Package {avlm}

Anytime-valid Conversion Generic Function

Description

This generic function converts a fitted model object into an anytime-valid version. The conversion is performed by the appropriate S3 method based on the class of the input model.

Usage

av(model, g = 1, ...)

Arguments

Value

An enhanced version of model with anytime-valid inference capabilities.

Convert an aov Object to Anytime-Valid aov (avaov)

Description

Converts an object of class aov to an anytime-valid version by setting the precision parameter g as an attribute and updating the class.

Usage

## S3 method for class 'aov'
av(model, g = 1, ...)

Arguments

Value

An object of class avaov with anytime-valid p-values.

Convert a Linear Model (lm) Object to Anytime-Valid lm (avlm)

Description

Converts an lm object into an anytime-valid version by storing a precision parameter g as an attribute and updating the object's class. The resulting object supports anytime-valid inference.

Usage

## S3 method for class 'lm'
av(model, g = 1, vcov_estimator = NULL, cluster = NULL, ...)

Arguments

Value

An enhanced lm object of class avlm with anytime-valid inference capabilities.

References

Lindon, M., Ham, D. W., Tingley, M., and Bojinov, I. (2026). Anytime-Valid Inference in Linear Models with Applications to Regression-Adjusted Causal Inference. Journal of the American Statistical Association. doi:10.1080/01621459.2026.2692052

Lindon, M. (2026). Anytime-Valid Inference in Linear Models with Clustered Outcomes: Exact Multivariate Tests and Cluster-Robust Confidence Sequences. arXiv:2610.25613. https://arxiv.org/abs/2610.25613

Examples

# Fit a linear model on the built-in mtcars dataset
fit <- lm(mpg ~ wt + hp, data = mtcars)

# Convert the standard lm object to an anytime-valid avlm object
av_fit <- av(fit, g = 1)

# Print the summary of the anytime-valid model
summary(av_fit)

# With cluster-robust standard errors, clustering on number of cylinders
av_fit_cl <- av(fit, g = 1, cluster = ~ cyl)
summary(av_fit_cl)

# Equivalent ways of specifying the clusters
av_fit_cl <- av(fit, g = 1, cluster = "cyl")
av_fit_cl <- av(fit, g = 1, cluster = mtcars$cyl)

Coefficient Covariance and Degrees of Freedom for Anytime-Valid Inference

Description

Computes, for an avlm object, the coefficient estimates, their covariance matrix and the two quantities the anytime-valid e-values need: the denominator degrees of freedom nu and the sample size n on which the precision g acts.

Usage

av_vcov(object)

Arguments

Details

• Classical: s^2 (X'X)^{-1}, \nu = n - k (Lindon et al., 2026, Section 4).

• Heteroskedasticity-robust (HC0–HC3): the sandwich (X'X)^{-1} X'\Omega X (X'X)^{-1}, \nu = n - k (Lindon et al., 2026, Section 5).

• Cluster-robust (CR1): the sandwich of the summed cluster scores scaled by G/(G-1), \nu = G - 1 and sample size G (Lindon, 2026, eq. CR1).

Aliased (NA) coefficients are dropped. For weighted fits, the rows of X and the residuals are scaled by \sqrt{w} and observations with zero weight are dropped.

Value

A list with elements coefficients (non-aliased estimates), vcov, nu, n, type ("classical", an HC type, or "CR1") and G (number of clusters, or NULL).

Validate the Precision Parameter g

Description

Validate the Precision Parameter g

Usage

check_g(g)

Arguments

Value

g, invisibly, if it is a single finite positive number.

Look Up a Cluster Variable in the Data a Model Was Fit With

Description

Look Up a Cluster Variable in the Data a Model Was Fit With

Usage

cluster_from_data(model, cluster)

Arguments

Value

The cluster variable, subset to the observations used in the fit.

Confidence Intervals for Anytime-Valid lm (avlm) Objects

Description

Computes confidence intervals for the coefficients of an avlm object by adjusting the standard errors using the precision parameter g and an anytime-valid approach.

Usage

## S3 method for class 'avlm'
confint(object, parm, level = 0.95, ...)

Arguments

Value

A matrix with the lower and upper confidence limits for the specified parameters.

Examples

# Fit a simple linear model using the mtcars dataset
fit <- lm(mpg ~ wt + hp, data = mtcars)

# Convert the standard lm object to an anytime-valid avlm object with precision parameter g = 1
av_fit <- av(fit, g = 1)

# Calculate and print confidence intervals for the coefficients
conf_intervals <- confint(av_fit)
print(conf_intervals)

Check Whether a Covariance Matrix Is Numerically Singular

Description

Scale-invariant: checks the smallest eigenvalue of the implied correlation matrix.

