Abstract: Classical Gaussian factor models can be extended to conditional independence models where observed variables (not necessarily Gaussian distributed) are conditionally independent given one or more latent variables.
The residual terms are conditionally normally distributed and serially uncorrelated.
We analysed the QOL scores as a conditionally normally distributed continuous outcome and this would seem sensible given the 140 point scale produced by this instrument.
In agreement with previous analyses performed by Grandjean et al. [ 5, 23], the neuropsychological outcome variables are all modeled as continuous (conditionally) normally distributed variables.
However, in the special case where all responses are continuous (and conditionally normally distributed) the likelihood function is simpler, and maximum likelihood estimation can be achieved even when some subjects have missing values.
Equivalently, for data which are conditionally Gaussian-distributed, one may also use nonlinear least squares.
Given β and b, the liabilities l i j k are conditionally independent and distributed as where σ ε 2 is fixed to 1 to achieve identifiability in the likelihood because the liabilities are unobservable.
It was assumed that, given the location parameters β and a, the underlying variable l i of animal i is conditionally independent and distributed as (6) l i | β, a ∼ N (x i ′ β + ∑ k = 1 K z ik a k, σ e 2 ).
Conditionally, n12 is binomially distributed with parameters n= n12+ n21 and p=1/2 under the null hypothesis.
and the ξ j 's are conditionally independent r.v.'s, possibly non-identically distributed.
This was probably because the partially observed continuous variables in our data were approximately normally distributed; predictive mean matching may be preferred for variables that are not (conditionally) normally distributed (35).
