Fig. 3.

Structural equation models (based on Lövdén et al., 2012). Squares represent manifest variables (O₁ is the score in the observed pretest, $O_1^{\prime }$ is the score in alternative measures of the observed pretest, and O₂ and $O_2^{\prime }$ are scores in post-tests). Circles represent latent variables, V ₁ reflects unobserved pretest performance, V ₂ reflects unobserved post-test performance, and Δ indicates gain. The triangle represents a constant. Each solid arrow represents a nonzero parameter. Each named arrow represents a free parameter. The models differ only in the ρ parameter (dashed arrow), which represents the correlation between variance of baseline performance (V ₁ ∗) and variance of gain (Δ ∗). In the first model ρ is fixed to 0, whereas in the second model this parameter is free