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Estimation

Overview

The function <submodule>.estimate(<args>) can be used in all submodules to run the estimation and collect inference statistics (p-value, z-scores, etc.). For instance, to estimate a DiD model, use:

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from causalinf import did

mod = did.estimate(<args>, data=<DataFrame>)

<args> vary across submodules depending on the method used.

The object created by estimate() is method-specific, but it contains some key information about the estimation procedure, including the fit statistics, the statistical model (e.g., logit, linear model, non-parametric difference in averages, etc.) used to compute the parameter(s), the estimated parameters, standard errors, and additional options used by the statistical model. The way the information is stored in the estimate() object is standardized across causal models.

Example

Let us use a Structural Causal Model (SCM) to illustrate the estimate() object, with an example (see Examples) with simulated data (see Simulate Data) from a Linear Structural Equation Model (LSEM) created from the SCM (see SCM).

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from causalinf import simulate
from causalinf import gcm
from causalinf import scm

# get the example
G = gcm.examples('Two confounders')
# simulate the data from LSEM
sim = simulate.lsem(G, seed=1)

G.plot()

Here is the data:

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df = sim.data
print(df)

shape: (1_000, 4)
┌───────────────────────────────┐
│    Z2      Z1       D       Y │
│   f64     f64     f64     f64 │
╞═══════════════════════════════╡
│  1.62   -0.15    2.03   -1.17 │
│ -0.61   -2.43   -0.03    0.76 │
│ -0.53    0.51    0.97    1.02 │
│     …       …       …       … │
│ -0.07   -0.92    1.25    1.95 │
│  0.35    0.65   -0.13    0.08 │
│ -0.19    1.39    0.76   -1.21 │
└───────────────────────────────┘

Estimate

The model estimation is (for details of the default options to estimate SCM using estimate(), see here):

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mod = scm.estimate(G, data=df)

Estimating LSEM...done!

It produces the estimated object which in the code above was in mod:

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print(mod.__class__)

<class 'causalinf.scm.estimate'>

Properties

The main pieces of information that can be directly extracted from the estimate() object are (the same estimate() object properties are used in all other causal inference methods):

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mod.est.parameters.print() # mod.est.parameters is an dataframe from tidypolars4sci

print(mod.est.se)

print(mod.est.fit)

print(mod.est.fit_extra)

print(mod.est.options)

