argument, and will be discarded unless discard_tuned_samples is set to False.

• discard_tuned_samples (bool) – Whether to discard posterior samples of the tune interval. Defaults to True.

• omit_offsets (bool) – Omits offset terms in the InferenceData object when the model includes group specific effects. Defaults to True.

• method (str) – The method to use for fitting the model. By default, "mcmc". This automatically assigns a MCMC method best suited for each kind of variables, like NUTS for continuous variables and Metropolis for non-binary discrete ones. Alternatively, "advi", in which case the model will be fitted using automatic differentiation variational inference as implemented in PyMC3. Finally, "laplace", in which case a Laplace approximation is used and is not recommended other than for pedagogical use.

• init (str) – Initialization method. Defaults to "auto". The available methods are: * auto: Use "jitter+adapt_diag" and if this method fails it uses "adapt_diag". * adapt_diag: Start with a identity mass matrix and then adapt a diagonal based on the variance of the tuning samples. All chains use the test value (usually the prior mean) as starting point. * jitter+adapt_diag: Same as "adapt_diag", but use test value plus a uniform jitter in [-1, 1] as starting point in each chain. * advi+adapt_diag: Run ADVI and then adapt the resulting diagonal mass matrix based on the sample variance of the tuning samples. * advi+adapt_diag_grad: Run ADVI and then adapt the resulting diagonal mass matrix based on the variance of the gradients during tuning. This is experimental and might be removed in a future release. * advi: Run ADVI to estimate posterior mean and diagonal mass matrix. * advi_map: Initialize ADVI with MAP and use MAP as starting point. * map: Use the MAP as starting point. This is strongly discouraged. * adapt_full: Adapt a dense mass matrix using the sample covariances. All chains use the test value (usually the prior mean) as starting point. * jitter+adapt_full: Same as "adapt_full", but use test value plus a uniform jitter in [-1, 1] as starting point in each chain.

• n_init (int) – Number of initialization iterations. Only works for "advi" init methods.

• chains (int) – The number of chains to sample. Running independent chains is important for some convergence statistics and can also reveal multiple modes in the posterior. If None, then set to either cores or 2, whichever is larger.

• cores (int) – The number of chains to run in parallel. If None, it is equal to the number of CPUs in the system unless there are more than 4 CPUs, in which case it is set to 4.

• random_seed (int or list of ints) – A list is accepted if cores is greater than one.

• **kwargs – For other kwargs see the documentation for pymc3.sample().

Returns

Return type

An ArviZ InferenceData instance.

graph(formatting='plain', name=None, figsize=None, dpi=300, fmt='png')

Produce a graphviz Digraph from a built Bambi model.

Requires graphviz, which may be installed most easily with

conda install -c conda-forge python-graphviz

Alternatively, you may install the graphviz binaries yourself, and then pip install graphviz to get the python bindings. See http://graphviz.readthedocs.io/en/stable/manual.html for more information.

Parameters

• formatting (str) – One of "plain" or "plain_with_params". Defaults to "plain".

• name (str) – Name of the figure to save. Defaults to None, no figure is saved.

• figsize (tuple) – Maximum width and height of figure in inches. Defaults to None, the figure size is set automatically. If defined and the drawing is larger than the given size, the drawing is uniformly scaled down so that it fits within the given size. Only works if name is not None.

• dpi (int) – Point per inch of the figure to save. Defaults to 300. Only works if name is not None.

• fmt (str) – Format of the figure to save. Defaults to "png". Only works if name is not None.

Example

>>> model = Model("y ~ x + (1|z)")
>>> model.build()
>>> model.graph()

>>> model = Model("y ~ x + (1|z)")
>>> model.fit()
>>> model.graph()

property group_specific_terms

Return dict of all and only group specific effects in model.

property intercept_term

Return the intercept term

plot_priors(draws=5000, var_names=None, random_seed=None, figsize=None, textsize=None, hdi_prob=None, round_to=2, point_estimate='mean', kind='kde', bins=None, omit_offsets=True, omit_group_specific=True, ax=None)

Samples from the prior distribution and plots its marginals.

Parameters

• draws (int) – Number of draws to sample from the prior predictive distribution. Defaults to 5000.

• var_names (str or list) – A list of names of variables for which to compute the posterior predictive distribution. Defaults to None which means to include both observed and unobserved RVs.

• random_seed (int) – Seed for the random number generator.

• figsize (tuple) – Figure size. If None it will be defined automatically.

