R

A few datasets that I’ve seen have come with several different columns representing binary responses to questions. Naturally, there are missing values scattered throughout, so some amount of imputation had to occur. I decided to try coding up a way to do this by picking the mode of rows that were as similar as possible to the row with missing values.

The data being considered is a set of binary response variables to something like yes-no survey questions, not for something like one-hot columns. This method is also just generally very slow, so it’s not recommended for much – it just seemed like an interesting experiment.

This is a quick post intended for animating how the transition matrix of a Markov chain changes between larger time steps, as well as showing the probability of the chain being in any specified state over time. This post uses the tidyverse, along with gganimate.

> library(tidyverse)
> library(magrittr)  ## using some aliases not loaded by default
> library(gganimate)

I recently encountered a 2018 paper called “The next-generation \(k\)-means algorithm”. It proposes and compiles advancements and theoretical justifications for \(k\)-means and \(k\)-medians clustering. One part that caught my eye was the proposed “broken-line algorithm” for finding the optimal number of clusters in \(k\)-means. Though it explains how they tested the idea, the paper contains no code and I couldn’t find any other repositories for the paper. This post covers an attempt to replicate the code, as well as attempting a slightly more intensive battery of tests, as there was only one test method in the paper.

The magrittr package is a part of the extended tidyverse – i.e., not one of the ones normally loaded. It is the one that supplies the pipe operator (%>%), but it turns out that the package actually contains four pipe operators in total. All are intended to streamline and improve the readability of code, though the three non-basic ones are a bit more situational, and I’ve rarely seen them used, so I thought I would go into them a bit.

The CRAN page for magrittr is here; much of this post is based off of the package’s vignettes and documentation.

Missing values are inevitable in data science, and handling them is a constant issue. In the case of Boolean logic, it can behave fairly differently depending on the order of arguments and exactly how it is set up, unlike a lot of other data types. Whether this is useful or not depends on the scenario, but the behavior is something to keep in mind.

Partial regression plots – also called added variable plots, among other things – are a type of diagnostic plot for multivariate linear regression models. More specifically, they attempt to show the effect of adding a new variable to an existing model by controlling for the effect of the predictors already in use. They’re useful for spotting points with high influence or leverage, as well as seeing the partial correlation between the response and the new predictor.

There are plenty of methods to choose from for classification problems, all with their own strengths and weaknesses. This post will try to compare three of the more basic ones: linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), and logistic regression.

The t-test is a common, reliable way to check for differences between two samples. When dealing with multivariate data, one can simply run t-tests on each variable and see if there are differences. This could lead to scenarios where individual t-tests suggest that there is no difference, although looking at all variables jointly will show a difference. When a multivariate test is preferred, the obvious choice is the Hotelling’s \(T^2\) test.

Hotelling’s test has the same overall flexibility that the t-test does, in that it can also work on paired data, or even a single dataset, though this example will only cover the two-sample case.

I recently had to go through some matrix operations in R and then write up the results in LaTeX. Formatting the R output to get it into a form for LaTeX isn’t particularly hard, but it’s tedious and it has a regular structure, so it seemed like it would be easy to code it up. So I decided to try it for R, Python, and Julia.

As with most useful (collections of) libraries, the tidyverse has a lot to offer. One interesting bit that I found recently was the accumulate() function in the purrr library, which allows you to apply a function over a succession of values in a vector. This post is a quick example of its use, using linear regression models.