Instrumental variables¶

statspai.iv — the unified IV namespace: a fixest-style formula front end (sp.iv / sp.ivreg), a modern single-endogenous reporting bundle (sp.iv_diag), a k-class / JIVE estimator panel (sp.iv_compare), and two frontier estimators (sp.kernel_iv, sp.continuous_iv_late).

See also the decision guide: Choosing an IV estimator, and the exhaustive auto-generated listing under Full API reference → iv.

The formula front end — `sp.iv` / `sp.ivreg`¶

IV models use the fixest convention: endogenous regressors and their instruments go in parentheses, (endog ~ instruments). Everything outside the parentheses is exogenous.

import statspai as sp

data = sp.datasets.card_1995()

# Card (1995) returns to schooling: educ instrumented by college proximity.
r = sp.ivreg(
    "lwage ~ (educ ~ nearc4) + exper + expersq + black + south + smsa",
    data=data,
)
print(r.summary())

# Multiple excluded instruments + an exogenous control:
r = sp.iv("y ~ (d ~ z1 + z2) + x1", data=df)

# IV with high-dimensional fixed effects absorbed (reghdfe / ivreghdfe style):
r = sp.iv("y ~ (d ~ z1 + z2) + x1", data=df, absorb="firm + year")

sp.iv and sp.ivreg are the same estimator; ivreg is kept as the Stata-flavoured alias. Two-stage least squares is the default.

Modern reporting bundle — `sp.iv_diag`¶

For the common single-endogenous case, sp.iv_diag returns the full post-2022 reporting standard in one object: the point estimate, first-stage strength (effective F), weak-instrument-robust confidence intervals (Anderson–Rubin and, optionally, conditional-likelihood-ratio and k-class inversions), and bootstrap alternatives.

res = sp.iv_diag(
    data, y="lwage", endog="educ", instruments="nearc4",
    exog=["exper", "expersq", "black", "south", "smsa"],
    cluster="region",
    include_clr_ci=True,   # conditional likelihood-ratio CI
    include_k_ci=True,     # k-class CI
)
res.summary()

Always check the first stage

A weak first stage biases 2SLS toward OLS and breaks conventional standard errors. iv_diag reports the effective F-statistic and weak-IV-robust intervals precisely so you do not have to interpret a 2SLS point estimate in the dark. As a rule of thumb, treat a first stage below the usual thresholds as a signal to report the Anderson–Rubin interval rather than the 2SLS CI.

Comparing estimators — `sp.iv_compare`¶

With several (possibly many) instruments, 2SLS is biased in finite samples. sp.iv_compare runs a panel of k-class and jackknife estimators side by side so the many-instrument bias is visible:

tbl = sp.iv_compare(
    "y ~ (d ~ z1 + z2 + z3) + x1", data=df,
    methods=("2sls", "liml", "fuller", "jive"),
)
tbl   # one row per estimator: coefficient, SE, CI

2SLS — the workhorse; minimum-bias only with strong instruments.
LIML — limited-information ML; better-centred under many instruments.
Fuller — a finite-sample-adjusted LIML with finite moments.
JIVE — jackknife IV; removes the own-observation bias of 2SLS.

Frontier estimators¶

# Nonparametric IV via kernel ridge in RKHS (Y on D instrumented by Z):
k = sp.kernel_iv(data, y="y", treat="d", instrument="z")

# LATE with a continuous instrument (quantile-bin Wald estimator):
late = sp.continuous_iv_late(data, y="y", treat="d", instrument="z")

Identifying assumptions (agent-native)¶

Every IV estimator ships an agent card you can inspect before estimating:

sp.agent_card("kernel_iv")["assumptions"]
# instrument relevance · exclusion restriction · exogeneity · (LATE) monotonicity

The core requirements are relevance (a non-zero first stage), exclusion (the instrument affects the outcome only through the treatment), exogeneity / independence of the instrument, and — for a LATE interpretation — monotonicity (no defiers).

Method-level API¶

The public top-level entry points used in examples and agent workflows are documented here explicitly; the exhaustive namespace listing remains available under Full API reference -> iv.

`sp.iv(...)`¶

iv ¶

iv(formula: Optional[str] = None, data: Optional[DataFrame] = None, method: str = '2sls', robust: str = 'nonrobust', cluster: Optional[str] = None, fuller_alpha: float = 1.0, absorb: Optional[Union[str, List[str]]] = None, **kwargs) -> EconometricResults

Unified instrumental variables estimation.

