Statistics
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Computerized adaptive test item analysis
Computerized adaptive test item analysis evaluates and calibrates items intended for use in adaptive testing environments. Unlike fixed-form analysis, it accounts for the non-random item exposure inherent in adaptive administration, using i...
Disclosure Risk Assessment
Disclosure Risk Assessment is a probabilistic framework introduced by Duncan and Lambert (1989) for quantifying how likely it is that releasing microdata — individual-level records from surveys or administrative files — will allow an outsid...
Dyadic Analysis
Dyadic analysis treats the dyad — the pair of actors and the relation between them — as the unit of analysis, separating the relational outcome into what each actor brings to all their relationships and what is unique to the specific pair....
Ensemble Kalman Filter
The Ensemble Kalman Filter (EnKF) is a sequential Monte Carlo data assimilation algorithm introduced by Geir Evensen in 1994. It extends the classical Kalman filter to high-dimensional, nonlinear dynamical systems by representing the foreca...
Independent Component Analysis
Independent Component Analysis (ICA) is a computational method for separating a multivariate signal into additive, statistically independent subcomponents. Formalized by Pierre Comon in 1994, ICA became the foundational framework for blind...
Isomap
Isomap (Isometric Feature Mapping) is a manifold learning algorithm introduced by Tenenbaum, de Silva, and Langford in 2000 that discovers the intrinsic low-dimensional geometry of high-dimensional data by preserving geodesic — rather than...
Kernel PCA
Kernel Principal Component Analysis (Kernel PCA) is a nonlinear dimensionality-reduction method introduced by Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller in 1997–1998. It extends classical linear PCA to curved, non-linear d...
Latent Dirichlet Allocation
Latent Dirichlet Allocation (LDA) is a generative probabilistic model for collections of discrete data, introduced by Blei, Ng, and Jordan in 2003. It treats each document as a mixture of latent topics and each topic as a probability distri...
Linear Discriminant Analysis
Linear Discriminant Analysis is a supervised method for dimensionality reduction and classification, introduced by Ronald A. Fisher in 1936, that finds linear combinations of features which maximally separate predefined classes while preser...
Longitudinal Item Analysis
Longitudinal item analysis examines how the statistical properties of individual scale items — difficulty, discrimination, factor loadings, and fit — remain stable or change systematically across repeated measurement occasions. It is the it...
MRQAP Network Regression
Multiple regression quadratic assignment procedure (MRQAP) extends QAP to the regression setting: it predicts a dependent relational matrix from several independent relational matrices on the same actors — for example, modeling who collabor...
Moralizing Gods Database Analysis
Moralizing gods database analysis is a cross-cultural quantitative method that codes the presence of moralizing or 'big' supernatural enforcers and measures of social complexity across many historical polities over time, then models their r...
Network Autocorrelation Model
The network autocorrelation model adapts spatial-econometric regression to social networks to estimate peer influence: it explains an actor's outcome — an attitude, behavior, or performance — as a function of their own covariates plus a wei...
Non-negative Matrix Factorization
Non-negative Matrix Factorization (NMF) is a family of algorithms, introduced by Lee and Seung in their landmark 1999 Nature paper, that decomposes a non-negative data matrix V into the product of two lower-rank non-negative matrices W (bas...
Quadratic Discriminant Analysis
Quadratic discriminant analysis is a generative classifier that models each class with its own multivariate Gaussian distribution, allowing each class a separate covariance matrix. Unlike linear discriminant analysis, which assumes a shared...
Relational Event Model
The relational event model (REM), introduced by Carter Butts in 2008, analyzes streams of time-stamped interactions — emails, radio calls, messages, citations — as a continuous-time event-history process. Rather than treating a network as a...
Restricted Boltzmann Machine
A Restricted Boltzmann Machine is a two-layer generative probabilistic model consisting of visible (observed) and hidden (latent) binary units connected by an undirected bipartite graph with no within-layer connections. Originally introduce...
Robust Rasch Model
The robust Rasch model applies the standard one-parameter logistic Rasch framework with estimation procedures designed to limit the influence of outlying item responses, aberrant respondents, or mild model violations, producing stable item...
Self-Organized Criticality
Self-Organized Criticality (SOC) is a dynamical systems framework introduced by Per Bak, Chao Tang, and Kurt Wiesenfeld in 1987 to explain how large, dissipative systems spontaneously evolve toward a critical state without external fine-tun...
Short form Rasch model
The short form Rasch model applies Rasch measurement theory to abbreviated instrument versions. Rather than using all items from a full scale, researchers select a reduced item set and calibrate it under the Rasch model to verify that the s...
Short-Form IRT
Short-form item response theory applies IRT calibration and scoring to abbreviated or shortened psychological scales. It uses item information functions to guide which items to retain from a full-length instrument, then estimates latent tra...
Tourism CGE Modeling
Tourism computable general equilibrium (CGE) modeling simulates how a change in tourism — a surge in inbound visitors, a major event, a new tax, or a demand collapse — ripples through an entire economy when prices, wages, exchange rates, an...
Value at Risk
Value at Risk is a financial risk measure that estimates the maximum loss a position or portfolio could suffer over a fixed holding period at a given confidence level. It is the standard benchmark in risk management and regulatory capital c...
Wavelet Financial Analysis
Wavelet financial analysis decomposes a financial time series into different frequency bands (time scales) so short- and long-term relationships can be studied at the same time. Drawing on the treatments of Gençay, Selçuk and Whitcher (2001...