I am running models of GxE where I have age as a continuous moderator of a continuous phenotype. I have initially run the standard linear GxE model as outlined by Purcell (2002). However, I had problems getting this to fit. Out of interest, I ran the non-linear script, and this was successful. In addition to running the full model I have run nested models where the influence of the moderating terms are successively dropped. I am just wondering whether it is logically implausible to run a model where I retain quadratic paths (for the non-linear interaction), but drop the linear ones? The best fitting model appears to be one where only the quadratic moderation of E is retained and all other moderating paths (i.e. linear A, C, E, quadratic A and C) are dropped.

Any advice would be much appreciated! Thanks!

Sounds fine for age x E to be entirely quadratic.

It is not implausible, over some developmental range, that the E-component is growing quadratically. Salary for instance might increment as a percentage, increasing the variance in salary in your population as a quadratic function of age.

years = 18:55; base = 100

salary = base*1.05^(years-18); plot(years, salary)

Great, thanks for your advice!

Note that there is an inherent quadratic effect in the standard linear model. So if we moderate a by making the path from genotype to phenotype a + b*AGE, the net effect on the phenotypic variance is a^2 + 2abAge + b^2Age^2. If you have entered Age^2 on the path, then effectively the interaction is specified as quartic in the variance.

You do not say exactly why the linear model wouldn't work. In my experience it is often best to work with age in centuries rather than years. Doing so typically does a better job of keeping the predicted variances and covariances in reasonable range when the optimizer is hunting for the solution.