Supports multiple methods through the method parameter:

'2sls' — Two-Stage Least Squares (default).
'liml' — Limited Information Maximum Likelihood. Better finite- sample properties under weak instruments; approximately median-unbiased.
'fuller' — Fuller (1977) modified LIML with finite-sample bias correction. fuller_alpha=1 removes first-order bias; fuller_alpha=4 minimises MSE under normality.
'gmm' — Efficient two-step GMM. More efficient than 2SLS under heteroskedasticity when over-identified.
'jive' — Jackknife IV (Angrist, Imbens & Krueger 1999). Reduces many-instrument bias by using leave-one-out fitted values.

For DeepIV (neural network IV) use sp.deepiv(). For Bartik shift-share IV use sp.bartik().

Parameters:

Name	Type	Description	Default
`formula`	`str`	IV formula: `"y ~ (endog ~ z1 + z2) + exog1 + exog2"` Variables in parentheses before `~`: endogenous regressors Variables in parentheses after `~`: excluded instruments Variables outside parentheses: exogenous controls	`None`
`data`	`DataFrame`	Data containing all variables.	`None`
`method`	`str`	Estimation method: '2sls', 'liml', 'fuller', 'gmm', 'jive'.	`'2sls'`
`robust`	`str`	Standard-error type ('nonrobust', 'hc0', 'hc1', 'hc2', 'hc3').	`'nonrobust'`
`cluster`	`str`	Variable name for clustered standard errors.	`None`
`fuller_alpha`	`float`	Fuller modification constant (only used when `method='fuller'`).	`1.0`
`absorb`	`str or list of str`	Column name(s) of high-dimensional fixed effects to partial out before fitting (e.g. `absorb="firm"` or `absorb=["firm", "year"]`). Routes `y`, exogenous controls, endogenous regressors, and instruments through :func:`sp.fast.demean` (Rust HDFE backend) and drops singletons, then runs 2SLS in residualised space. The intercept is dropped because the absorbed FEs span the constant. The residual DOF is adjusted by `sum(G_k - 1)`, mirroring :func:`sp.fast.feols(absorb=...)`. Currently only wired for `method='2sls'`; LIML / Fuller / GMM / JIVE raise `NotImplementedError` (Phase 3b).	`None`

Returns:

Type	Description
`EconometricResults`	Fitted model results with integrated IV diagnostics: First-stage F-statistics and partial R² Sargan/Hansen J overidentification test (when over-identified) Durbin-Wu-Hausman endogeneity test Weak instrument warnings

Examples:

>>> # Standard 2SLS
>>> result = sp.iv("wage ~ (education ~ parent_edu + distance) + experience",
...               data=df)
>>> print(result.summary())

>>> # LIML (better with weak instruments)
>>> result = sp.iv("wage ~ (education ~ parent_edu + distance) + experience",
...               data=df, method='liml')

>>> # Fuller with bias correction
>>> result = sp.iv("wage ~ (education ~ parent_edu) + experience",
...               data=df, method='fuller', fuller_alpha=1)

>>> # Efficient GMM with robust SEs
>>> result = sp.iv("wage ~ (education ~ parent_edu + distance) + experience",
...               data=df, method='gmm', robust='hc1')

>>> # JIVE (many instruments)
>>> result = sp.iv("wage ~ (education ~ z1 + z2 + z3 + z4 + z5) + experience",
...               data=df, method='jive')

Notes

Which method to choose?

Start with '2sls'. If first-stage F < 10, switch to 'liml' or 'fuller'.
If you have many instruments (m >> k₂) and worry about bias, use 'jive' or 'liml'.
If over-identified and you suspect heteroskedasticity, use 'gmm' for efficiency.
For nonparametric / ML-based IV, see sp.deepiv().

Diagnostics included automatically:

First-stage F < 10 triggers a weak-instrument warning.
Sargan test (2SLS/LIML/Fuller/JIVE) or Hansen J (GMM) for overidentification.
Durbin-Wu-Hausman test for endogeneity.

References

Wooldridge (2010), Ch. 5-8.
Stock & Yogo (2005), for weak-instrument critical values.
Fuller (1977), for the finite-sample correction.
Hansen (1982), for GMM.
Angrist, Imbens & Krueger (1999), for JIVE.

