issue that is important to the voter. A moderate pro-choice voter would
prefer an extreme pro-choice candidate to a moderate pro-life candidate.
20. Brady ( 1991b)
showed that a Poole-like estimator
actually does produce statistically consistent estimates of both factor
scores and factor loadings in a linear factor model. Rivers ( 1987)
result, then, is partly the result of the non-linearities inherent in ideal
point models. It can also be shown that the Poole estimator would yield
correct results if there were no error in the model. These results
suggest that the Poole estimator may not produce much bias if the
amount of error is small.
21. Jackson and
Kingdon ( 1992)
have criticized the use of
interest group scores to explain congressional votes, but their argument
does not bear on the debate about the number of dimensions in
Indeed, Poole and Rosenthal recognized that the
standard proof of consistency for maximum likelihood does not apply,
but they made the odd statement (1991, 272) that "At a practical level,
this caveat is not important. The key point is that data is being added at
a far faster rate than parameters." Yet there are many examples in
statistics where adding data faster than parameters does not ensure
consistency. The Monte Carlo reports in their paper are more
convincing; but much more work still needs to be done to assay the
statistical properties of their innovative method for scaling roll-call
This section draws heavily upon Bartels ( 1990)
some related points are discussed in more detail.
Fascinating questions about the role of theoretical
expectations in statistical inference were raised by a Box-Jenkins
ARIMA analysis in the Journal of Conflict Resolution
al. 1988), demonstrating that "a very small group practicing [the
Maharishi technology of the unified field] in East Jerusalem appeared to
influence overall quality of life in Jerusalem, Israel, and even in
neighboring Lebanon." The editor of the journal ( Russett 1988, 773
did not know what to make of the finding and admitted that "The
hypothesis has no place within the normal paradigm of conflict and
peace research. Yet the hypothesis seems logically derived from the
initial premises, and its empirical testing seems competently executed." Schrodt ( 1990)
questioned whether the research was, in fact,
competently executed; but whatever the truth in this case, the original
article raises significant questions about what scientific hypotheses we
should be willing to entertain and what proof we should require for their
demonstration. How strongly should theory incline us to believe or
disbelieve that there are "long cycles" in the severity of war in the
international system ( Goldstein 1988, 1991
; Beck 1991
), or that postwar U.S. savings rates were influenced by changes in public perceptions of
the threat of nuclear war ( Slemrod 1986
)? As we add new and more
powerful techniques to our kitbag of tools, it is worth remembering that
good inferences require more than powerful techniques and large t-
It is striking how seldom, in footnotes of this sort,
trying something different makes the results come out different.
The cross-validation criterion is simply the square root
of the PRESS (PRediction Error Sum of Squares) criterion of Allen
and is also closely related to the jackknife and bootstrap
techniques ( Efron and
Of course, the least squares and maximum likelihood
criteria sometimes lead to the same estimator, as in the case of ordinary
regression with normally distributed errors. In cases like this,
researchers did maximum likelihood estimation in the same way they
wrote prose, without knowing it.
28. King ( 1991, 2-3)
reported the results of a content
analysis in which the proportion of American Political Science Review
articles using "quantitative data and methods in some way" has
fluctuated around 50% since 1969.
Another approach to the problem of mass belief systems
has been to reconceptualize political sophistication and ideological
constraint. Luskin ( 1987)
provided a magisterial overview of various
measures of political sophistication and some of his own suggestions. Peffley and
Hurwitz ( 1985)
and Hurwitz and
Peffley ( 1987)
an interesting approach based upon a hierarchical structure of attitudes
with core beliefs informing broad postures which, in turn, are the basis
for specific beliefs.
Later, Palmquist and
Green ( 1992, 128)
showed that the
identification problem is even worse than in Achen's telling because
"standard errors for the measurement error parameters [of the Wiley
Wiley ( 1974)
model with correlated errors] are typically so large
that it is not hard to see how implausible values could result simply
from sampling error." With three waves of data it is not only
impossible to distinguish between the two models but also virtually
impossible to get informative estimates of the parameter estimates of the
correlated error model.
31. Rivers ( 1986)
independently proposed a similar solution
to the Kramer problem, albeit with a somewhat different model and
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