For the simple example below, you can see that there are certain points that are identified in the ensuing plots. How can I extract the row numbers identified in these plots, especially the Normal Q-Q plot?
set.seed(2016)
maya <- data.frame(rnorm(100))
names(maya)[1] <- "a"
maya$b <- rnorm(100)
mara <- lm(b~a, data=maya)
plot(mara)
I tried using str(mara) to see if I could find a list there, but I can't see any of the numbers from the Normal Q-Q plot there. Thoughts?
I have edited your question using set.seed(2016) for reproducibility. To answer your question, I need to explain how to produce the Q-Q plot you see.
se <- sqrt(sum(mara$residuals^2) / mara$df.residual) ## Pearson residual standard error
hii <- lm.influence(mara, do.coef = FALSE)$hat ## leverage
std.resi <- mara$residuals / (se * sqrt(1 - hii)) ## standardized residuals
## these three lines can be replaced by: std.resi <- rstandard(mara)
Now, let's compare the Q-Q plot we generate ourselves and that generated by plot.lm:
par(mfrow = c(1,2))
qqnorm(std.resi, main = "my Q-Q"); qqline(std.resi, lty = 2)
plot(mara, which = 2) ## only display Q-Q plot
The same, right?
Now, the only issue left is how the numbers are labelled. Those labelled points mark the largest 3 absolute standardised residuals. Consider:
x <- sort(abs(std.resi), decreasing = TRUE)
id <- as.integer(names(x))
id[1:3]
# [1] 23 8 12
Now, if you look at the graph closely, you can see that those three numbers are exactly what is shown. Knowing this, you can also check out, for example, id[1:5].
Related
I have some experience in using PCA, but this is the first time I am attempting to use PCA for spectral data...
I have a large data with spectra where I used prcomp command to calculated PCA for the whole dataset. My results show that 3 components explain 99% of the variance.
I would like to plot the contribution of each of the three PCA components at every wavelength (in steps of 4, 200-1000 nm) like the example of a plot 2 I found on this site:
https://learnche.org/pid/latent-variable-modelling/principal-component-analysis/pca-example-analysis-of-spectral-data
Does anyone have a code how I could do this in R?
Thank you
I believe the matrix of variable loadings is found in model.pca$rotation, see prcomp documentation.
So something like this should do (using the example on your linked website):
file <- 'http://openmv.net/file/tablet-spectra.csv'
spectra <- read.csv(file, header = FALSE)
n.comp <- 4
model.pca <- prcomp(spectra[,2:651],
center = TRUE,
scale =TRUE,
rank. = n.comp)
summary(model.pca)
par(mfrow=c(n.comp,1))
sapply(1:n.comp, function(comp){
plot(2:651, model.pca$rotation[,comp], type='l', lwd=2,
main=paste("Comp.", comp), xlab="Wavelength INDEX")
})
I don't have the wavelength values, so I used the indices of the array here ; output below.
I have a measurment of which should fit an hysteresis. For visualisation purpose I would like to plot a line approximating the hysteresis to help explain this pattern.
I created an example in the following image using the code below.
I would like to have an output similar to the green curve - however I don't have this data directly available, and I don't care whether it is pointy.
However most smoothing functions such as smooth.spline which I plotted in blue - allow no loops. The closest I can find is from the bezier library - plotted in red. Not nicely visible here but it produces a loop, however it fits poorly (and gives some warnings and takes quite some time).
Can you suggest a method?
set.seed(12345)
up <- seq(0,1,length.out=100)^3
down <- sqrt(seq(1,0,length.out=100))
x <- c(seq(0,1,length.out=length(up)),
seq(1,0, length.out=length(down)))
data <- data.frame(x=x, y=c(up,down),
measuredx=x + rnorm(length(x))*0.01,
measuredy=c(up,down) + rnorm(length(up)+length(down))*0.03)
with(data,plot(measuredx,measuredy, type = "p"))
with(data,lines(x,y, col='green'))
sp <- with(data,smooth.spline(measuredx, measuredy))
with(sp, lines(x,y, col="blue"))
library(bezier)
bf <- bezierCurveFit(as.matrix(data[,c(1,3)]))
lines(bezier(t=seq(0, 1, length=500), p=bf$p), col="red", cex=0.25)
UPDATE
As it turns out my actual problem is slightly different I ask another question to reflect my actual issue in the question: How to fit a smooth hysteresis in a poorly distributed data set?
set.seed(12345)
up <- seq(0,1,length.out=100)^3
down <- sqrt(seq(1,0,length.out=100))
x <- c(seq(0,1,length.out=length(up)),
seq(1,0, length.out=length(down)))
data <- data.frame(x=x, y=c(up,down),
measuredx=x + rnorm(length(x))*0.01,
measuredy=c(up,down) + rnorm(length(up)+length(down))*0.03)
Instead of smoothing data$measuredy directly over data$measuredx, do two separate smoothing, by smoothing each against a time stamp variable. Then combine the fitted values from two smoothing. This is a general way for smoothing a closed curve or a loop. (See also Q & A: Smoothing Continuous 2D Points)
t <- seq_len(nrow(data) + 1)
xs <- smooth.spline(t, c(data$measuredx, data$measuredx[1]))$y
ys <- smooth.spline(t, c(data$measuredy, data$measuredy[1]))$y
with(data, plot(measuredx, measuredy))
lines(xs, ys)
c(data$measuredx, data$measuredx[1]) for example is just to ensure that the last value in the vector agrees with the first, so that it completes a cycle.