`sp.ivreg(...)`¶

ivreg ¶

ivreg(formula: str, data: DataFrame, robust: str = 'nonrobust', cluster: Optional[str] = None, **kwargs) -> EconometricResults

Instrumental variables regression (2SLS).

.. deprecated:: Use sp.iv(formula, data, method='2sls') instead. ivreg is kept for backward compatibility.

Parameters:

Name	Type	Description	Default
`formula`	`str`	IV formula: `"y ~ (endog ~ z1 + z2) + exog1 + exog2"`	required
`data`	`DataFrame`		required
`robust`	`str`		`'nonrobust'`
`cluster`	`str`		`None`

Returns:

Type	Description
`EconometricResults`

`sp.kernel_iv(...)`¶

kernel_iv ¶

Kernel IV regression with uniform inference (Lob et al. 2025, arXiv 2511.21603).

Estimates the structural function h*(D) = E[Y | do(D)] non- parametrically using kernel ridge regression in a reproducing kernel Hilbert space, with a uniform confidence band (vs. pointwise CIs).

KernelIVResult `dataclass` ¶

Output of kernel IV regression.

kernel_iv ¶

kernel_iv(data: DataFrame, y: str, treat: str, instrument: str, grid: Optional[ndarray] = None, bandwidth: Optional[float] = None, ridge: float = 0.001, alpha: float = 0.05, n_boot: int = 100, seed: int = 0) -> KernelIVResult

Kernel IV regression of Y on D instrumented by Z.

Parameters:

Name	Type	Description	Default
`data`	`DataFrame`		required
`y`	`str`		required
`treat`	`str`		required
`instrument`	`str`		required
`grid`	`array`	Grid of treatment values to evaluate h(d); defaults to the empirical 5–95th percentile range with 30 points.	`None`
`bandwidth`	`float`		`None`
`ridge`	`float`	Tikhonov regularisation.	`1e-3`
`alpha`	`float`		`0.05`
`n_boot`	`int`	Bootstrap reps for the uniform CI.	`100`
`seed`	`int`		`0`

Returns:

Type	Description
`KernelIVResult`

`sp.continuous_iv_late(...)`¶

continuous_iv_late ¶

continuous_iv_late(data: DataFrame, y: str, treat: str, instrument: str, n_quantiles: int = 4, alpha: float = 0.05, n_boot: int = 200, seed: int = 0) -> ContinuousLATEResult

LATE with a continuous instrument via quantile-bin Wald estimator.

Parameters:

Name	Type	Description	Default
`data`	`DataFrame`		required
`y`	`str`		required
`treat`	`str`		required
`instrument`	`str`		required
`n_quantiles`	`int`	Number of quantile bins of the instrument; LATE is averaged across bins weighted by complier share.	`4`
`alpha`	`float`		`0.05`
`n_boot`	`int`		`200`
`seed`	`int`		`0`

Returns:

Type	Description
`ContinuousLATEResult`

`sp.iv_diag(...)`¶

iv_diag ¶

Modern IV reporting bundle — sp.iv.iv_diag.

This is the StatsPAI port of the post-2022 reporting standard for linear IV in applied work, mirroring R ivDiag (Lal et al. 2024) and going a step further by integrating the weak-IV-robust confidence sets (:mod:statspai.iv.weak_iv_ci) and the Conley–Hansen–Rossi sensitivity toolkit (:mod:statspai.iv.plausibly_exogenous) into a single object.

What it returns

:class:IVDiagResult — a structured bundle with:

2SLS (and optional OLS) point estimate with analytic + bootstrap standard errors (pairs and / or wild bootstrap; cluster-aware).
Effective F (Olea–Pflueger 2013) and tF-corrected critical value (Lee–McCrary–Moreira–Porter 2022, AER 112, 3260–3290).
Anderson–Rubin (1949) F at H0 and the AR confidence set; optional CLR / K confidence sets via :mod:statspai.iv.weak_iv_ci.
Kleibergen–Paap (2006) rk LM and Wald F.
Conley–Hansen–Rossi (2012) plausibly-exogenous LTZ sensitivity.
A reading of the "TSLS-as-LATE" caveat (Blandhol–Bonney–Mogstad–Torgovitsky 2022/2025; Słoczyński 2024) when covariates are present and the endogenous regressor is binary.

