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Bayesian Structural Equation Modeling

Project description


semba is a Python package for bayesian and (soon) probabalistic structural equation modelling (SEM). The project is powered by the other SEM software semopy and probabalistic programming framework Numpyro. One can think of semba as a bayesian offspring of semopy, and indeed, there is little difference between and the two in terms of usability.

What semba has to offer?

semba is a very young package that, at the time of me writing this readme, is days old, and many features are still planned, yet at the moment its selling points are:

  • Impose arbitrary priors on model parameters;
  • Efficient parameter estimation by means of Markov Chain Monte Carlo (MCMC) methods;
  • Almost complete mimicria of semopy models and methods: no need to learn two different packages.

What will semba offer in the foreseeable future?

  • Not almost, but a complete mimicria;
  • Bayesian treatment of the Gaussian Process SEM proposed here under the notion of ModelGeneralizedEffects that can be used to model complex phenomena such as spatial, temporal data or even both;
  • Probabalistic approach to SEM that lets user to impose arbitrary distribution assumptions on variables and to introduce complex nonlinearity.

Where to start?

The best place to start is to get familar with semopy first at its website as there is no difference in core syntax.

Then, one can proceed to installing semba via pip:

pip install semba

See that using semba is no different from using semopy:

from semopy.examples import political_democracy as ex
import semba

desc, data = ex.get_model(), ex.get_data()
model = semba.Model(desc)
ins = model.inspect()

That produces an output:

       lval op   rval   Estimate       5.0%      95.0%        std      n_eff      r_hat
_b12  dem60  ~  ind60       1.32       0.72       1.86       0.35   1,098.38       1.00
_b13  dem65  ~  ind60       0.52       0.14       0.89       0.23   1,119.16       1.00
_b14  dem65  ~  dem60       0.90       0.71       1.07       0.11     479.93       1.00
_b1      x1  ~  ind60       1.00          -          -          -          -          -
_b2      x2  ~  ind60       2.17       1.94       2.39       0.14   1,028.65       1.00

Imposing custom priors

After you learn about the model syntax, you can impose priors onto model parameters by means of PRIOR operation, for example:

y ~ a1 * x1 + a2 * x2 + a3 * x3

PRIOR(Normal, loc=1, scale=0.1) a1 a2 a3

This will impose a normal prior on regression coefficients a1, a2, a3 with a center at 1 and standard deviation 0.1. PRIOR operation overrides default priors. In semba, the default priors for regression coefficients are normal with a scale 0.5, covariances are normal and the default priors for variance parameters is half-normal, all centered at starting values. Default priors can be overriden by using operations PRIOR_LOADING, PRIOR_VARIANCE, PRIOR_COVARIANCE, PRIOR_VARIANCE_LATENT and PRIOR_COVARIANCE_LATENT. The latter two are used for (co)variances of latent factors -- covariances are standard normal and variances are half-normal with a center at 1.0 (this is likely a subject to change in a future version to accomodate for a scenarios where variances are far-off from the regular range 0-10).

In PRIORx operations, any distribution can be supplied, as long as it is supported by Numpyro (see documentation for a list of available distribution).

MCMC settings

Number of samples, burn-in (or warmup) iterations and number of chains can be supplied to the fit method via arguments num_samples, num_warmup and num_chains respectively. By default, num_samples is set to a number of parameters in a model times 30, and a number of warmup iterations is 1/5th of that. num_chains is set to 1 by default.

semba relies on Numpyro MCMC kernels, and any Numpyro MCMC kernel is easily available to a user: one should pass a name of the kernel to the solver argument of the method fit. The default one is NUTS.

More information

semba has its own little website at

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