Plot x-y Points with Locally Smoothed Mean and Standard Deviation

Plot x-y points with curves for locally smoothed mean and standard deviation.

bandplot(x,...)
# S3 method for formula
bandplot(x, data, subset, na.action, ...,
           xlab=NULL, ylab=NULL, add = FALSE, sd = c(-2:2),
           sd.col=c("magenta", "blue", "red", "blue", "magenta"),
           sd.lwd=c(2, 2, 3, 2, 2),  sd.lty=c(2, 1, 1, 1, 2),
           method = "frac", width = 1/5, n=50)
# S3 method for default
bandplot(x, y, ..., add = FALSE, sd = c(-2:2),
           sd.col=c("magenta", "blue", "red", "blue", "magenta"),
           sd.lwd=c(2, 2, 3, 2, 2),  sd.lty=c(2, 1, 1, 1, 2),
           method = "frac", width = 1/5, n=50)

Arguments

x

either formula providing a single dependent variable (y) and an single independent variable (x) to use as coordinates in the scatter plot or a numeric vector of x locations
y

numeric vector of y locations
data

an optional data.frame, list, or environment contianing the variables used in the model (and in subset). If not found in data, the variables are taken from environment(formula), typically the environment from which lm is called.
subset

an optional vector specifying a subset of observations to be used in the fitting process.
na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The factory-fresh default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.
...

Additional plotting parameters
xlab, ylab

x and y axis labels
add

Boolean indicating whether the local mean and standard deviation lines should be added to an existing plot. Defaults to FALSE.
sd

Vector of multiples of the standard devation that should be plotted. 0 gives the mean, -1 gives the mean minus one standard deviation, etc. Defaults to -2:2.
sd.col,sd.lwd,sd.lty

Color, line width, and line type of each plotted line.
method, width, n

Parameters controlling the smoothing. See the help page for wapply for details.

Details

bandplot was created to look for changes in the mean or variance of scatter plots, particularly plots of regression residuals.

The local mean and standard deviation are calculated by calling 'wapply'. By default, bandplot asks wapply to smooth using intervals that include the nearest 1/5 of the data. See the documentation of that function for details on the algorithm.

Value

Invisibly returns a list containing the x,y points plotted for each line.

See also

wapply, lowess

Examples


# fixed mean, changing variance
x <- 1:1000
y <- rnorm(1000, mean=1, sd=1 + x/1000 )
bandplot(x,y)
bandplot(y~x)

# fixed varance, changing mean
x <- 1:1000
y <- rnorm(1000, mean=x/1000, sd=1)
bandplot(x,y)

#
# changing mean and variance
#
x <- abs(rnorm(500))
y <- rnorm(500, mean=2*x, sd=2+2*x)

# the changing mean and dispersion are hard to see whith the points alone:
plot(x,y )

# regression picks up the mean trend, but not the change in variance
reg <- lm(y~x)
summary(reg)
#> 
#> Call:
#> lm(formula = y ~ x)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -12.0831  -2.2161  -0.0745   2.2350  15.6152 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)   0.2574     0.2886   0.892    0.373    
#> x             1.5967     0.2915   5.477 6.88e-08 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 3.845 on 498 degrees of freedom
#> Multiple R-squared:  0.05681,	Adjusted R-squared:  0.05492 
#> F-statistic:    30 on 1 and 498 DF,  p-value: 6.875e-08
#> 
abline(reg=reg, col="blue", lwd=2)

# using bandplot on the original data helps to show the mean and
# variance trend
bandplot(y ~ x)

# using bandplot on the residuals helps to see that regression removes
# the mean trend but leaves the trend in variability
bandplot(predict(reg),resid(reg))