The result object exposes .summary(), .to_frame(), .to_dict(), .to_latex(), .to_excel(), .to_word(), and .plot() for one-call report output.

References

Anderson, T.W. and Rubin, H. (1949). [@anderson1949estimation]

Olea, J.L.M. and Pflueger, C. (2013). [@olea2013robust]

Conley, T.G., Hansen, C.B. and Rossi, P.E. (2012). [@conley2012plausibly]

Lee, D.S., McCrary, J., Moreira, M.J. and Porter, J. (2022). AER 112, 3260–3290. [@lee2022valid]

Young, A. (2022). EER 147, 104112. [@young2022consistency]

Keane, M.P. and Neal, T. (2024). Annual Review of Economics 16, 185–212. [@keane2024practical]

Lal, A., Lockhart, M., Xu, Y. and Zu, Z. (2024). Political Analysis 32(4), 521–540. [@lal2024much]

Blandhol, C., Bonney, J., Mogstad, M. and Torgovitsky, A. (2022/2025). NBER WP 29709. [@blandhol2025tsls]

Słoczyński, T. (2024). arXiv:2011.06695. [@sloczynski2024should]

IVDiagResult `dataclass` ¶

Container for :func:iv_diag output.

Attributes:

Name	Type	Description
`n`	`int`	Sample size after listwise deletion.
`n_endog, n_instruments, n_exog`	`int`	Counts of endogenous regressors, excluded instruments, included exogenous controls (excluding intercept).
`endog, instruments, exog`	`list[str]`	Variable names.
`beta_2sls, se_2sls, t_2sls, p_2sls`	`float`	2SLS point estimate, analytic SE, t-ratio, p-value (single endogenous regressor).
`ci_analytic_2sls`	`tuple[float, float]`	Analytic Wald CI based on `se_2sls` (level = `1 - alpha`).
`beta_ols, se_ols, ci_ols`	`(float, float, tuple[float, float])`	OLS counterpart (informative comparator; not causal).
`first_stage_F`	`float`	Classical first-stage F.
`effective_F`	`float`	Olea–Pflueger (2013) robust effective F.
`tF_critical_value`	`float`	Lee et al. (2022, AER) tF adjusted 5 % critical value at the observed first-stage F. `inf` if F < 3.84.
`ar_stat, ar_pvalue`	`float`	Anderson–Rubin (1949) F-statistic and p-value at `h0`.
`ar_ci`	`tuple[float, float]`	AR confidence set (grid-inverted). `±inf` flags a one-/two- sided unbounded set.
`clr_ci, k_ci`	`tuple[float, float] \| None`	Moreira (2003) CLR and Kleibergen (2002) K confidence sets. `None` if not requested.
`kp_rk_lm, kp_rk_lm_pvalue, kp_rk_f`	`float \| None`	Kleibergen–Paap (2006) rk LM, p-value, Wald F.
`bootstrap_ci_analytic, bootstrap_ci_pairs, bootstrap_ci_wild`		Pair-/wild-bootstrap CI tuples (or `None`).
`bootstrap_se_pairs, bootstrap_se_wild`	`float \| None`	Bootstrap standard errors (matching CI sources).
`bootstrap_n`	`int`	Number of bootstrap replications actually used.
`ltz_ci, ltz_warning`	`(tuple[float, float] \| None, str \| None)`	Conley–Hansen–Rossi LTZ sensitivity CI under `gamma_var = (gamma_sd) ** 2`.
`tF_adjusted_ci`	`tuple[float, float] \| None`	`beta ± tF_critical_value × se`. Falls back to `±inf` when `F < 3.84` (per LMMP 2022).
`tsls_late_caveat`	`str \| None`	BBMT (2022/2025) / Słoczyński (2024) caveat text whenever the specification is at risk of negative-weight LATE pathologies.
`diagnostics`	`dict`	All numeric outputs in a flat dict (also returned by :meth:`to_dict`). Useful for downstream agent workflows.
`raw`	`dict`	Internal scratchpad with arrays (residuals, fitted values).

to_frame ¶

to_frame() -> DataFrame

Return a tidy summary table — one row per estimator/metric.

to_dict ¶

to_dict() -> Dict[str, Any]

Return all numeric diagnostics as a flat dict (jsonable).

to_latex ¶

to_latex(caption: Optional[str] = None, label: Optional[str] = None, float_format: str = '%.4f') -> str

Render the summary table as a LaTeX tabular string.

to_excel ¶

to_excel(path: str) -> None

Write the summary table to path (one sheet).

to_word ¶

to_word(path: str, title: Optional[str] = None) -> None

Write the summary table to a .docx file (requires python-docx).

plot ¶

plot(kind: str = 'diagnostic', **kwargs)

Dispatch to :mod:statspai.iv.plot plotting helpers.