The curve is not really closed at the bottom left corner, because smooth.spline is doing smoothing not interpolation, so even if we have ensure that data vector completes a cycle, the fitted one may not be a closed one. A practical workaround is to use weighted regression, imposing heavy weight on this spot to make it closed.
t <- seq_len(nrow(data) + 1)
w <- rep(1, length(t)) ## initially identical weight everywhere
w[c(1, length(w))] <- 100000 ## give heavy weight
xs <- smooth.spline(t, c(data$measuredx, data$measuredx[1]), w)$y
ys <- smooth.spline(t, c(data$measuredy, data$measuredy[1]), w)$y
with(data, plot(measuredx, measuredy), col = 8)
lines(xs, ys, lwd = 2)
I'm working on the PCA section from Michael Faraway's Linear Models with R (chapter 11, page 164).
PCA analysis is sensitive to outliers and the Mahalanobis distance helps us identify them.
The author checks for outliers by plotting the Mahalanobis distance against the quantiles of a chi-squared distribution.
if require(faraway)==F install.packages("faraway"); require(faraway)
data(fat, package='faraway')
cfat <- fat[,9:18]
n <- nrow(cfat); p <- ncol(cfat)
plot(qchisq(1:n/(n+1),p), sort(md), xlab=expression(paste(chi^2,
"quantiles")),
ylab = "Sorted Mahalanobis distances")
abline(0,1)
I identify the points:
identify(qchisq(1:n/(n+1),p), sort(md))
It appears that the outliers are in rows 242:252. I remove these outliers and re-create the QQ Plot:
cfat.mod <- cfat[-c(242:252),] #remove outliers
robfat <- cov.rob(cfat.mod)
md <- mahalanobis(cfat.mod, center=robfat$center, cov=robfat$cov)
n <- nrow(cfat.mod); p <- ncol(cfat.mod)
plot(qchisq(1:n/(n+1),p), sort(md), xlab=expression(paste(chi^2,
"quantiles")),
ylab = "Sorted Mahalanobis distances")
abline(0,1)
identify(qchisq(1:n/(n+1),p), sort(md))
Alas, it appears now that a new set of points (rows 234:241) are now outliers. This keeps happening every time I remove additional outliers.
Look forward to understanding what I'm doing wrong.
To identify the points correctly, make sure the labels correspond to the positions of the points in the data. The functions order or sort with index.return=TRUE will give the sorted indices. Here is an example, arbitrarily removing the points with md greater than a threshold.
## Your data
data(fat, package='faraway')
cfat <- fat[, 9:18]
n <- nrow(cfat)
p <- ncol(cfat)
md <- sort(mahalanobis(cfat, colMeans(cfat), cov(cfat)), index.return=TRUE)
xs <- qchisq(1:n/(n+1), p)
plot(xs, md$x, xlab=expression(paste(chi^2, 'quantiles')))
## Use indices in data as labels for interactive identify
identify(xs, md$x, labels=md$ix)
## remove those with md>25, for example
inds <- md$x > 25
cfat.mod <- cfat[-md$ix[inds], ]
nn <- nrow(cfat.mod)
md1 <- mahalanobis(cfat.mod, colMeans(cfat.mod), cov(cfat.mod))
## Plot the new data
par(mfrow=c(1, 2))
plot(qchisq(1:nn/(nn+1), p), sort(md1), xlab='chisq quantiles', ylab='')
abline(0, 1, col='red')
car::qqPlot(md1, distribution='chisq', df=p, line='robust', main='With car::qqPlot')
There are similar questions on the website, but I could not find an answer to this seemingly very simple problem. I fit a mixture of two gaussians on the Old Faithful Dataset:
if(!require("mixtools")) { install.packages("mixtools"); require("mixtools") }
data_f <- faithful
plot(data_f$waiting, data_f$eruptions)
data_f.k2 = mvnormalmixEM(as.matrix(data_f), k=2, maxit=100, epsilon=0.01)
data_f.k2$mu # estimated mean coordinates for the 2 multivariate Gaussians
data_f.k2$sigma # estimated covariance matrix
I simply want to super-impose two ellipses for the two Gaussian components of the model described by the mean vectors data_f.k2$mu and the covariance matrices data_f.k2$sigma. To get something like:
For those interested, here is the MatLab solution that created the plot above.
If you are interested in the colors as well, you can use the posterior to get the appropriate groups. I did it with ggplot2, but first I show the colored solution using #Julian's code.
# group data for coloring
data_f$group <- factor(apply(data_f.k2$posterior, 1, which.max))
# plotting
plot(data_f$eruptions, data_f$waiting, col = data_f$group)
for (i in 1: length(data_f.k2$mu)) ellipse(data_f.k2$mu[[i]],data_f.k2$sigma[[i]], col=i)
And for my version using ggplot2.
