Overview
Leo A. Goodman (1928–2020) was a statistician and sociologist at the University of Chicago (later UC Berkeley), a leading figure in the analysis of categorical data and contingency tables. In statistics he is best known for deriving the EM-type iterative algorithm for maximum likelihood estimation of latent class models (Goodman 1974), published three years before Dempster-Laird-Rubin (1977) formalised the general EM framework. He received the National Medal of Science (2009).
Key Contributions / Features
- EM algorithm for latent class models (1974): Derived the iterative E-M procedure for ML estimation of the T-class latent structure model with m polytomous manifest variables. Extended earlier dichotomous-only work (McHugh 1956, 1958) to general polytomous variables; showed how imposing equality restrictions on latent class parameters simply merges the EM update equations, requiring no re-derivation.
- Identifiability diagnostics (1974): Necessary counting condition IJKL≥(I+J+K+L−3)T; Jacobian rank test for local identifiability of the MLE π^ specifically (not just the population π); practical exploratory strategy of fitting unidentifiable models to obtain the unique π^ijkl, then recovering an equivalent identifiable restricted structure.
- Restricted latent structures (1974): Systematic taxonomy of equality constraints across latent classes; three collapsibility conditions (m, m−1, m−2 variables equal) that force unidentifiability; modified identifiability check via merged Jacobian columns.
- Log-linear models: Extensive development of log-linear modelling for multi-way contingency tables (1970s); quasi-independence (Goodman 1968); association models and row-column interaction; connections to latent class analysis.
- Social mobility: Applied categorical methods to occupational mobility tables; mobility indices; latent structure models for social stratification data.
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