AR(1) stands for which covariance structure?

• A. Autocorrelation
• B. Anderson-Rubin method
• C. First-order autoregressive structure
• D. Analysis of Variance

Answer: (C)

This question tests understanding of how covariance is structured in longitudinal or repeated-measures data, specifically what AR(1) denotes. AR stands for autoregressive, and the 1 signals first-order: each observation is directly related to the previous one, with the strength of that relationship diminishing as the time gap grows. In a covariance matrix, this creates a pattern where Cov(Y_t, Y_s) = σ^2 ρ^{|t−s|}, meaning adjacent time points are most correlated (approximately ρ), two time points apart are about ρ^2, and so on. So the correlations decay exponentially with the lag, which is exactly what a first-order autoregressive structure encodes. The other options aren’t named covariance structures: autocorrelation is a general concept of correlation across lags, Anderson-Rubin is a statistical test, and Analysis of Variance is a different analysis framework.