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Anytime-Valid replacements for base R’s lm and aov functions (with additional robust standard error functionality).
https://arxiv.org/abs/2210.08589.
Contributors: - Michael Lindon (michael.s.lindon@gmail.com)
devtools::install_github("michaellindon/avlm")
# Generate Data
set.seed(1)
n = 100
X = scale(replicate(3, rnorm(n)), center = TRUE, scale = FALSE)
trt = sample(c(0, 1), size = n, replace = TRUE)
y = 1 + 0*X[,1] + 0*X[,2] + 1.4*X[,3] + 2.3*trt + 2*X[,1]*trt + 3*X[,2]*trt + 0*X[,3]*trt + 1*rnorm(n)
df = data.frame(X)
df$trt = trt
df$y = y
# Tune g to minimize the width of the confidence interval at n
alpha = 0.05
number_of_coefficients = ncol(model.matrix(y ~ . + trt * ., data = df))
g_star = optimal_g(n, number_of_coefficients, alpha)
# Summary
classic_fit = lm(y ~ . + trt * ., data = df)
av_fit = av(classic_fit, g = g_star)
summary(av_fit)
confint(av_fit)Call:
lm(formula = y ~ . + trt * ., data = df)
Residuals:
Min 1Q Median 3Q Max
-3.00823 -0.56961 0.07473 0.78458 1.92584
Coefficients:
Estimate Std. Error t value p value
(Intercept) 0.91630 0.15864 5.776 9.77e-06 ***
X1 -0.12768 0.18087 -0.706 1
X2 -0.14966 0.18283 -0.819 1
X3 1.30556 0.15941 8.190 8.07e-10 ***
trt 2.32245 0.21566 10.769 3.19e-14 ***
X1:trt 2.29985 0.24141 9.527 3.98e-12 ***
X2:trt 3.31166 0.23251 14.243 < 2e-16 ***
X3:trt 0.08015 0.21122 0.379 1
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.065 on 92 degrees of freedom
Multiple R-squared: 0.9164, Adjusted R-squared: 0.91
F-statistic: 144 on 7 and 92 DF, p-value: < 2.2e-16
Anytime-Valid: TRUE
2.5 % 97.5 %
(Intercept) 0.4238730 1.4087195
X1 -0.6890957 0.4337358
X2 -0.7171420 0.4178268
X3 0.8107460 1.8003705
trt 1.6530529 2.9918408
X1:trt 1.5505190 3.0491788
X2:trt 2.5899720 4.0333555
X3:trt -0.5754734 0.7357662You can use robust standard errors with HC0, HC1, HC2 and HC3. ## Code
av_fit = av(classic_fit, g=g_star, vcov_estimator = "HC0")
summary(av_fit)
confint(av_fit)Call:
lm(formula = y ~ . + trt * ., data = df)
Residuals:
Min 1Q Median 3Q Max
-3.00823 -0.56961 0.07473 0.78458 1.92584
Coefficients:
Estimate Std. Error t value p value
(Intercept) 0.91630 0.15234 6.015 4.00e-06 ***
X1 -0.12768 0.15327 -0.833 1
X2 -0.14966 0.17150 -0.873 1
X3 1.30556 0.13238 9.862 1.07e-12 ***
trt 2.32245 0.20302 11.439 2.54e-15 ***
X1:trt 2.29985 0.21114 10.893 1.99e-14 ***
X2:trt 3.31166 0.20403 16.232 < 2e-16 ***
X3:trt 0.08015 0.18154 0.441 1
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Multiple R-squared: 0.9164, Adjusted R-squared: 0.91
F-statistic: 1496 on 7 and 92 DF, p-value: < 2.2e-16
Anytime-Valid: TRUE
Robust Standard Error Type: HC0
2.5 % 97.5 %
(Intercept) 0.4434498 1.3891427
X1 -0.6034239 0.3480640
X2 -0.6819698 0.3826546
X3 0.8946528 1.7164637
trt 1.6922727 2.9526209
X1:trt 1.6444954 2.9552024
X2:trt 2.6783800 3.9449474
X3:trt -0.4833522 0.6436451classic_aov <- aov(Sepal.Length ~ Species, data = iris)
av_aov = av(classic_aov)
summary(av_aov) Df Sum Sq Mean Sq F value p value
Species 2 63.21 31.606 119.3 <2e-16 ***
Residuals 147 38.96 0.265
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Anytime-Valid: TRUEThese binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.