Statistics — Page 34
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
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...
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...
Particle Filter with Measurement Error
A particle filter with explicit measurement error is a Sequential Monte Carlo algorithm that tracks the hidden state of a nonlinear, non-Gaussian dynamic system while formally modelling noise in the observations. A population of weighted ra...
Particle Filter with Missing Data
A particle filter adapted for state-space models in which some observations are absent. The algorithm tracks a hidden state over time using a cloud of weighted random samples (particles); when a time step has no observed value, the weight-u...
Partisan Business Cycle Analysis
Partisan business cycle analysis tests whether left-wing and right-wing governments produce systematically different macroeconomic outcomes. Douglas Hibbs's 1977 partisan theory argued that because left and right parties represent constitue...
Path Analysis
Path analysis tests a researcher-specified causal diagram among observed variables by decomposing their intercorrelations into direct effects, indirect (mediated) effects, and spurious associations. Developed by Sewall Wright in 1921, it is...
Peace Duration Analysis
Peace duration analysis applies survival (time-to-event) methods to study how long peace lasts after a conflict ends and what makes it endure or collapse. The unit is the post-conflict peace spell, observed from a settlement or cessation un...
Pearson Correlation
Pearson correlation measures the direction and strength of linear association between two variables. It is their covariance divided by the product of their standard deviations.
Perceptual and Preference Mapping
Perceptual and preference mapping is a family of multivariate techniques that simultaneously positions competing objects—brands, products, or stimuli—and respondent preferences within a common low-dimensional space. Introduced systematicall...
Permutation Test
The permutation test is a nonparametric resampling procedure that builds the sampling distribution of a test statistic directly from the data by repeatedly shuffling the group labels. Developed in the resampling tradition and treated system...
Pesaran CD Test
The Pesaran CD test is a general diagnostic procedure for detecting cross-sectional dependence in panel data models. Developed by M. Hashem Pesaran (2021), it is applicable to both balanced and unbalanced panels with large N and T, and reta...
Pesaran-Timmermann Test
Introduced by Pesaran and Timmermann (1992), the PT test is a nonparametric procedure that evaluates whether a forecasting model correctly predicts the direction (sign) of a target variable more often than would be expected by chance. It is...
Phillips-Ouliaris Test
The Phillips-Ouliaris test, introduced by Phillips and Ouliaris in their 1990 Econometrica article, is a residual-based nonparametric procedure for testing the null hypothesis of no cointegration among a set of integrated I(1) time series....
Phillips-Perron Test
The Phillips-Perron test, proposed by Peter Phillips and Pierre Perron in 1988, tests for a unit root in a time series, like the Augmented Dickey-Fuller test, but corrects for autocorrelation and heteroskedasticity in the errors non-paramet...
Phillips-Perron unit root test
The Phillips-Perron (PP) test is a nonparametric unit root test for time series that corrects for serial correlation and heteroscedasticity in the error term without adding lagged differences. Introduced by Phillips and Perron (1988), it ap...
Place-to-Place Migration Model
The place-to-place migration model explains and predicts the gross number of people moving from each origin region to each destination region as a function of conditions at both ends and the distance between them. It descends from the gravi...
Placebo Test in Education Research
A placebo test is a falsification check used in quasi-experimental education research to validate a causal design. By applying the same estimator to a time period, group, or outcome where no real effect should exist, researchers verify that...
Point-Biserial Correlation
The point-biserial correlation coefficient (r_pb) measures the strength and direction of the linear association between one naturally dichotomous variable (coded 0/1) and one continuous variable. It is a special case of the Pearson product-...
Poisson Rate Regression
Poisson rate regression is the standard generalized linear model for analyzing event rates and counts, such as the number of deaths, hospitalizations, or new cases observed over a span of person-time. It models the logarithm of the expected...