This analysis revisits the classical barley leaf blotch dataset to assess variance specification in binomial generalized linear models. Evidence from residual diagnostics and dispersion estimates suggests that the standard binomial assumption does not adequately capture the variability in the data. Using a quasi-likelihood framework, the binomial, quasi-binomial, and a quasi-custom variance model are compared. Model evaluation is based on QAIC, dispersion, and deviance statistics. Results indicate that the quasi-custom specification better reflects the empirical heterogeneity present in the dataset, leading to more stable standard errors and more reliable statistical inference for overdispersed proportion data.

This analysis explores the application of Linear Mixed Models (LMM) to hierarchical education data from the Junior School Project (JSP) dataset. The study compares two estimation approaches for variance components: Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML). Using both full sample and reduced (small sample) data, the analysis demonstrates how ML and REML behave under different sample sizes, with particular emphasis on the estimation of between-school variance and the Intraclass Correlation Coefficient (ICC). Results show that while ML and REML produce nearly identical estimates in large samples, ML tends to underestimate variance components in smaller samples. REML provides more stable and theoretically less biased estimates, especially when the number of clusters is limited.