 Component complementarity in the simple view of reading

ID: component-complementarity-in-the-simple-view-of-reading

In the idealised model

R = D C

, changing decoding by

h

with comprehension fixed changes the product by

h C

, since

(D + h) C - D C = h C

. Similarly, changing comprehension by

k

changes it by

k D

. Thus

\frac{\partial R}{\partial D} = C, \frac{\partial R}{\partial C} = D .

If either component is zero, increasing only the other leaves the product zero. Equal products can arise from different profiles:

0.3 \times 0.9 = 0.9 \times 0.3 = 0.27

. These algebraic properties explain the model's complementarity; they are not estimates of treatment response or diagnostic cutoffs.

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