The mixture of generalised linear models (MGLM) requires knowledge about each mixture
component’s specific exponential family (EF) distribution. This assumption is relaxed and a mixture
of semi-parametric generalised linear models (MSPGLM) approach is proposed, which allows for
unknown distributions of the EF for each mixture component while much of the parametric structure
of the traditional MGLM is retained. Such an approach inherently allows for both symmetric and
non-symmetric component distributions, frequently leading to non-symmetrical response variable
distributions. It is assumed that the random component of each mixture component follows an
unknown distribution of the EF. The specific member can either be from the standard class of
distributions or from the broader set of admissible distributions of the EF which is accessible through
the semi-parametric procedure. Since the inverse link functions of the mixture components are
unknown, the MSPGLM estimates each mixture component’s inverse link function using a kernel
smoother. The MSPGLM algorithm alternates the estimation of the regression parameters with the
estimation of the inverse link functions. The properties of the proposed MSPGLM are illustrated
through a simulation study on the separable individual components. The MSPGLM procedure is also
applied on two data sets.
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