Statistics — Page 47
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Panel Quantile-on-Quantile Regression
Panel quantile-on-quantile (QQ) regression jointly maps any quantile of the outcome distribution onto any quantile of the predictor distribution across multiple cross-sectional units observed over time. It generalises Sim and Zhou's (2015)...
Panel Random Effects Model
The panel random effects (RE) model treats individual-specific effects as random draws from a population distribution rather than fixed constants, enabling efficient estimation by generalised least squares and allowing inference about time-...
Panel SARIMA model
The Panel SARIMA model applies the Seasonal Autoregressive Integrated Moving Average (SARIMA) framework to panel data, fitting individual or pooled seasonal time series models across multiple cross-sectional units. It captures both non-seas...
Panel SVAR model
The Panel SVAR model extends the Structural VAR framework to panel data, jointly modelling multiple endogenous time-series variables across several cross-sectional units (e.g., countries or firms). Structural restrictions — short-run, long-...
Panel Simple Linear Regression
Panel simple linear regression models a continuous outcome as a linear function of a single predictor using data that track the same entities (individuals, firms, countries) across multiple time periods. It separates within-entity variation...
Panel Smooth Transition Regression
Panel Smooth Transition Regression (PSTR) models nonlinear panel relationships where coefficients transition smoothly (rather than abruptly) between regimes as a transition variable crosses thresholds. Introduced by Gonzalez et al. (2005),...
Panel Spatial Autocorrelation
Panel Spatial Autocorrelation measures whether observations that are geographically close also tend to have similar values across repeated time periods. It extends classic cross-sectional spatial autocorrelation statistics such as Moran's I...
Panel Spatial Durbin Model
The Panel Spatial Durbin Model (PSDM) extends the cross-sectional Spatial Durbin Model to panel data, capturing both spatial lag dependence in the outcome and spatial spillovers from neighbouring units' explanatory variables across multiple...
Panel Spatial Error Model
The Panel Spatial Error Model (panel SEM) extends the classical spatial error model to panel data, allowing spatial dependence to enter through the error term across cross-sectional units over multiple time periods. It accounts for spatiall...
Panel Spatial Regression
Panel Spatial Regression extends standard panel data models by explicitly accounting for spatial dependence among cross-sectional units observed over time. It combines the temporal control of panel fixed or random effects with a spatial wei...
Panel System GMM
Panel System GMM is a two-equation GMM estimator for dynamic panel data that stacks the differenced equation (using lagged levels as instruments) with the levels equation (using lagged differences as instruments). Developed by Blundell and...
Panel TGARCH
Panel TGARCH extends the Threshold GARCH (GJR-GARCH) model to panel data, allowing each cross-sectional unit to exhibit asymmetric volatility responses — where negative shocks generate larger variance increases than positive shocks of the s...
Panel Toda-Yamamoto Causality
The Panel Toda-Yamamoto (PTY) causality test extends the Toda-Yamamoto modified Wald approach to panel data, allowing researchers to test Granger non-causality across multiple cross-sectional units without requiring pre-testing for cointegr...
Panel Universal Kriging
Panel Universal Kriging extends Universal Kriging to data structures with repeated spatial observations over time (panel or longitudinal format). It simultaneously estimates a deterministic trend surface — incorporating covariates that vary...
Panel VAR
Panel VAR extends the vector autoregression model to panel data, modelling the dynamic interactions among several variables while controlling for cross-unit heterogeneity through fixed effects. It was introduced by Holtz-Eakin, Newey and Ro...
Panel VARX
Panel VARX extends vector autoregression to heterogeneous panels with exogenous variables, enabling simultaneous modeling of multiple endogenous variables alongside observed external factors across many units. Introduced by Holtz-Eakin et a...
Panel VECM
Panel VECM combines vector error correction modelling with panel data, simultaneously capturing the long-run cointegrating equilibrium among multiple I(1) variables and their short-run adjustment dynamics across multiple cross-sectional uni...
Panel Zivot-Andrews test
The Panel Zivot-Andrews test extends the single-series Zivot-Andrews (1992) structural break unit root test to panel data, allowing each cross-sectional unit to have its own endogenously determined break date. It tests the null of a unit ro...
Parametric Bootstrap
The parametric bootstrap is a resampling method that estimates standard errors and confidence intervals by drawing repeated samples from a parametric model that has been fitted to the data. Developed in the bootstrap literature of Efron and...
Pareto/NBD Model
The Pareto/NBD model is the foundational buy-till-you-die model of customer-base analysis, answering the question of which customers are still active and how many transactions they will make in the future from a non-contractual purchase his...
Partial Correlation
Partial correlation measures the linear relationship between two continuous variables after removing the shared influence of one or more control variables. The technique was formalised by R. A. Fisher in 1924 and is the standard approach wh...
Partial Least Squares Structural Equation Modeling
PLS-SEM is a variance-based approach to structural equation modeling developed by Herman Wold (1985) that estimates latent variable models by maximizing the variance explained in dependent variables. Unlike covariance-based SEM, PLS-SEM is...
Participation and Environment Measure
The Participation and Environment Measure for Children and Youth (PEM-CY) is a caregiver-report instrument that measures how children aged 5 to 17, with and without disabilities, participate in the home, school, and community, and the envir...
Particle Filter
The particle filter, introduced by Gordon, Salmond, and Smith in 1993, is a sequential Monte Carlo algorithm that approximates the Bayesian filtering distribution for nonlinear and non-Gaussian state-space models. Rather than tracking a sin...