This is a long-winded question but I'll try to paint the picture. I'm using structural equation modeling using Amos software to study relationships between brain and behaviour. I have three condition types - 1, 2, 3 (for simplicity). Within each condition, I have 2 variables that are bidirectionally connected. the variables (brain regions) are the same across conditions but the correlation between the 2 variables are different for each condition. In a stacked model, I'm comparing pairwise the connections between 1 and 2. In a separate model, I compare 1 and 3. Since the betas are semi-partial correlation coefficients, I should obtain similar values for comparison 1 (1 and 2) and 2 (1 and 3) for condition 1 but these are different. I fix the error variances or residuals for each variable in a particular condition. I'm not obtaining similar betas, I'm wondering what may be the cause of this?
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