shape: (16, 9)
┌────────────────────────────────────────────────────────────────────────────────────────────────────────────┐
│ term                            label           estimate   sig     se      lo      hi   statistic   pvalue │
│ str                             str                  f64   str    f64     f64     f64         f64      f64 │
╞════════════════════════════════════════════════════════════════════════════════════════════════════════════╡
│ D ~ 1                           beta_0D             0.42   ***   0.03    0.35    0.48       13.27     0.00 │
│ D ~ Z1                          beta_Z1.D          -0.68   ***   0.03   -0.74   -0.62      -22.50     0.00 │
│ D ~ Z2                          beta_Z2.D           0.73   ***   0.03    0.66    0.79       22.75     0.00 │
│ Y ~ 1                           beta_0Y            -0.27   ***   0.03   -0.34   -0.20       -7.84     0.00 │
│ Y ~ Z1                          beta_Z1.Y          -0.36   ***   0.04   -0.43   -0.28       -9.47     0.00 │
│ Y ~ D                           beta_D.Y           -0.22   ***   0.03   -0.29   -0.16       -6.97     0.00 │
│ Y ~ Z2                          beta_Z2.Y          -0.89   ***   0.04   -0.97   -0.81      -22.40     0.00 │
│ D ~~ D                                              0.98   ***   0.04    0.89    1.06       22.36     0.00 │
│ Y ~~ Y                                              1.00   ***   0.04    0.91    1.09       22.36     0.00 │
│ Z1 ~~ Z1                                            1.06         0.00    1.06    1.06        null     null │
│ Z1 ~~ Z2                                            0.02         0.00    0.02    0.02        null     null │
│ Z2 ~~ Z2                                            0.96         0.00    0.96    0.96        null     null │
│ Z1 ~ 1                                              0.03         0.00    0.03    0.03        null     null │
│ Z2 ~ 1                                              0.04         0.00    0.04    0.04        null     null │
│ Direct_effect := (beta_D.Y)     Direct_effect      -0.22   ***   0.03   -0.29   -0.16       -6.97     0.00 │
│ Total_effect := Direct_effect   Total_effect       -0.22   ***   0.03   -0.29   -0.16       -6.97     0.00 │
└────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
{'type': 'classic', 'description': 'Standard errors: classic'}
{'Model': '(footnote)', 'Outcome_type': '(footnote)', 'Estimator': 'ML', 'Std_Error': 'classic', 'N_obs': 1000, 'RMSE': 0.0, 'AIC': 5670.735569404551, 'BIC': 5714.90536691539, 'R2': None, 'R2_adj': None, 'DF_resid': None, 'DF_model': 0}
{'npar': 9.0, 'fmin': 4.440892098500626e-16, 'chisq': 8.881784197001252e-13, 'df': 0.0, 'pvalue': nan, 'baseline.chisq': 1467.3085145359757, 'baseline.df': 5.0, 'baseline.pvalue': 0.0, 'cfi': 0.9999999999999994, 'tli': 1.0, 'nnfi': 1.0, 'rfi': 1.0, 'nfi': 1.0, 'pnfi': 0.0, 'ifi': 0.9999999999999993, 'rni': 0.9999999999999994, 'logl': -2826.3677847022755, 'unrestricted.logl': -2826.3677847022745, 'aic': 5670.735569404551, 'bic': 5714.90536691539, 'ntotal': 1000.0, 'bic2': 5686.320864466223, 'rmsea': 0.0, 'rmsea.ci.lower': 0.0, 'rmsea.ci.upper': 0.0, 'rmsea.ci.level': 0.9, 'rmsea.pvalue': nan, 'rmsea.close.h0': 0.05, 'rmsea.notclose.pvalue': nan, 'rmsea.notclose.h0': 0.08, 'rmr': 1.3290420955907656e-16, 'rmr_nomean': 1.5725438145225752e-16, 'srmr': 4.261310602042481e-17, 'srmr_bentler': 4.261310602042481e-17, 'srmr_bentler_nomean': 5.042050700450315e-17, 'crmr': 8.233634315563857e-17, 'crmr_nomean': 1.0629576194313574e-16, 'srmr_mplus': 6.401670237871737e-17, 'srmr_mplus_nomean': 7.368340834761536e-17, 'cn_05': 1.0, 'cn_01': 1.0, 'gfi': 1.0, 'agfi': 1.0, 'pgfi': 0.0, 'mfi': 0.9999999999999996, 'ecvi': 0.018000000000000887}
{'model.type': 'sem', 'mimic': 'lavaan', 'meanstructure': True, 'int.ov.free': True, 'int.lv.free': False, 'marker.int.zero': False, 'conditional.x': False, 'fixed.x': True, 'orthogonal': False, 'orthogonal.x': False, 'orthogonal.y': False, 'std.lv': False, 'correlation': False, 'effect.coding': '', 'ceq.simple': False, 'parameterization': 'delta', 'auto.fix.first': True, 'auto.fix.single': True, 'auto.var': True, 'auto.cov.lv.x': True, 'auto.cov.y': True, 'auto.th': True, 'auto.delta': True, 'auto.efa': True, 'rotation': 'geomin', 'rotation.se': 'bordered', 'rotation.args': {'orthogonal': False, 'row.weights': 'none', 'std.ov': True, 'geomin.epsilon': 0.001, 'orthomax.gamma': 1.0, 'cf.gamma': 0.0, 'oblimin.gamma': 0.0, 'promax.kappa': 4.0, 'target': [], 'target.mask': [], 'rstarts': 30, 'algorithm': 'gpa', 'reflect': True, 'order.lv.by': 'index', 'gpa.tol': 1e-05, 'tol': 1e-08, 'warn': False, 'verbose': False, 'jac.init.rot': True, 'max.iter': 10000}, 'std.ov': False, 'missing': 'listwise', 'sampling.weights.normalization': 'total', 'samplestats': True, 'sample.cov.rescale': True, 'sample.cov.robust': False, 'sample.icov': True, 'ridge': False, 'ridge.constant': 'default', 'group.label': None, 'group.equal': [], 'group.partial': [], 'group.w.free': False, 'level.label': None, 'estimator': 'ML', 'estimator.orig': 'ML', 'estimator.args': [], 'likelihood': 'normal', 'link': 'default', 'representation': 'LISREL', 'do.fit': True, 'bounds': 'none', 'rstarts': 0, 'se': 'standard', 'test': 'standard', 'information': ['expected', 'expected'], 'h1.information': ['structured', 'structured'], 'observed.information': ['hessian', 'hessian'], 'information.meat': 'first.order', 'h1.information.meat': 'structured', 'omega.information': 'expected', 'omega.h1.information': 'unstructured', 'omega.information.meat': 'first.order', 'omega.h1.information.meat': 'unstructured', 'scaled.test': 'standard', 'ug2.old.approach': False, 'bootstrap': 1000, 'gamma.n.minus.one': False, 'gamma.unbiased': False, 'control': [], 'optim.method': 'nlminb', 'optim.attempts': 4, 'optim.force.converged': False, 'optim.gradient': 'analytic', 'optim.init_nelder_mead': False, 'optim.var.transform': 'none', 'optim.parscale': 'none', 'optim.partrace': False, 'optim.dx.tol': 0.001, 'optim.bounds': {'lower': [], 'upper': []}, 'em.iter.max': 10000, 'em.fx.tol': 1e-08, 'em.dx.tol': 0.0001, 'em.zerovar.offset': 0.0001, 'em.h1.iter.max': 500, 'em.h1.tol': 1e-05, 'em.h1.warn': True, 'optim.gn.iter.max': 200, 'optim.gn.stephalf.max': 10, 'optim.gn.tol.x': 1e-05, 'integration.ngh': 21, 'parallel': 'no', 'ncpus': 7, 'cl': None, 'iseed': None, 'zero.add': [0.5, 0.0], 'zero.keep.margins': True, 'zero.cell.warn': False, 'cat.wls.w': True, 'start': 'default', 'check.start': True, 'check.post': True, 'check.gradient': True, 'check.vcov': True, 'check.lv.names': True, 'check.lv.interaction': True, 'h1': True, 'baseline': True, 'baseline.conditional.x.free.slopes': True, 'implied': True, 'loglik': True, 'store.vcov': 'default', 'parser': 'new', 'categorical': False, '.categorical': False, '.clustered': False, '.multilevel': False}