= Estimability from within-block differences
For a <linear regression> model $Y_{bj}=\alpha_b+f(x_{bj})^T\beta+\epsilon_{bj}$ with one unrestricted <intercept> per two-run <experimental block>, differencing the responses removes all <experimental block> effects. The parameter vector $\beta$ is identifiable precisely when the <matrix> whose rows are $f(x_{b1})-f(x_{b2})$ has full column <rank>. This criterion applies to arbitrary pairings, including nonregular <factorial designs>; requiring regular <orthogonal> confounding is a stronger constraint.
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