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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | e0a1a48 | Matthew Stephens | 2024-02-18 | workflowr::wflow_publish("irls.Rmd") |
I wanted to use IRLS to fit a simple logistic regression.
logistic_IRLS_simple <- function(x, y, max_iter = 100, tolerance = 1e-6) {
# Initialize coefficients
mu <- 0
beta <- 0
converged <- FALSE
for (iter in 1:max_iter) {
eta <- mu + x * beta # Linear predictor
pi <- exp(eta) / (1 + exp(eta)) # Predicted probabilities
# Weights for IRLS
w <- pi * (1 - pi)
# Working response variable
z <- eta + (y - pi) / (pi * (1 - pi))
# Weighted least squares update
#These are the elements of the X'X matrix (a b) (c d)
a = sum(w)
b = sum(w*x)
c = sum(w*x)
d = sum(w*x^2)
wz = sum(w*z)
wxz = sum(w*x*z)
new_mu <- (d*wz - b*wxz) / (a*d - b*c)
new_beta <- (-c*wz + a*wxz) / (a*d - b*c)
# Check for convergence
if (all(abs(new_beta - beta) < tolerance)) {
converged = TRUE
break
}
beta <- new_beta
mu <- new_mu
}
# Return fitted coefficients
return(list(mu = mu, beta = beta, converged = converged, iter=iter))
}Now I want to test the function with some simulated data. Simulate a simple logistic regression:
set.seed(1)
n <- 10000
x <- rnorm(n)
eta <- 10 + 2*x
pi <- exp(eta) / (1 + exp(eta))
y <- rbinom(n, 1, pi)
logistic_IRLS_simple(x, y)$mu
[1] 10.77451
$beta
[1] 2.297807
$converged
[1] TRUE
$iter
[1] 14glm(y~x, family = binomial)
Call: glm(formula = y ~ x, family = binomial)
Coefficients:
(Intercept) x
10.775 2.298
Degrees of Freedom: 9999 Total (i.e. Null); 9998 Residual
Null Deviance: 54.67
Residual Deviance: 40.21 AIC: 44.21
sessionInfo()R version 4.2.1 (2022-06-23)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur ... 10.16
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
loaded via a namespace (and not attached):
[1] Rcpp_1.0.12 rstudioapi_0.15.0 whisker_0.4.1 knitr_1.45
[5] magrittr_2.0.3 workflowr_1.7.1 R6_2.5.1 rlang_1.1.2
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[37] jsonlite_1.8.8 httpuv_1.6.13 pkgconfig_2.0.3