• textsize (float) – Text size scaling factor for labels, titles and lines. If None it will be autoscaled based on figsize.

• hdi_prob (float or str) – Plots highest density interval for chosen percentage of density. Use "hide" to hide the highest density interval. Defaults to 0.94.

• round_to (int) – Controls formatting of floats. Defaults to 2 or the integer part, whichever is bigger.

• point_estimate (str) – Plot point estimate per variable. Values should be "mean", "median", "mode" or None. Defaults to "auto" i.e. it falls back to default set in ArviZ’s rcParams.

• kind (str) – Type of plot to display ("kde" or "hist") For discrete variables this argument is ignored and a histogram is always used.

• bins (integer or sequence or "auto") – Controls the number of bins, accepts the same keywords matplotlib.pyplot.hist() does. Only works if kind == "hist". If None (default) it will use "auto" for continuous variables and range(xmin, xmax + 1) for discrete variables.

• omit_offsets (bool) – Whether to omit offset terms in the plot. Defaults to True.

• omit_group_specific (bool) – Whether to omit group specific effects in the plot. Defaults to True.

• ax (numpy array-like of matplotlib axes or bokeh figures) – A 2D array of locations into which to plot the densities. If not supplied, ArviZ will create its own array of plot areas (and return it).

• **kwargs – Passed as-is to matplotlib.pyplot.hist() or matplotlib.pyplot.plot() function depending on the value of kind.

Returns

axes

Return type

matplotlib axes

predict(idata, kind='mean', data=None, draws=None, inplace=True)

Predict method for Bambi models

Obtains in-sample and out-of-sample predictions from a fitted Bambi model.

Parameters

• idata (InferenceData) – The InferenceData instance returned by .fit().

• kind (str) – Indicates the type of prediction required. Can be "mean" or "pps". The first returns draws from the posterior distribution of the mean, while the latter returns the draws from the posterior predictive distribution (i.e. the posterior probability distribution for a new observation). Defaults to "mean".

• data (pandas.DataFrame or None) – An optional data frame with values for the predictors that are used to obtain out-of-sample predictions. If omitted, the original dataset is used.

• draws (None) – The number of random draws per chain. Only used if kind="pps". Not recommended unless more than ndraws times nchains posterior predictive samples are needed. Defaults to None which means ndraws times nchains draws are obtained.

• inplace (bool) – If True it will modify idata in-place. Otherwise, it will return a copy of idata with the predictions added. If kind="mean", a new variable ending in "_mean" is added to the posterior group. If kind="pps", it appends a posterior_predictive group to idata. If any of these already exist, it will be overwritten.

Returns

Return type

InferenceData or None

prior_predictive(draws=500, var_names=None, omit_offsets=True, random_seed=None)

Generate samples from the prior predictive distribution.

Parameters

• draws (int) – Number of draws to sample from the prior predictive distribution. Defaults to 500.

• var_names (str or list) – A list of names of variables for which to compute the prior predictive distribution. Defaults to None which means both observed and unobserved RVs.

• random_seed (int) – Seed for the random number generator.

Returns

InferenceData object with the groups prior, prior_predictive and observed_data.

Return type

InferenceData

set_priors(priors=None, common=None, group_specific=None)

Set priors for one or more existing terms.

Parameters

• priors (dict) – Dictionary of priors to update. Keys are names of terms to update; values are the new priors (either a Prior instance, or an int or float that scales the default priors). Note that a tuple can be passed as the key, in which case the same prior will be applied to all terms named in the tuple.

• common (Prior, int, float or str) – A prior specification to apply to all common terms included in the model.

• group_specific (Prior, int, float or str) – A prior specification to apply to all group specific terms included in the model.

property term_names

Return names of all terms in order of addition to model.

bambi.priors

Classes to represent prior distributions and methods to set automatic priors

class bambi.priors.Prior(name, auto_scale=True, scale=None, **kwargs)

Abstract specification of a term prior.

Parameters

• name (str) – Name of prior distribution. Must be the name of a PyMC3 distribution (e.g., "Normal", "Bernoulli", etc.)

• auto_scale (bool) – Whether to adjust the parameters of the prior or use them as passed. Default to True.

• scale (num or str) – How to scale the prior. If a number, must be within 0 and 1. If a string, must be one of "narrow", "medium", "wide", or "superwide". Only used when the model was created with automatic_priors="mle".

