A Bilinear Reduced Rank Model
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This article considers a bilinear model that includes two different latent effects. The first effect has a direct influence on the response variable, whereas the second latent effect is assumed to first influence other latent variables, which in turn affect the response variable. In this article, latent variables are modelled via rank restrictions on unknown mean parameters and the models which are used are often referred to as reduced rank regression models. This article presents a likelihood-based approach that results in explicit estimators. In our model, the latent variables act as covariates that we know exist, but their direct influence is unknown and will therefore not be considered in detail. One example is if we observe hundreds of weather variables, but we cannot say which or how these variables affect plant growth.
Chengcheng Hao and Feng Li are supported by the National Natural Science Foundation of China (no. 11601319 and no. 11501587, respectively). Feng Li is also supported by Beijing Universities Advanced Disciplines Initiative (no. 6JJ2019163). Dietrich von Rosen is supported by the Swedish Research Council (2017-03003).