Statistical modelling of data in real-world scenarios often require models that can accommodate variability and dependence in a plethora of different ways. Within the generalized linear modelling framework, various extended models are available to address these commonly found problems. In this context, goodness-of-fit assessment is pivotal for ensuring reliable inferential results. This includes, but is not limited to, graphical tools, which can be helpful when deciding whether a data sample can be a plausible realisation of a fitted model. In this thesis, we focussed on the development of diagnostic measures and the comparison of different modelling approaches, when applied to diverse types of data. Initially, we present an overview of diagnostic analyses stemming from generalized linear models, whilst illustrating different tools using two case studies from experiments in ecology and agriculture. Then, we extend the graphical model selection method known as half-normal plots with a simulated envelope. The simulated envelope is such that, under a well-fitted model, the majority of points should fall within its bounds. Nonetheless, closely related models tend to produce very similar graphs. We propose a new distance-based framework that acts as an added quantitative summary to the half-normal plot with a simulated envelope. This new measure can effectively determine the most appropriate model when closely related models are included. An extensive simulation study was carried out taking into account many different scenarios. The results showed that the distance framework exhibits robust performance in finding the true model and is comparable to BIC; in some instances, it even displays superior efficacy. Finally, we present a comparative analysis of different modelling frameworks applied to interval-censored longitudinal data, which is bounded in the interval (0, 1). We considered three approaches, where the first and second involved mixed and marginal models using a transformation of the interval-censored response, and the third incorporated the interval-censored nature in the likelihood. We found that the accounting for the interval-censored nature of the data improved model goodness-of-fit. However, the conclusions drawn from all three approaches were qualitatively similar.