Error in predict.lm() for models without intercept?

Hi Rolf,

Thanks very much for your response.   You are right - my simulated
example works as intended, so it can't be used to get to the bottom of
this problem (if it is a problem at all).

Here is another example, which is the one I actually worked with when I
thought maybe something is not quite right in the universe.

The example is based on a real data set (please keep it confidential),
which is attached to this e-mail as *mod.data.csv*.   This data set
includes terminal run numbers for salmon, recorded at Age_5, Age_4,
Age_3 and Age_2.  A model of the form lm(Age_5 ~ 0 + Age_4 + Age_3 +
Age_2) is fitted to these data and the goal is to visualize the effects
of Age_4, Age_3 and Age_2 on Age_5.  For biological reasons, this model
is supposed to not have an intercept.

The attachment Effect_1.pdf shows what these effects look like.  If the
model has no intercept, should the confidence bands still flare up
as one moves away from the value of the predictor whose effect we care
about?

The attachment Effect_2.pdf replicates the effects plots but this time
using the effects package.

If predict() is correct, should we expect from statistical theory to see
that the confidence bands have this particular behaviour?  Intuitively,
I would have expected them to look like a fan plot that starts out at
zero and then flares up as we move away from zero.

Here is the R code I used to create the two attached plots (with R x64
3.1.0).  In this code, Age_5 becomes y, Age_4 becomes x, Age_3 becomes z
and Age_2 becomes v.

## read mod.data into R

mod.data <- read.csv("mod.data.csv")

## compute confidence bands (i.e., fitted values +/- 1.96 standard
errors of fitted values)

y <- mod.data$Age_5
x <- mod.data$Age_4
z <- mod.data$Age_3
v <- mod.data$Age_2

mod <- lm(y ~ 0 + x)

conf.band.x <- predict(mod,newdata=data.frame(x =
seq(from=0,to=max(x),by=100)),
                interval="confidence")

## display confidence bands

conf.band.x <- data.frame(lwr=conf.band.x[,"lwr"],
                           fit=conf.band.x[,"fit"],
                           upr=conf.band.x[,"upr"])

matplot(x=seq(from=0,to=floor(max(x)),by=100), y=conf.band.x, type="l",
xlab="x", ylab="y")
## abline(v=0,lty=3,col="magenta")
title("Effect of x on y")

## linear model with no intercept but with three predictors

par(mfrow=c(2,2))

mod <- lm(y ~ 0 + x + z + v)

## effect of x on y

conf.band.x <- predict(mod,newdata=data.frame(x =
seq(from=0,to=max(x),by=100),
              z = mean(z),
              v=mean(v)),
             interval="confidence")

conf.band.x <- data.frame(lwr=conf.band.x[,"lwr"],
  fit=conf.band.x[,"fit"],
upr=conf.band.x[,"upr"])

matplot(x=seq(from=0,to=max(x),by=100), y=conf.band.x, type="l",
xlab="x", ylab="y")
abline(v=mean(x),lty=3,col="magenta")
title("Effect of x on y (obtained by setting z and v to their average
levels)")


## effect of z on y
conf.band.z <- predict(mod,newdata=data.frame(z = seq(0,to=max(z),by=100),
              x = mean(x),v=mean(v)),
             interval="confidence")

conf.band.z <- data.frame(lwr=conf.band.z[,"lwr"],
  fit=conf.band.z[,"fit"],
upr=conf.band.z[,"upr"])

matplot(seq(from=0,to=max(z),by=100), y=conf.band.z, type="l", xlab="z",
ylab="y")
abline(v=mean(z),lty=3,col="magenta")
title("Effect of z on y (obtained by setting x and v to their average
levels)")


## effect of v on y
conf.band.v <- predict(mod,newdata=data.frame(v = seq(0,to=max(v),by=100),
              x = mean(x),z=mean(z)),
             interval="confidence")

conf.band.v <- data.frame(lwr=conf.band.v[,"lwr"],
  fit=conf.band.v[,"fit"],
  upr=conf.band.v[,"upr"])

matplot(seq(from=0,to=max(v),by=100), y=conf.band.v, type="l", xlab="v",
ylab="y")
abline(v=mean(v),lty=3,col="magenta")
title("Effect of v on y (obtained by setting x and z to their average
levels)")

###
### Replicate effect plots using effects package
###

require(effects)
plot(allEffects(mod))

Maybe my intuition is playing tricks on me - if you have any idea as to
what may be going on here, please let me know.

	The example is based on a real data set (please keep it
confidential), which is attached to this e-mail as mod.data.csv.