We considered identification of phenotype (at occasion t) to environment (at occasion t ? 1) transmission in longitudinal model comprising genetic, common and unique environmental simplex models (autoregressions). This type of transmission, which gives rise to genotype-environment covariance, is considered to be important in developmental psychology. Having established identifying constraints, we addressed the issue of statistical power to detect such transmission given a limited set of parameter values. The power is very poor in theACEsimplex, but is good in theAEmodel.We investigated misspecification, and found that fitting the standard ACE simplex to covariance matrices generated by an AE simplex with phenotype to E transmission produces the particular result of a rank 1 C (common environment) covariance matrix with positive transmission, and a rank 1 D (dominance) matrix given negative transmission. We applied the models to mother ratings of anxiety in female twins (aged 3, 7, 10, and 12 years), and obtained support for the positive effect of one twin's phenotype on the other twin's environment. © 2014 Springer Science+Business Media New York.