Plotting newton-raphson/fisher scoring iterations in R - r

Question

Is there a package in R plotting newton-raphson/fisher scoring iterations when fitting a glm modelel (from the stats package)?

Answer 1

I answered a very similar question yesterday. In your case however, things are a little simpler.
Note that when you call glm, it eventually calls glm.fit (or any other method argument you specify to glm) which computes the solution path in the loop from lines 78 to 170. The current iteration's value of the coefficients is computed on line 97 using a .Call to a C function C_Cdqrls. As a hack, you can extract the current value of the coefficients to the global environment (fit$coefficients), within this loop, by modifying the glm.fit function like so:
glm.fit.new = function (x, y, weights = rep(1, nobs), start = NULL, etastart = NULL,
mustart = NULL, offset = rep(0, nobs), family = gaussian(),
control = list(), intercept = TRUE) {
control <- do.call("glm.control", control)
x <- as.matrix(x)
xnames <- dimnames(x)[[2L]]
ynames <- if (is.matrix(y))
rownames(y)
else names(y)
conv <- FALSE
nobs <- NROW(y)
nvars <- ncol(x)
EMPTY <- nvars == 0
if (is.null(weights))
weights <- rep.int(1, nobs)
if (is.null(offset))
offset <- rep.int(0, nobs)
variance <- family$variance
linkinv <- family$linkinv
if (!is.function(variance) || !is.function(linkinv))
stop("'family' argument seems not to be a valid family object",
call. = FALSE)
dev.resids <- family$dev.resids
aic <- family$aic
mu.eta <- family$mu.eta
unless.null <- function(x, if.null) if (is.null(x))
if.null
else x
valideta <- unless.null(family$valideta, function(eta) TRUE)
validmu <- unless.null(family$validmu, function(mu) TRUE)
if (is.null(mustart)) {
eval(family$initialize)
}
else {
mukeep <- mustart
eval(family$initialize)
mustart <- mukeep
}
if (EMPTY) {
eta <- rep.int(0, nobs) + offset
if (!valideta(eta))
stop("invalid linear predictor values in empty model",
call. = FALSE)
mu <- linkinv(eta)
if (!validmu(mu))
stop("invalid fitted means in empty model", call. = FALSE)
dev <- sum(dev.resids(y, mu, weights))
w <- ((weights * mu.eta(eta)^2)/variance(mu))^0.5
residuals <- (y - mu)/mu.eta(eta)
good <- rep_len(TRUE, length(residuals))
boundary <- conv <- TRUE
coef <- numeric()
iter <- 0L
}
else {
coefold <- NULL
eta <- if (!is.null(etastart))
etastart
else if (!is.null(start))
if (length(start) != nvars)
stop(gettextf("length of 'start' should equal %d and correspond to initial coefs for %s",
nvars, paste(deparse(xnames), collapse = ", ")),
domain = NA)
else {
coefold <- start
offset + as.vector(if (NCOL(x) == 1L)
x * start
else x %*% start)
}
else family$linkfun(mustart)
mu <- linkinv(eta)
if (!(validmu(mu) && valideta(eta)))
stop("cannot find valid starting values: please specify some",
call. = FALSE)
devold <- sum(dev.resids(y, mu, weights))
boundary <- conv <- FALSE
# EDIT: counter to create track of iterations
i <<- 1
for (iter in 1L:control$maxit) {
good <- weights > 0
varmu <- variance(mu)[good]
if (anyNA(varmu))
stop("NAs in V(mu)")
if (any(varmu == 0))
stop("0s in V(mu)")
mu.eta.val <- mu.eta(eta)
if (any(is.na(mu.eta.val[good])))
stop("NAs in d(mu)/d(eta)")
good <- (weights > 0) & (mu.eta.val != 0)
if (all(!good)) {
conv <- FALSE
warning(gettextf("no observations informative at iteration %d",
iter), domain = NA)
break
}
z <- (eta - offset)[good] + (y - mu)[good]/mu.eta.val[good]
w <- sqrt((weights[good] * mu.eta.val[good]^2)/variance(mu)[good])
fit <- .Call(stats:::C_Cdqrls, x[good, , drop = FALSE] *
w, z * w, min(1e-07, control$epsilon/1000), check = FALSE)
#======================================================
# EDIT: assign the coefficients to variables in the global namespace
#======================================================
assign(paste0("iteration_x_", i), fit$coefficients,
envir = .GlobalEnv)
i <<- i + 1 # increase the counter
if (any(!is.finite(fit$coefficients))) {
conv <- FALSE
warning(gettextf("non-finite coefficients at iteration %d",
iter), domain = NA)
break
}
if (nobs < fit$rank)
stop(sprintf(ngettext(nobs, "X matrix has rank %d, but only %d observation",
"X matrix has rank %d, but only %d observations"),
fit$rank, nobs), domain = NA)
start[fit$pivot] <- fit$coefficients
eta <- drop(x %*% start)
mu <- linkinv(eta <- eta + offset)
dev <- sum(dev.resids(y, mu, weights))
if (control$trace)
cat("Deviance = ", dev, " Iterations - ", iter,
"\n", sep = "")
boundary <- FALSE
if (!is.finite(dev)) {
if (is.null(coefold))