• kwargs (dict) – Optional keywords specifying the parameters of the named distribution.

update(**kwargs)

Update the arguments of the prior with additional arguments.

Parameters

kwargs (dict) – Optional keyword arguments to add to prior args.

class bambi.priors.PriorScaler(model)

Scale prior distributions parameters.

class bambi.priors.PriorScalerMLE(model, taylor)

Scale prior distributions parameters.

Used internally. Based on https://arxiv.org/abs/1702.01201

fit_mle()

Fits MLE of the common part of the model.

This used to be called in the class instantiation, but there is no need to fit the GLM when there are no automatic priors. So this method is only called when needed.

get_slope_stats(exog, name, values, sigma_corr, points=4, full_model=None)

Parameters

• name (str) – Name of the term

• values (np.array) – Values of the term

• full_model (statsmodels.genmod.generalized_linear_model.GLM) – Statsmodels GLM to replace MLE model. For when 'predictor' is not in the common part of the model.

• points (int) – Number of points to use for LL approximation.

scale_common(term)

Scale common terms, excluding intercepts.

bambi.families

Classes to construct model families.

class bambi.families.Family(name, likelihood, link)

A specification of model family.

Parameters

• name (str) – The name of the family. It can be any string.

• likelihood (Likelihood) – A bambi.families.Likelihood instace specifying the model likelihood function.

• link (str or Link) – The name of the link function or a bambi.families.Link instance. The link function transforms the linear model prediction to the mean parameter of the likelihood funtion.

Examples

>>> import bambi as bmb

Replicate the Gaussian built-in family.

>>> sigma_prior = bmb.Prior("HalfNormal", sigma=1)
>>> likelihood = bmb.Likelihood("Gaussian", parent="mu", sigma=sigma_prior)
>>> family = bmb.Family("my_gaussian", likelihood, "identity")
>>> # Then you can do
>>> # bmb.Model("y ~ x", data, family=family)

Replicate the Bernoulli built-in family.

>>> likelihood = bmb.Likelihood("Bernoulli", parent="p")
>>> family = bmb.Family("bernoulli2", likelihood, "logit")

class bambi.families.Likelihood(name, parent=None, pps=None, **kwargs)

Representation of a Likelihood function for a Bambi model.

Notes: * parent must not be in kwargs. * parent is inferred from the name if it is a known name

Parameters

• name (str) – Name of the likelihood function. Must be a valid PyMC3 distribution name.

• parent (str) – Optional specification of the name of the mean parameter in the likelihood. This is the parameter whose transformation is modeled by the linear predictor.

• kwargs – Keyword arguments that indicate prior distributions for auxiliary parameters in the likelihood.

class bambi.families.Link(name, link=None, linkinv=None, linkinv_backend=None)

Representation of link function.

This object contains two main functions. One is the link function itself, the function that maps values in the response scale to the linear predictor, and the other is the inverse of the link function, that maps values of the linear predictor to the response scale.

The great majority of users will never interact with this class unless they want to create a custom Family with a custom Link. This is automatically handled for all the built-in families.

Parameters

• name (str) – The name of the link function. If it is a known name, it’s not necessary to pass any other arguments because functions are already defined internally. If not known, all of link, linkinv and linkinv_backend must be specified.

• link (function) – A function that maps the response to the linear predictor. Known as the \(g\) function in GLM jargon. Does not need to be specified when name is a known name.

• linkinv (function) – A function that maps the linear predictor to the response. Known as the \(g^{-1}\) function in GLM jargon. Does not need to be specified when name is a known name.

• linkinv_backend (function) – Same than linkinv but must be something that works with PyMC3 backend (i.e. it must work with Theano tensors). Does not need to be specified when name is a known name.

bambi.data

Code for loading datasets.

bambi.data.clear_data_home(data_home=None)

Delete all the content of the data home cache.

Parameters

data_home (str) – The path to Bambi data dir. By default a folder named "bambi_data" in the user home folder.

bambi.data.load_data(dataset=None, data_home=None)

Load a dataset.

Run with no parameters to get a list of all available data sets.

The directory to save can also be set with the environment variable BAMBI_HOME. The checksum of the dataset is checked against a hardcoded value to watch for data corruption. Run bmb.clear_data_home() to clear the data directory.

Parameters

• dataset (str) – Name of dataset to load.

• data_home (str, optional) – Where to save remote datasets

Returns

Return type

Pandas DataFrame

Logistic Regression and Model Comparison with Bambi and ArviZ Frequently Asked Questions