Usage

is_singular_vcov(V, tol = 1e-10)

Arguments

Value

TRUE if V is numerically singular.

Log Cluster-Robust e-Value for a Joint Wald Test

Description

The cluster-robust e-process of Lindon (2026), eq. (ECR), with \nu = G - 1 and exponent G/2 for any number q of tested coefficients:

E_G = \left(\frac{g}{g+G}\right)^{q/2} \left(\frac{1 + Q/(G-1)}{1 + \frac{g}{g+G} Q/(G-1)}\right)^{G/2}.

Usage

log_E_CR(Q, q, G, g)

Arguments

Value

The log e-value.

References

Lindon, M. (2026). Anytime-Valid Inference in Linear Models with Clustered Outcomes: Exact Multivariate Tests and Cluster-Robust Confidence Sequences. arXiv:2610.25613. https://arxiv.org/abs/2610.25613

Computes the value of g such that width of the 1-\alpha confidence interval at sample size n is minimized

Description

Minimizes the radius R(g, n, 1, \alpha) of the asymptotic t confidence sequence (Lindon et al., 2026, Section 5.1) over g.

Usage

optimal_g(n, number_of_coefficients, alpha, nu = n - number_of_coefficients)

Arguments

Value

A positive numeric scalar representing the optimal g that minimizes the CI width.

Examples

n <- 10000
alpha <- 0.05
g_star <- optimal_g(n, 5, alpha)
cat("The optimal g is:", g_star, "\n")

# cluster-robust inference with 200 clusters
optimal_g(200, alpha = 0.05, nu = 199)

Print Method for summary.avaov Objects

Description

This method prints the summary of an avaov object. It captures the output from the default printing method, substitutes the header "Pr(>F)" with "p value", and adds a note indicating that anytime-valid inference is used.

Usage

## S3 method for class 'summary.avaov'
print(
  x,
  digits = max(3L, getOption("digits") - 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

Arguments

Value

Invisibly returns the summary object.

Print Method for summary.avlm Objects

Description

Custom print method for summary.avlm objects that mimics the standard summary.lm output, but replaces p-value column headers and includes anytime-valid annotations.

Usage

## S3 method for class 'summary.avlm'
print(
  x,
  digits = max(3L, getOption("digits") - 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

Arguments

Value

Invisibly returns the summary object.

Resolve a Cluster Argument into a Factor Aligned with the Fitted Model

Description

Resolve a Cluster Argument into a Factor Aligned with the Fitted Model

Usage

resolve_cluster_factor(model, cluster)

Arguments

Value

A factor of cluster identifiers, or NULL if cluster is NULL.

Summary Method for Anytime-Valid aov Objects

Description

This method produces a summary for objects of class avaov. It first calls the default summary.aov method and then replaces the standard p-values with anytime-valid p-values calculated using the precision parameter g.

Usage

## S3 method for class 'avaov'
summary(object, ...)

Arguments

Value

A summary object of class summary.avaov that includes the anytime-valid p-values.

Examples

# Fit an ANOVA model to the iris dataset.
# This model tests whether the sepal length differs by species.
fit_aov <- aov(Sepal.Length ~ Species, data = iris)

# Convert the standard aov object to an anytime-valid aov (avaov) with precision parameter g = 1.
av_fit_aov <- av(fit_aov, g = 1)

# Print the summary of the anytime-valid ANOVA model.
# The summary replaces standard p-values with anytime-valid p-values.
summary(av_fit_aov)

Summary Method for Anytime-Valid lm (avlm) Objects

Description

Computes a summary for an avlm object, a linear model enhanced with anytime-valid inference. In addition to the standard lm summary statistics, the p-values for the coefficient tests are recalculated using an anytime-valid method.

Usage

## S3 method for class 'avlm'
summary(object, ...)

Arguments

Value

A summary object of class summary.avlm that includes updated p-values for the coefficients.

Covariance Matrix for Anytime-Valid lm (avlm) Objects

Description

Returns the covariance matrix used for anytime-valid inference: the classical one, or the heteroskedasticity-robust or cluster-robust one requested in av.lm.

Usage

## S3 method for class 'avlm'
vcov(object, complete = TRUE, ...)

Arguments

Value

A covariance matrix.

Examples

fit <- av(lm(mpg ~ wt + hp, data = mtcars), cluster = ~ cyl)
vcov(fit)