A common problem in contingency table analysis involves finding relationships between variables in an I×J contingency table, where either I or J, or both, are greater than 2. We partition (decompose) a 3×3 contingency table of psychiatrists cross-classified as to their School of psychiatric thought (Eclectic, Medical, or Psychoanalytic) vs. their opinions about the Origin of schizophrenia (Biogenic, Environmental, or as a Combination of the two). The decomposition involves the partitioning of the contingency table into orthogonal, additive components, each component associated with its corresponding Likelihood Ratio Chi-Square statistic. We attack/analyze the problem in detail.

We explore, review and analyze the ergoStool data in the first chapter of Mixed Effects Models in S and S-Plus by Pinheiro and Bates (2000). The ergoStool data provide an example of a randomized block design that may be analyzed within the framework of mixed effects models, those which contain both fixed and random factors. The data are available from the nlme package. We comment on some observations/insights regarding the use of R Markdown and on some differences found in generating PDF and HTML files.

Using RMarkdown, we explore, review and analyze the Rail data in the first chapter of _Mixed Effects Models in S and S-Plus_ by Pinheiro and Bates (2000). Following Pinheiro and Bates, the Rail data are modeled with a mixed effects model, one containing both fixed and random factors, as part of the nlme package.

A common problem in contingency table analysis is to find relationships between variables in an I×J contingency table, where either I or J, or both, are greater than 2. The problem is to partition, or decompose, a 5×2 contingency table the table in a statistically rigorous way to describe similarities and differences between the variables in the table. The decomposition involves the partitioning of the contingency table and its corresponding Likelihood Ratio Chi-Square statistic, LR χ2, into orthogonal, additive components.

Analyze a repeated measures, occasions within phases, data set by Crowder and Hand (1990). Derive Expected Mean Squares by Cornfield-Tukey Algorithm (1956) for proper F test to determine phase shifts are significant.