Kotlarski's lemma for dyadic models

We show how to identify the distributions of the latent components in the two-way dyadic model for bipartite networks $y_{i,\mathrm{\ell }}={\alpha }_i+{\eta }_{\mathrm{\ell }}+{\epsilon }_{i,\mathrm{\ell }}$. This is achieved by a repeated application of the extension of the classical lemma of Kotlarski (1967) in Evdokimov and White (2012). We provide two separate sets of assumptions under which all the latent distributions are identified. Both rely on some of the latent components being identically distributed.