Understanding loess errors in R

问题:

I'm trying to fit a model using loess, and I'm getting errors such as "pseudoinverse used at 3", "neighborhood radius 1", and "reciprocal condition number 0". Here's a MWE:

x = 1:19
y = c(NA,71.5,53.1,53.9,55.9,54.9,60.5,NA,NA,NA
      ,NA,NA,178.0,180.9,180.9,NA,NA,192.5,194.7)
fit = loess(formula = y ~ x,
        control = loess.control(surface = "direct"),
        span = 0.3, degree = 1)
x2 = seq(0,20,.1)
library(ggplot2)
qplot(x=x2
    ,y=predict(fit, newdata=data.frame(x=x2))
    ,geom="line")

I realize I can fix these errors by choosing a larger span value. However, I'm trying to automate this fit, as I have about 100,000 time series (each of length about 20) similar to this. Is there a way that I can automatically choose a span value that will prevent these errors while still providing a fairly flexible fit to the data? Or, can anyone explain what these errors mean? I did a bit of poking around in the loess() and simpleLoess() functions, but I gave up at the point when C code was called.

回答1:

Compare fit$fitted to y. You'll notice that something is wrong with your regression. Choose adequate bandwidth, otherwise it'll just interpolate the data. With too few data points, linear function behaves like constant on small bandwidth and triggers collinearity. Thus, you see the errors warning pseudoinverses, singularities. You wont see such errors if you use degree=0 or ksmooth. One intelligible, data-driven choice of span is to use to cross-validation, about which you can ask at Cross Validated.

> fit$fitted
 [1]  71.5  53.1  53.9  55.9  54.9  60.5 178.0 180.9 180.9 192.5 194.7
> y
 [1]    NA  71.5  53.1  53.9  55.9  54.9  60.5    NA    NA    NA    NA    NA 178.0
[14] 180.9 180.9    NA    NA 192.5 194.7

You see over-fit( perfect-fit) because in your model number of parameters are as many as effective sample size.

fit
#Call:
#loess(formula = y ~ x, span = 0.3, degree = 1, control = loess.control(surface = "direct"))

#Number of Observations: 11 
#Equivalent Number of Parameters: 11 
#Residual Standard Error: Inf 

Or, you might as well just use automated geom_smooth. (again setting geom_smooth(span=0.3) throws warnings)

ggplot(data=data.frame(x, y), aes(x, y)) + 
  geom_point() + geom_smooth()