This corresponds to a representation of the molecular wave function where the variables corresponding to the molecular geometry and the electronic degrees of freedom are separated.
The four subscales were recoded to dichotomous variables corresponding to agree or not agree.
Here the dependent variables corresponding to such future application would be subject to the same types of observation error as those in the data used for fitting.
The variables corresponding to the columns of the identity matrix are called basic variables while the remaining variables are called nonbasic or free variables.
The variables corresponding to the remaining edges on these paths will be reverse variables.
(We changed the sign of the dual variables corresponding to rows when going from TRP to TP.)
The infinite set of random variables corresponding to the marginal distribution of these samples is a Dirichlet process with parameters and .
As an example, given a set of people, we can consider the set of categorical variables corresponding to their last names.
In fact, there generally will be no variables at all corresponding to concepts such as "sample mean" or "sample variance".
Unlike quantum mechanics, the more complete theory contains variables corresponding to all the "elements of reality".