Plots for uncertainty budgets produced by uncert calls.
# S3 method for uncert
plot(x, which = c(1,2,4,5), main = paste(deparse(substitute(x))),
ask = prod(par("mfcol")) < length(which) && dev.interactive(),
caption = list("Variance and covariance contributions",
expression(sqrt(group("|", "Variance and covariance contributions", "|"))),
expression("Contribution " * u[i](y) == c[i] * u[i]),
"Combined contribution", "Correlation (x,y)",
"Covariances (x,y)"), cex.caption = 1, ...)An object of class uncert produced by a call to uncert().
Integer in 1:6; the particular variant(s) of plot required. A vector is permitted, in which case plots are produced in ascending order.
Main title for the plot
logical; if 'TRUE', the user is _ask_ed before each plot, see 'par("ask=")'
A list of captions for all the different plots.
Text size for captions. Note that if the number of figures per page is over 2, captions are further scaled by 0.8
Further parameters passed to plot() (mostly barplot).
Invisibly returns the default return value for the last plot produced.
For uncert objects created with methods other than MC, the plot types are:
which=1A barplot of all non-zero contributions to the combined
uncertainty. These are derived from the covariance matrix and the coefficients \(c_i\).
For terms on the diagonal of the covariance matrix, these are \((c_i*u_i)^2\); for
off-diagonal terms (the correlation terms), \(2*(c_i*u_i)*(c_j*u_j)*r_ij\).
The threshold for deciding an off-diagonal term is nonzero is that its magnitude
is greater than 2*.Machine$double.eps. Note that off-diagonal contributions
may be negative.
which=2As for which=1 except that the square root of the
absolute value is plotted. For the 'diagonal' terms, these are just eqnu_i(y)
in the nomenclature used by the GUM.
which=3A barplot of \(u_i(y)^2\), without the correlation terms.
which=4A barplot of the sum of all (co)variance contributions associated with each \(x_i\), that is, $$contrib(i)=(c_{i}u_{i})^2+\sum\nolimits _{j\neq{}i} 2(c_{i}u_{i})(c_{j}u_{j})r_{i,j}$$.
which=5A barplot of the theoretical correlations \(cov(x_i,y)/u(x_i)u_y\).
which=6A barplot of the theoretical covariances \(cov(x_i,y)\).
Values of which outside this range are silently ignored.
For the X-Y correlation and covariance plots, the covariances are calculated from the
covariance matrix \(V\) (supplied to uncert() as cov
or calculated as outer(u,u,"*")*cor) and sensitivity coefficients \(c_i\)
as \(cov(x_i,y) = \sum\nolimits _{j} V_{j,i}c_j \).
In fact the calculation used is simpler: cov.xy <- V %*% ci. The correlations
are calculated in turn from these using \(cov(x_i,y)/u(x_i)u_y\).
Perhaps the most informative plots are for which=1, which=2,
which=4 and which=5. The first of these includes all nonzero signed contributions,
making the negative contributions visible; the second (which=2) makes direct
comparison of magnitudes easier. The combined contribution plot is the effect on
the total variance of removing all terms associated with a particular variable; it
shows how much \(u_y^2\) would reduce if the uncertainty for \(x_i\) were
reduced to zero. Note that in some cases with negative correlation the combined uncertainty can increase,
on dropping a variable, shown by a negative reduction in the plot. (which=5) is among the most
direct indications of the relative importance of individual parameters.
Objects created with the MC method are passed to plot.uncertMC.
None.
# NOT RUN {
#An example with negative correlation
x <- list(a=1, b=3, c=2, d=11)
u <- lapply(x, function(x) x/10)
u.cor<-diag(1,4)
u.cor[3,4]<-u.cor[4,3]<- -0.5
u.form.c<-uncert(~a+b*2+c*3+d/2, x, u, method="NUM", cor=u.cor)
par(mfrow=c(3,2))
plot(u.form.c, which=1:6, las=1, horiz=TRUE) #Note use of barplot parameters
# }
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