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Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more manageable. This Element offers readers a suite of modern unsupervised dimension reduction techniques along with hundreds of lines of R code, to efficiently represent the original high dimensional data space in a simplified, lower dimensional subspace. Launching from the earliest dimension reduction technique principal components analysis and using real social science data, I introduce and walk readers through application of the following techniques: locally linear embedding, t-distributed stochastic neighbor embedding (t-SNE), uniform manifold approximation and projection, self-organizing maps, and deep autoencoders. The result is a well-stocked toolbox of unsupervised algorithms for tackling the complexities of high dimensional data so common in modern

This Element discusses how shiny, an R package, can help instructors teach quantitative methods more effectively by way of interactive web apps. The interactivity increases instructors' effectiveness by making students more active participants in the learning process, allowing them to engage with otherwise complex material in an accessible, dynamic way. The Element offers four detailed apps that cover two fundamental linear regression topics: estimation methods (least squares, maximum likelihood) and the classic linear regression assumptions. It includes a summary of what the apps can be used to demonstrate, detailed descriptions of the apps' full capabilities, vignettes from actual class use, and example activities. Two other apps pertain to a more advanced topic (LASSO), with similar supporting material. For instructors interested in modifying the apps, the Element also documents the main apps' general code structure, highlights some of the more likely modifications, and goes

Social interactions are rich, complex, and dynamic. One way to understand these is to model interactions that fascinate us. Some of the more realistic and powerful models are computer simulations. Simple, elegant and powerful, tools are available in user-friendly free software to help you design, build and run your own models of social interactions that intrigue you, and do this on the most basic laptop computer. Focusing on a well-known model of housing segregation, this Element is about how to unleash that power, setting out the fundamentals of what is now known as 'agent based modeling'.

Building on the Cambridge Element Agent Based Models of Social Life: Fundamentals (Cambridge, 2020), we move on to the next level. We do this by building agent based models of polarization and ethnocentrism. In the process, we develop: stochastic models, which add a crucial element of uncertainty to human interaction; models of human interactions structured by social networks; and 'evolutionary' models in which agents using more effective decision rules are more likely to survive and prosper than others. The aim is to leave readers with an effective toolkit for building, running and analyzing agent based modes of social interaction.

In the age of data-driven problem-solving, applying sophisticated computational tools for explaining substantive phenomena is a valuable skill. Yet, application of methods assumes an understanding of the data, structure, and patterns that influence the broader research program. This Element offers researchers and teachers an introduction to clustering, which is a prominent class of unsupervised machine learning for exploring and understanding latent, non-random structure in data. A suite of widely used clustering techniques is covered in this Element, in addition to R code and real data to facilitate interaction with the concepts. Upon setting the stage for clustering, the following algorithms are detailed: agglomerative hierarchical clustering, k-means clustering, Gaussian mixture models, and at a higher-level, fuzzy C-means clustering, DBSCAN, and partitioning around medoids (k-medoids) clustering.

We elaborate a general workflow of weighting-based survey inference, decomposing it into two main tasks. The first is the estimation of population targets from one or more sources of auxiliary information. The second is the construction of weights that calibrate the survey sample to the population targets. We emphasize that these tasks are predicated on models of the measurement, sampling, and nonresponse process whose assumptions cannot be fully tested. After describing this workflow in abstract terms, we then describe in detail how it can be applied to the analysis of historical and contemporary opinion polls. We also discuss extensions of the basic workflow, particularly inference for causal quantities and multilevel regression and poststratification.

Text is everywhere, and it is a fantastic resource for social scientists. However, because it is so abundant, and because language is so variable, it is often difficult to extract the information we want. There is a whole subfield of AI concerned with text analysis (natural language processing). Many of the basic analysis methods developed are now readily available as Python implementations. This Element will teach you when to use which method, the mathematical background of how it works, and the Python code to implement it.