# needs ggplot2 package
require("ggplot2")
# ellipsis data
ell <- cbind(data.frame(group=factor(rep(1:length(data_f.k2$mu), each=250))),
do.call(rbind, mapply(ellipse, data_f.k2$mu, data_f.k2$sigma,
npoints=250, SIMPLIFY=FALSE)))
# plotting command
p <- ggplot(data_f, aes(color=group)) +
geom_point(aes(waiting, eruptions)) +
geom_path(data=ell, aes(x=`2`, y=`1`)) +
theme_bw(base_size=16)
print(p)
You can use the ellipse-function from package mixtools. The initial problem was that this function swaps x and y from your plot. I'll try to figure this out and update the answe. (I'll leave the colors to somebody else...)
plot( data_f$eruptions,data_f$waiting)
for (i in 1: length(data_f.k2$mu)) ellipse(data_f.k2$mu[[i]],data_f.k2$sigma[[i]])
Using mixtools internal plotting function:
plot.mixEM(data_f.k2, whichplots=2)
I just came by the following plot:
And wondered how can it be done in R? (or other softwares)
Update 10.03.11: Thank you everyone who participated in answering this question - you gave wonderful solutions! I've compiled all the solution presented here (as well as some others I've came by online) in a post on my blog.
Make.Funny.Plot does more or less what I think it should do. To be adapted according to your own needs, and might be optimized a bit, but this should be a nice start.
Make.Funny.Plot <- function(x){
unique.vals <- length(unique(x))
N <- length(x)
N.val <- min(N/20,unique.vals)
if(unique.vals>N.val){
x <- ave(x,cut(x,N.val),FUN=min)
x <- signif(x,4)
}
# construct the outline of the plot
outline <- as.vector(table(x))
outline <- outline/max(outline)
# determine some correction to make the V shape,
# based on the range
y.corr <- diff(range(x))*0.05
# Get the unique values
yval <- sort(unique(x))
plot(c(-1,1),c(min(yval),max(yval)),
type="n",xaxt="n",xlab="")
for(i in 1:length(yval)){
n <- sum(x==yval[i])
x.plot <- seq(-outline[i],outline[i],length=n)
y.plot <- yval[i]+abs(x.plot)*y.corr
points(x.plot,y.plot,pch=19,cex=0.5)
}
}
N <- 500
x <- rpois(N,4)+abs(rnorm(N))
Make.Funny.Plot(x)
EDIT : corrected so it always works.
I recently came upon the beeswarm package, that bears some similarity.
The bee swarm plot is a
one-dimensional scatter plot like
"stripchart", but with closely-packed,
non-overlapping points.
Here's an example:
library(beeswarm)
beeswarm(time_survival ~ event_survival, data = breast,
method = 'smile',
pch = 16, pwcol = as.numeric(ER),
xlab = '', ylab = 'Follow-up time (months)',
labels = c('Censored', 'Metastasis'))
legend('topright', legend = levels(breast$ER),
title = 'ER', pch = 16, col = 1:2)
(source: eklund at www.cbs.dtu.dk)
I have come up with the code similar to Joris, still I think this is more than a stem plot; here I mean that they y value in each series is a absolute value of a distance to the in-bin mean, and x value is more about whether the value is lower or higher than mean.
Example code (sometimes throws warnings but works):
px<-function(x,N=40,...){
x<-sort(x);
#Cutting in bins
cut(x,N)->p;
#Calculate the means over bins
sapply(levels(p),function(i) mean(x[p==i]))->meansl;
means<-meansl[p];
#Calculate the mins over bins
sapply(levels(p),function(i) min(x[p==i]))->minl;
mins<-minl[p];
#Each dot is one value.
#X is an order of a value inside bin, moved so that the values lower than bin mean go below 0
X<-rep(0,length(x));
for(e in levels(p)) X[p==e]<-(1:sum(p==e))-1-sum((x-means)[p==e]<0);
#Y is a bin minum + absolute value of a difference between value and its bin mean
plot(X,mins+abs(x-means),pch=19,cex=0.5,...);
}
Try the vioplot package:
library(vioplot)
vioplot(rnorm(100))
(with awful default color ;-)
There is also wvioplot() in the wvioplot package, for weighted violin plot, and beanplot, which combines violin and rug plots. They are also available through the lattice package, see ?panel.violin.
Since this hasn't been mentioned yet, there is also ggbeeswarm as a relatively new R package based on ggplot2.
Which adds another geom to ggplot to be used instead of geom_jitter or the like.
In particular geom_quasirandom (see second example below) produces really good results and I have in fact adapted it as default plot.
Noteworthy is also the package vipor (VIolin POints in R) which produces plots using the standard R graphics and is in fact also used by ggbeeswarm behind the scenes.
set.seed(12345)
install.packages('ggbeeswarm')
library(ggplot2)
library(ggbeeswarm)
ggplot(iris,aes(Species, Sepal.Length)) + geom_beeswarm()
ggplot(iris,aes(Species, Sepal.Length)) + geom_quasirandom()
#compare to jitter
ggplot(iris,aes(Species, Sepal.Length)) + geom_jitter()