A randomForest model does a pretty good job for predicting price:

MASS::boxcox(price~., data=ggplot2::diamonds)  # Suggests a log transform
 # although what matters is the distribution of residuals after the fit
diamonds <- ggplot2::diamonds; Y <- diamonds[,"price", drop=T]
samp5K <- sample(1:nrow(diamonds), size=5000)
library(randomForest)
(diamond5K.rf <- randomForest(x=diamonds[samp5K,-7], y=log(Y[samp5K]),
                   xtest=diamonds[-samp5K,-7], ytest=log(Y[-samp5K])))
. . .
          Mean of squared residuals: 0.01350986
                    % Var explained: 98.66
                       Test set MSE: 0.01
                    % Var explained: 98.65

Chris, What kind of modeling did or do you have in mind?  I have not tried, but I suspect that it will be hard to find a GAM or more conventional regression model that does anything like as well.  Incidentally, fitting single regression tree generates a tree with ~2400 leaves, and still does somewhat more poorly than the random forest model.  This suggests to me that there are some quite hard to chase down interactions involved.

Chris Lloyd wrote:

Replying to John. If you plot price against say carats, you will see the truncation very clearly (at about $19,000).

Chris, the real issue is that the distribution of values of 'carat' is strongly banded, which gives the dark vertical bands in the plots to which you refer.  Most of the points are concentrated in these bands, so that one does not see the dropoff in density as the price increases.  One needs to use smoothScatter() or an equivalent to see a more visually meaningful picture.  I am attaching the plot from
with(ggplot::diamonds,(smoothScatter(carat,price)))

Or, repeat the ggplot2 plot with a small enough sample of data that the dark bands separate out to show the separate points.  Possibly also an issue is that only for higher valued diamonds is there finesse in setting the carat, setting it higher and moving the carat measures for high dollar diamonds up and away from the dark vertical bands. The second plot is from a sample of 1000 points.
samp1K <- diamonds[sample(1:nrow(diamonds),1000),]
ggplot(aes(x=carat, y=price), data=samp1K) +
    geom_point(fill=I("#F79420"), color=I("black"), shape=21) +
    scale_x_continuous(lim = c(0, quantile(diamonds$carat, 0.99)) ) +
    scale_y_continuous(lim = c(0, quantile(diamonds$price, 0.99)) ) +
    ggtitle("Diamonds: Price vs. Carat")

Replying to John. If you plot price against say carats, you will see the truncation very clearly (at about $19,000).

Hi Chris,

The R package gamlss does censored and truncated regression, for any response distribution in its repertoire (gamlss.dist). 

Gillian

Hi Chris

No response yet. This can be a lonely forum

Sorry I have no knowledge of the dataset and my memories of truncated methods are very rusty

I am looking at it now out of curiosity but may not be able to help

I even feel unqualified to even comment and run the risk of saying something stupid even if I do. I thought most people ignored stuff like that. The further you get from the (possibly transformed) means of your data, maybe truncation doesn't matter much most of the time :) Can you not see from the truncated data what may be going on. Sorry

Hope somebody has helped

regards Duncan