Evolving notes, images and sounds by Luis Apiolaza
This post is one of those ‘explain to myself how things work’ documents, which are not necessarily completely correct but are close enough to facilitate understanding.
Let’s assume that we are working with a fairly simple linear model, where we only have a response variable (say tree stem diameter in cm). If we want to ‘guess’ the diameter for a tree (yi) our best bet is the average (μ) and we will have a residual (εi). The model equation then looks like:
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Every year there is at least a couple of occasions when I have to simulate multivariate data that follow a given covariance matrix. For example, let’s say that we want to create an example of the effect of collinearity when fitting multiple linear regressions, so we want to create one variable (the response) that is correlated with a number of explanatory variables and the explanatory variables have different correlations with each other.
There is a matrix operation called Cholesky decomposition, sort of equivalent to taking a square root with scalars, that is useful to produce correlated data. If we have a covariance matrix M, the Cholesky descomposition is a lower triangular matrix L, such as that M = L L'. How does this connect to our simulated data? Let’s assume that we generate a vector z of random normally independently distributed numbers with mean zero and variance one (with length equal to the dimension of M), we can create a realization of our multivariate distribution using the product L z.
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This is simple example code to display side-by-side lattice plots or ggplot2 plots, using the mtcars dataset that comes with any R installation. We will display a scatterplot of miles per US gallon (mpg) on car weight (wt) next to another scatterplot of the same data, but using different colors by number of engine cylinders (cyl, treated as factor) and adding a smooth line (under the type option).
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I tend not to upgrade R very often—running from 6 months to 1 year behind in version numbers—because I had to reinstall all packages: a real pain. A quick search shows that people have managed to come up with good solutions to this problem, as presented in this stackoverflow thread. I used the code in my mac:
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We were talking with one of my colleagues about doing some text analysis—that, by the way, I have never done before—for which the first issue is to get text in R. Not any text, but files that can be accessed through internet. In summary, we need to access an HTML file, parse it so we can access specific content and then remove the HTML tags. Finally, we may want to replace some text (the end of lines, \n, for example) before continue processing the files.
The package XML has the necessary functionality to deal with HTML, while the rest is done using a few standard R functions.
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