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# Selecting the best model for LGM Twin model

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Selecting the best model for LGM Twin model
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Hello everyone,

in my work, I am trying to capture longitudinal development of depression with a biometrical quadratic LGM model following model described in Reynolds, Finkel, McArdle, Gatz, Berg, & Pedersen (2005; see Figure 2). Here are the specifications:

-four waves, Intercept, Linear Slope, and Quadratic Slope, same-sex only, controlling for sex and age on the intercept, residual variances fixed to equality within a twin pair, residual variances at the same timepoint allowed to covary, full Cholesky decomposition (quadratic regressed on slope and intercept A,C,E, slope regressed on intercept A, C, E).

To estimate the significance of heritable (h2), shared environmental (c2), and non-shared environmental effects (e2), I created these parameters in Mplus (h2 = a^2/(a^2 + c^2 + e^2) etc.) and then used bootstrapping to obtain 95% CI.

Here is my question: how do I select the best model? Since one can theoretically have ACE/AE/CE for I, S, Q, this gives a total of 27 possible models where I (ACE), S (ACE), Q (ACE) is the comparison model.

I modeled the 27 models also in AMOS just because it is quicker to change the specifications. Attached is the overview of the models.

Based on relative model fit (AIC and BCC), it would appear that Model 26/27 is the best model. However, the comparison model (Model 1) showed statistically significant h2, c2, and e2 for Intercept, suggesting that perhaps I should keep Intercept ACE (and not disregard c2).

If this is the case, I should be only selecting from Models 8 or 9.

To refine my question: if the h2, c2, e2 part of the Intercept is statistically significant, does it mean that I should keep the Intercept ACE or does the lower relative fit (Models 26, 27 etc) have priority in choosing the best model? Which model should I choose?

I am sorry for this extensive question and I hope that someone will know how to help me.

Thank you

Reference:
Reynolds, C. A., Finkel, D., McArdle, J. J., Gatz, M., Berg, S., & Pedersen, N. L. (2005). Quantitative genetic analysis of latent growth curve models of cognitive abilities in adulthood. Developmental Psychology, 41(1), 3-16.