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520 – Leveraging the American Community Survey as a Sampling Frame for the National Survey of College Graduates
Automated Univariate Analysis of Variance Methods for Nested Mixed Effects Linear Models
Timothy Hall
PQI Consulting
A complete univariate Analysis of Variance (ANOVA) of a mixed effects linear model with nested factors may become extremely complicated when the data justify the use of some terms in the fully factorial, i.e., unconditional, model while failing to accept others at a given level of significance. This paper presents an analytical routine (written in elementary ANSI C code) that automatically calculates the applicable ANOVA table, including the Expected Mean Squares (EMS) expressions, and exact and Welch-Satterthwaite approximate F tests and statistics, that a given dataset would present as significant at a given level of Type I error. The output is the Plain TeX code that displays the ANOVA table and a listing of the intermediate steps taken to calculate the final model. Also included is a discussion of the possible valid adjustments an analyst may make to non-fully factorial datasets, or datasets with an unequal number of within-factor observations, to make them appropriate for use with this code.