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Table 2 Illustration of the models used to estimate the residuals for each of the growth pattern contrasts for the birth to 6 week period. The outcome can then be regressed onto the residuals in a second analytical modela

From: Regression models for linking patterns of growth to a later outcome: infant growth and childhood overweight

Model Model to estimate residual for the birth to 6 week periodb
(a) Conditional growth: z 1.5, i  = λ 0 + λ 1 z 0,i  + ε i
(b) Being bigger: z 0, i  = η 0 + η 1(z 1.5,i  − z 0,i ) + ε i
(c) Becoming bigger and staying bigger: (z 1.5, i  − z 0, i ) = λ 0 + λ 1 z 0 + λ 2(z 3 − z 1.5) + λ 3(z 6 − z 3) + λ 4(z 12 − z 6) + λ 5(z 24 − z 12) + ε i
(d) Growing faster versus being bigger: (z 1.5, i  − z 0, i ) = λ 0 + λ 1 z 1.5 + ε i
(e) Becoming bigger versus being bigger: (z 1.5, i  − z 0, i ) = λ 0 + λ 1(z 3 − z 1.5) + λ 2(z 6 − z 3) + λ 3(z 12 − z 6) + λ 4(z 24 − z 12) + λ 5 z 24 + ε i
  1. aThe residuals ε i are divided by their standard deviation prior to being entered into the analytical model ie. \( \frac{\varepsilon_i}{\mathrm{SD}\left({\varepsilon}_i\right)} \) . In our example the analytical models were also adjusted for sex and gestational age
  2. bwhere z ti is the z-score for weight for length at age t months for subject i, and ε i is the residual for child i