QuantDev Brownbag - Generalized Latent Variable Models for Location, Scale, and Shape parameters

We introduce a novel class of Generalized Latent Variable Models for Location, Scale, and Shape parameters (GLVM-LSS). This model extends the generalized linear latent variable model in two important ways. First, the exponential family distribution assumption for the manifest variables is replaced by a broader distribution family that encompasses distributions with skewness and kurtosis. Secondly, the model's systematic component enables the modeling of not only the mean (location) but also other parameters of the manifest variables' distribution, such as scale and shape parameters. These parameters are represented as linear functions of the latent variables and potentially observed covariates. The estimation of model parameters employs maximum likelihood estimation. We discuss real-world applications from educational testing and public opinion research. This is joint work with Prof. Irini Moustaki (LSE), Dr. Yunxiao Chen (LSE), and Prof. Giampiero Marra (UCL).