= Residualized psychological resilience score
{title2=$R_i=\widehat m(S_i)-D_i$}
An <exposure>-conditioned adaptation measure. With distress $D_i$, <exposure> $S_i$ and predicted distress $\widehat m(S_i)$, the displayed convention makes higher scores mean less distress than predicted. The result depends on <exposure> measurement, reference population and model. A <regression residual> can include <measurement error> and omitted causes rather than a distinct protective capacity.
For <ordinary least squares> $D=X\widehat\beta+e$, the <normal equation> gives $X^Te=0$. Thus $R=-e$ is also orthogonal to the fitted predictors; with an intercept its sample mean is zero. A zero in-sample linear association between <exposure> and this score can therefore be an algebraic consequence of its construction, not evidence that <exposure> has no effect. Independent validation is needed before assigning substantive meaning to the <regression residual>.
Back to article page