Parameters:

Name	Type	Description	Default
`kind`	`('diagnostic', 'forest', 'weak_iv', 'first_stage')`	Which plot to render. `'diagnostic'` returns the 2x2 panel.	`'diagnostic'`

iv_diag ¶

iv_diag(data: DataFrame, y: str, endog: str, instruments: Union[str, Sequence[str]], exog: Optional[Union[str, Sequence[str]]] = None, *, cluster: Optional[Union[str, ndarray]] = None, h0: float = 0.0, alpha: float = 0.05, vcov: str = 'HC1', n_boot: int = 1000, boot_methods: Sequence[str] = ('pairs',), include_clr_ci: bool = False, include_k_ci: bool = False, grid_size: int = 401, ltz_gamma_sd: Optional[float] = None, random_state: Optional[int] = None) -> IVDiagResult

Modern IV reporting bundle (single-endogenous, post-2022 standard).

Returns a single :class:IVDiagResult containing:

2SLS point estimate, analytic + bootstrap SEs, and Wald CI;
Olea–Pflueger effective F + Lee–McCrary–Moreira–Porter (2022) tF adjusted critical value and tF-corrected CI;
Anderson–Rubin (1949) F + AR confidence set; optional CLR / K confidence sets (Moreira 2003; Kleibergen 2002, 2005);
Kleibergen–Paap (2006) rk LM and Wald F;
Conley–Hansen–Rossi (2012) plausibly-exogenous LTZ sensitivity CI when ltz_gamma_sd is supplied;
the BBMT (2022/2025) / Słoczyński (2024) "TSLS-vs-LATE" caveat when covariates are present and the endogenous regressor is binary;
OLS comparator (informative; not causal).

Parameters:

Name	Type	Description	Default
`data`	`DataFrame`		required
`y`	`str`		required
`endog`	`str`	Outcome and (single) endogenous regressor column names.	required
`instruments`	`str or list[str]`	Excluded instruments.	required
`exog`	`str or list[str]`	Included exogenous controls (intercept added automatically).	`None`
`cluster`	`str or array - like`	Cluster variable for cluster-robust SEs and cluster bootstrap.	`None`
`h0`	`float`	Null hypothesis value used by AR / CLR / K test.	`0.0`
`alpha`	`float`	Significance level for all CIs.	`0.05`
`vcov`	`('HC0', 'HC1', 'classic')`	Heteroskedasticity-robust covariance type for the analytic SE and the Olea–Pflueger effective F.	`'HC0'`
`n_boot`	`int`	Bootstrap replications. Set to `0` to skip bootstrap.	`1000`
`boot_methods`	`tuple of {'pairs', 'wild'}`	Which bootstraps to run. Both can be requested.	`('pairs',)`
`include_clr_ci`	`bool`	Optionally invert CLR / K tests on a grid for the matching confidence set (slower; CLR uses Monte-Carlo critical values).	`False`
`include_k_ci`	`bool`	Optionally invert CLR / K tests on a grid for the matching confidence set (slower; CLR uses Monte-Carlo critical values).	`False`
`grid_size`	`int`	Resolution of the AR / CLR / K grid inversion.	`401`
`ltz_gamma_sd`	`float`	If supplied, run Conley–Hansen–Rossi LTZ sensitivity with prior `γ ~ N(0, ltz_gamma_sd**2)`. Otherwise, LTZ is skipped.	`None`
`random_state`	`int`	Seed for bootstrap and CLR Monte-Carlo.	`None`

Returns:

Type	Description
`IVDiagResult`

Examples:

