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In this example we show that, even in a simple bivariate scenario, AISM schemes can be useful within a Gibbs sampler.
(1) Bivariate scenario: estimation of attenuation factors.
Since MixDTrees are based on first-order dependencies, it is sufficient to find the parameters in a simple bivariate scenario (X u, Xpa u )), where pa u)= v.
Finally, using structural equations modeling, we estimated attenuation factors associated with each dietary exposure to assess degree of measurement error in a bivariate scenario for regression calibration of logistic regression model.
According to Rosner and colleagues [ 56], if a primary regression model (Eq. 4.1) with a response variable Y contains only one error-prone explanatory variable Q j (bivariate scenario) correction for attenuation, consists simply of dividing the regression coefficient β naïve, j) of that variable Q j by the attenuation factor λj (Eq. 4.2).
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Each multivariable model included variables associated with HIV infection in any of the three bivariate scenarios at P < 0.10.
In an attempt to select the indicators based on the assessment of bivariate correlations, two scenarios were tested.
For all scenarios, we assume that the bivariate normal random variables (X, Y) have population parameters μ x = 0, σ x = σ y = 1.
We have therefore selected some scenarios that allowed comparison to previous findings of simpler bivariate associations [ 1].
The selection of bivariate distribution to be used should depend on considerations involving both the physical scenario at hand, and the properties of chosen distribution.
For each scenario, we simulated 2000 datasets and analyzed these using both the full bivariate moderation model (estimating moderation parameters on the cross paths as well as on the paths unique to T) and the extended univariate moderation model (estimating moderation on the variance components of the residual T″).
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