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12 December 2006

Naming Conventions

This discussion came up yesterday in the Bayes course. There is a plethora of names for multilevel models. Sociologists seem to prefer "hierarchical," many statisticians say "mixed effects," and there is heterogeneity about usage in economics. It seems reasonable to standardize, but this is unlikely to happen. Maybe the most common comes from the following. Given two data matrices, x_{ij} for individual i in cluster j, and z_j for cluster j, there are perhaps four canonical models:

"Pooled:" y_{ij} = \alpha + x_{ij}'\beta + z_j'\gamma + e_{ij}

"Fixed Effect:" y_{ij} = \alpha_j + x_{ij}'\beta + e_{ij}

"Random Effect:" y_{ij} = \alpha_j + x_{ij}'\beta + z_j'\gamma + e_{ij}

"Random Intercept and Random Slope:" y_{ij} = \alpha_j + x_{ij}'\beta_j + z_j'\gamma + e_{ij}

Some prefer "random intercepts" for "fixed effects" and perhaps we can consider these all to be members of a larger family where indices are turned-on turned-off systematically. On the other hand maybe it's just terminology and not worth worrying about too much. Thoughts?

Posted by Jeff Gill at December 12, 2006 10:23 AM