Aaron Schlegel's Notebook of Interesting Things

The Rpoet package is a wrapper of the PoetryDB API, which enables developers and other users to extract a vast amount of English-language poetry from nearly 130 authors. The package provides a simple R interface for interacting and accessing the PoetryDB database. This vignette will introduce the basic functionality of Rpoet and some example usages of the package.

The first post introduced and explored the basic usage of the PetfindeR library. In this post, we take a quick look at some of the additional uses of the library and its methods to extract data from the Petfinder database.

The goal of the PetfindeR package is to provide a simple and straightforward interface for interacting with the Petfinder API through R. The Petfinder database contains approximately 300,000 adoptable pet records and 11,000 animal welfare organization records, which makes it a handy and valuable source of data for those in the animal welfare community. However, the outputs from the Petfinder API are in messy JSON format and thus it makes it more time-consuming and often frustrating to coerce the output data into a form that is workable with R.

R and SQL make excellent complements for analyzing data due to their respective strengths. The sqldf package provides an interface for working with SQL in R by querying data from a database into an R data.frame. This post will demonstrate how to query and analyze data using the sqldf package in conjunction with the graphing libraries plotly and ggplot2 as well as some other packages that provide useful statistical tests and other functions.

A pair set is a set with two members, for example, {2, 3}, which can also be thought of as an unordered pair, in that {2, 3}={3, 2}. However, we seek a more a strict and rich object that tells us more about two sets and how their elements are ordered.

The set operations, union and intersection, the relative complement − and the inclusion relation (subsets) are known as the algebra of sets. The algebra of sets can be used to find many identities related to set relations.

Set unions and intersections can be extended to any number of sets. This post introduces notation to simplify the expression of n-sets and the set union and intersection operations themselves with R.

Combined linear congruential generators, as the name implies, are a type of PRNG (pseudorandom number generator) that combine two or more LCGs (linear congruential generators). The combination of two or more LCGs into one random number generator can result in a marked increase in the period length of the generator which makes them better suited for simulating more complex systems.

Multiplicative congruential generators, also known as Lehmer random number generators, is a type of linear congruential generator for generating uniform pseudorandom numbers. The multiplicative congruential generator, often abbreviated as MLCG or MCG, is defined as a recurrence relation similar to the LCG.

Linear congruential generators (LCGs) are a class of pseudorandom number generator (PRNG) algorithms used for generating sequences of random-like numbers. The generation of random numbers plays a large role in many applications ranging from cryptography to Monte Carlo methods. Linear congruential generators are one of the oldest and most well-known methods for generating random numbers primarily due to their comparative ease of implementation and speed and their need for little memory.

The set operations 'union' and 'intersection' should ring a bell for those who've worked with relational databases and Venn Diagrams. The 'union' of two of sets A and B represents a set that comprises all members of A and B (or both).

Sets define a 'collection' of objects, or things typically referred to as 'elements' or 'members.' The concept of sets arises naturally when dealing with any collection of objects, whether it be a group of numbers or anything else.

As discussed in a previous post on the principal component method of factor analysis, the \(\hat{\Psi}\) term in the estimated covariance matrix \(S\), \(S = \hat{\Lambda} \hat{\Lambda}' + \hat{\Psi}\), was excluded and we proceeded directly to factoring \(S\) and \(R\). The principal factor method of factor analysis (also called the principal axis method) finds an initial estimate of \(\hat{\Psi}\) and factors \(S - \hat{\Psi}\), or \(R - \hat{\Psi}\) for the correlation matrix.

Often, it is not helpful or informative to only look at all the variables in a dataset for correlations or covariances. A preferable approach is to derive new variables from the original variables that preserve most of the information given by their variances. Principal component analysis is a widely used and popular statistical method for reducing data with many dimensions (variables) by projecting the data with fewer dimensions using linear combinations of the variables, known as principal components.

SVD underpins many statistical and real-world