stop("no valid set of coefficients has been found: please supply starting values",
call. = FALSE)
warning("step size truncated due to divergence",
call. = FALSE)
ii <- 1
while (!is.finite(dev)) {
if (ii > control$maxit)
stop("inner loop 1; cannot correct step size",
call. = FALSE)
ii <- ii + 1
start <- (start + coefold)/2
eta <- drop(x %*% start)
mu <- linkinv(eta <- eta + offset)
dev <- sum(dev.resids(y, mu, weights))
}
boundary <- TRUE
if (control$trace)
cat("Step halved: new deviance = ", dev, "\n",
sep = "")
}
if (!(valideta(eta) && validmu(mu))) {
if (is.null(coefold))
stop("no valid set of coefficients has been found: please supply starting values",
call. = FALSE)
warning("step size truncated: out of bounds",
call. = FALSE)
ii <- 1
while (!(valideta(eta) && validmu(mu))) {
if (ii > control$maxit)
stop("inner loop 2; cannot correct step size",
call. = FALSE)
ii <- ii + 1
start <- (start + coefold)/2
eta <- drop(x %*% start)
mu <- linkinv(eta <- eta + offset)
}
boundary <- TRUE
dev <- sum(dev.resids(y, mu, weights))
if (control$trace)
cat("Step halved: new deviance = ", dev, "\n",
sep = "")
}
if (abs(dev - devold)/(0.1 + abs(dev)) < control$epsilon) {
conv <- TRUE
coef <- start
break
}
else {
devold <- dev
coef <- coefold <- start
}
}
if (!conv)
warning("glm.fit: algorithm did not converge", call. = FALSE)
if (boundary)
warning("glm.fit: algorithm stopped at boundary value",
call. = FALSE)
eps <- 10 * .Machine$double.eps
if (family$family == "binomial") {
if (any(mu > 1 - eps) || any(mu < eps))
warning("glm.fit: fitted probabilities numerically 0 or 1 occurred",
call. = FALSE)
}
if (family$family == "poisson") {
if (any(mu < eps))
warning("glm.fit: fitted rates numerically 0 occurred",
call. = FALSE)
}
if (fit$rank < nvars)
coef[fit$pivot][seq.int(fit$rank + 1, nvars)] <- NA
xxnames <- xnames[fit$pivot]
residuals <- (y - mu)/mu.eta(eta)
fit$qr <- as.matrix(fit$qr)
nr <- min(sum(good), nvars)
if (nr < nvars) {
Rmat <- diag(nvars)
Rmat[1L:nr, 1L:nvars] <- fit$qr[1L:nr, 1L:nvars]
}
else Rmat <- fit$qr[1L:nvars, 1L:nvars]
Rmat <- as.matrix(Rmat)
Rmat[row(Rmat) > col(Rmat)] <- 0
names(coef) <- xnames
colnames(fit$qr) <- xxnames
dimnames(Rmat) <- list(xxnames, xxnames)
}
names(residuals) <- ynames
names(mu) <- ynames
names(eta) <- ynames
wt <- rep.int(0, nobs)
wt[good] <- w^2
names(wt) <- ynames
names(weights) <- ynames
names(y) <- ynames
if (!EMPTY)
names(fit$effects) <- c(xxnames[seq_len(fit$rank)], rep.int("",
sum(good) - fit$rank))
wtdmu <- if (intercept)
sum(weights * y)/sum(weights)
else linkinv(offset)
nulldev <- sum(dev.resids(y, wtdmu, weights))
n.ok <- nobs - sum(weights == 0)
nulldf <- n.ok - as.integer(intercept)
rank <- if (EMPTY)
0
else fit$rank
resdf <- n.ok - rank
aic.model <- aic(y, n, mu, weights, dev) + 2 * rank
list(coefficients = coef, residuals = residuals, fitted.values = mu,
effects = if (!EMPTY) fit$effects, R = if (!EMPTY) Rmat,
rank = rank, qr = if (!EMPTY) structure(fit[c("qr", "rank",
"qraux", "pivot", "tol")], class = "qr"), family = family,
linear.predictors = eta, deviance = dev, aic = aic.model,
null.deviance = nulldev, iter = iter, weights = wt, prior.weights = weights,
df.residual = resdf, df.null = nulldf, y = y, converged = conv,
boundary = boundary)
}
Note that this is a hack for a couple of reasons:
1. The function C_Cdrqls is not exported by the package stats, and so we have to look for it within namespace:package:stats.
2. This pollutes your global environment with the iteration values via a side-effect of the call to glm.fit.new, creating one vector per iteration. Side-effects are generally frowned upon in functional languages like R. You can probably clean the multiple objects bit up by creating a matrix or a data.frame and assign within that.
However, once you have the iteration values extracted, you can do whatever you want with them, including plotting them.
Here is what a call to glm with the newly defined glm.fit.new method would look like:
counts = c(18,17,15,20,10,20,25,13,12)
outcome = gl(3,1,9)
treatment = gl(3,3)
print(d.AD = data.frame(treatment, outcome, counts))
glm.D93 = glm(counts ~ outcome + treatment, family = poisson(),
control = list(trace = TRUE, epsilon = 1e-16), method = "glm.fit.new")
You can check that the iteration parameter values have indeed been populated in the global environment:
> ls(pattern = "iteration_x_")
[1] "iteration_x_1" "iteration_x_10" "iteration_x_11" "iteration_x_2"
[5] "iteration_x_3" "iteration_x_4" "iteration_x_5" "iteration_x_6"
[9] "iteration_x_7" "iteration_x_8" "iteration_x_9"