>>> import statspai as sp
>>> r = sp.iv.iv_diag(df, y='wage', endog='educ',
...                   instruments=['nearc4', 'nearc2'],
...                   exog=['exper', 'south'],
...                   n_boot=500, ltz_gamma_sd=0.05,
...                   random_state=42)
>>> print(r.summary())
>>> r.to_frame()                 # tidy table
>>> r.plot('diagnostic')         # 2x2 diagnostic panel
>>> r.to_latex(caption='IV diagnostic bundle')

Notes

The bundle is single-endogenous by design; for multiple endogenous regressors use :func:sp.iv.weakrobust plus :func:sp.iv.sanderson_windmeijer per regressor.
The tF-corrected CI follows LMMP 2022: it widens (vs. the Wald CI) by exactly the multiplicative ratio c(F) / 1.96 and equals ±∞ when F < 3.84.
The bootstrap is implemented as a pairs (or wild Rademacher) bootstrap; see Young (2022, EER 147, 104112) for why analytic SEs can be unreliable. Cluster-bootstrap is used automatically when cluster is supplied.

iv_compare ¶

iv_compare(formula: Optional[str] = None, data: Optional[DataFrame] = None, *, methods: Sequence[str] = ('2sls', 'liml', 'fuller', 'jive'), alpha: float = 0.05, endog_name: Optional[str] = None, **kwargs) -> DataFrame

Run several k-class / JIVE estimators and return a one-row-per-method comparison table — useful for quick sensitivity checks across estimators.

Parameters:

Name	Type	Description	Default
`formula`	`str`	IV formula (`"y ~ (d ~ z) + x"`).	`None`
`data`	`DataFrame`		`None`
`methods`	`sequence of str`	Methods to dispatch through :func:`sp.iv` (and therefore the unified IV dispatcher).	`('2sls', 'liml', 'fuller', 'jive')`
`alpha`	`float`	For Wald-CI columns.	`0.05`

Returns:

Type	Description
`DataFrame`	columns `method`, `estimate`, `SE`, `CI lower`, `CI upper`, `first_stage_F`, `effective_F`.

`sp.iv_compare(...)`¶

iv_compare ¶

iv_compare(formula: Optional[str] = None, data: Optional[DataFrame] = None, *, methods: Sequence[str] = ('2sls', 'liml', 'fuller', 'jive'), alpha: float = 0.05, endog_name: Optional[str] = None, **kwargs) -> DataFrame

Run several k-class / JIVE estimators and return a one-row-per-method comparison table — useful for quick sensitivity checks across estimators.

Parameters:

Name	Type	Description	Default
`formula`	`str`	IV formula (`"y ~ (d ~ z) + x"`).	`None`
`data`	`DataFrame`		`None`
`methods`	`sequence of str`	Methods to dispatch through :func:`sp.iv` (and therefore the unified IV dispatcher).	`('2sls', 'liml', 'fuller', 'jive')`
`alpha`	`float`	For Wald-CI columns.	`0.05`

Returns:

Type	Description
`DataFrame`	columns `method`, `estimate`, `SE`, `CI lower`, `CI upper`, `first_stage_F`, `effective_F`.

Instrumental variables¶

The formula front end — sp.iv / sp.ivreg¶

Modern reporting bundle — sp.iv_diag¶

Comparing estimators — sp.iv_compare¶

Frontier estimators¶

Identifying assumptions (agent-native)¶

Method-level API¶

sp.iv(...)¶

iv ¶

sp.ivreg(...)¶

ivreg ¶

sp.kernel_iv(...)¶

kernel_iv ¶

KernelIVResult dataclass ¶

kernel_iv ¶

sp.continuous_iv_late(...)¶

continuous_iv_late ¶

sp.iv_diag(...)¶

iv_diag ¶

IVDiagResult dataclass ¶

to_frame ¶

to_dict ¶

to_latex ¶

to_excel ¶

to_word ¶

plot ¶

iv_diag ¶

iv_compare ¶

sp.iv_compare(...)¶

iv_compare ¶

The formula front end — `sp.iv` / `sp.ivreg`¶

Modern reporting bundle — `sp.iv_diag`¶

Comparing estimators — `sp.iv_compare`¶

`sp.iv(...)`¶

`sp.ivreg(...)`¶

`sp.kernel_iv(...)`¶

KernelIVResult `dataclass` ¶

`sp.continuous_iv_late(...)`¶

`sp.iv_diag(...)`¶

IVDiagResult `dataclass` ¶

`sp.iv_compare(...)`¶