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. 2009 Feb;46(1):65–83. doi: 10.1353/dem.0.0041

Table 3.

Mean Squared Deviation (MSD)a of the Intercept Parameter: Unconstrained, Exact Constraints, and Bayesian Constraints Models

Assumed Prior Model Type
Unconstrained Exact Constraints Bayesian Constraints
Main Prior
   (1) Mean squared bias 0.0042 0.0070 0.0000
   (2) Sampling variance 0.0587 0.0219 0.0220
   (3) Constraint variance 0.0025 0.0025 0.0025
  MSD 0.0654 0.0315 0.0245
High-Bias Prior
   (1) Mean squared bias 0.0017 0.0361 0.0000
   (2) Sampling variance 0.0587 0.0219 0.0221
   (3) Constraint variance 0.0114 0.0114 0.0114
  MSD 0.0719 0.0694 0.0335
High-Bias, High-Variance Prior
   (1) Mean squared bias 0.0029 0.0408 0.0000
   (2) Sampling variance 0.0587 0.0219 0.0220
   (3) Constraint variance 0.0479 0.0479 0.0479
  MSD 0.1094 0.1106 0.0699
a

Mean squared deviation (MSD) = sum of rows (1), (2), and (3). Row (1) = point estimate of β0 under Bayesian prior. Row (2) = asymptotic variance for the each regression estimate of β0, given by [SE(β0)]2. Row (3) = variance in β0 due to uncertainty about the true population constraint value.