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Bayesian Estimation Using a Non-Diffuse Prior Distribution
experimental condition, measured their levels of depression, treated the experimental
group, and then re-measured participants’ depression. The researchers did not rely on
a single measure of depression. Instead, they used two well-known depression scales,
the Beck Depression Inventory (Beck, 1967) and the Hamilton Rating Scale for
Depression (Hamilton, 1960). We will call them BDI and HRSD for short. The data
are in the file feelinggood.sav.
Fitting a Model by Maximum Likelihood
The following figure shows the results of using maximum likelihood estimation to fit
a model for the effect of treatment (
COND) on depression at Time 2. Depression at
Time 1 is used as a covariate. At Time 1 and then again at Time 2, BDI and HRSD are
modeled as indicators of a single underlying variable, depression (DEPR).
The path diagram for this model is in Ex27.amw. The chi-square statistic of 0.059 with
one degree of freedom indicates a good fit, but the negative residual variance for post-
therapy HRSD makes the solution improper.