 |
|
Standard NAEP analysis is based on the evaluation of
plausible values. Plausible values are random draws on the posterior distribution
resulting from the the product of an empirical prior based on a
composite marginal maximum likelihood regression (in which the predictors are a set of
principle components from all of the data collected on the background surveys) and the measurement
likelihood of the item responses.
NAEP uses a normal approximation to the posterior distribution, taking the mean and variance of the composite posterior distribution (actually, an approximation to it--see Thomas, 1993), and drawing randomly from a normal distribution with those moments.
|