9
testing the assertion that dual or multiple dimensions within one of our major policy
domains could actually be collapsed to a single dimension. Either way, confirmatory
analyses were conducted for all domains in all years when there were at least four items
available per domain. (CFA models are saturated with three items or less, and cannot
produce fit statistics.)
The result has the extra presentational advantage of generating issue structures
(and subsequent voting models) in figurative form. Note three aspects of this
presentation, in particular (Figures 1ff.):
•
Since the latent factors would not perfectly explain the observed variables
even in theory, the small ellipses in these diagrams represent errors in predicting
the observed variables from the postulated solution.
•
The number on each path between a factor and an observed variable is the
standardized regression coefficient that results from regressing the observed
indicator onto the factor.
•
The number at the top of each rectangle (or ellipse, if a first-order factor is
hypothesized to be caused by another factor) is the squared multiple correlation
between the variable and the factor or factors that are hypothesized to have
produced it. Said differently, this is the proportion of the variance in the issue
variable that is explained by the factors or factors that generated it.
AMOS (Analysis of Moment Structures), a modeling program for structural
equations, was used to estimate the confirmatory factor analyses as well as the voting
models. (For greater details on this specific analysis, see Claggett and Shafer 2002.) An
important advantage of AMOS is that it uses full-information maximum-likelihood
estimation in the presence of missing data. This is a much better means of handling this
problem than the usual strategy of list-wise deletion. Structural equation models have the
additional advantage of being able to test how well postulated structures—in our case,
both the within-domain and the cross-domain issue structures, plus the vote choice
Convention