```
# NOT RUN {
pneumo <- transform(pneumo, let = log(exposure.time))
(fit <- vglm(cbind(normal, mild, severe) ~ let,
cumulative(parallel = TRUE, reverse = TRUE), data = pneumo))
depvar(fit) # These are sample proportions
weights(fit, type = "prior", matrix = FALSE) # Number of observations
# Look at the working residuals
nn <- nrow(model.matrix(fit, type = "lm"))
M <- ncol(predict(fit))
wwt <- weights(fit, type = "working", deriv = TRUE) # In matrix-band format
wz <- m2a(wwt$weights, M = M) # In array format
wzinv <- array(apply(wz, 3, solve), c(M, M, nn))
wresid <- matrix(NA, nn, M) # Working residuals
for (ii in 1:nn)
wresid[ii, ] <- wzinv[, , ii, drop = TRUE] %*% wwt$deriv[ii, ]
max(abs(c(resid(fit, type = "work")) - c(wresid))) # Should be 0
(zedd <- predict(fit) + wresid) # Adjusted dependent vector
# }
```

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