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NOTE S
L
1Usage of the term "model" varies widely within and between sciences.
m e model of this chapter consists, at a minimum, of a set of structural
equations. A more encompassing use of the term "model" would include not
only the structural equations, but the verbal definitions of the vari-
ables, and the reasoning behind assignments of exogeneity, endogeneity,
and mixed status (endogenous with respect to some variables, exogenous
with respect to others). A stir' more encompassing use of the term
"model" would include the reasoning and hypotheses about coeff icient
variability across contexts, or the lack thereof .
20ur use of terms such as "cause,n Causality," and "causal links" is
compatible with longstanding tradition in the study of problems not
generally susceptible to experimental manipulation. Recognizing that
there will always be philosophical dispute in science about causality, it
should be noted that the intellectual position manifested in this report
can be traced at least as far back as the work of Durkheim (1897~. Other
relevant contributors to this general stance include, among many others,
Wright {1921, 1923), Simon (1952, 1953r 1954~; Tukey (1954~; Blalock
(1961~; Fisher (19611; and Duncan (1975~.
3More formally, we exploit Nelder and Wedderburn's (1972) distinction
between systematic and error components in generalized linear models.
Our presentation is in terms of the systematic component of each struc-
tural equation. In actual empirical research, estimation of the full set
of structural equations will be problematic because the nature of the
error components will not necessarily be the same for each equation.
However, recent statistical progress, summarized and synthesized by
Winship and Mare (1981), should eventually mitigate estimation problems.
Since the term "linear" in generalized linear models" may be confusing
to some, it should be noted that ~linear" here means linear in the
Parameters; explanatory variables may have nonlinear effects on the
response variables. Where we postulate linearity and additivity, we do
so for two reasons. First, for discrete response variables, we wish to
think of the functional relationships in linear model terms (rather than
"multiplicativen). Thus, for example, we prefer to treat a discrete
response variable in terms of a "log-linear. equation in which the
~response" is a logit, as distinguished from a multiplicative equation in

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which the "response" is a probability. Second, and more important, when
we postulate linearity and additivity, we do so because we think it is
substantively appropriate. Certain, but not all, equations contain
nonlinearity and interaction terms. Where this occurs, the increased
complexity is always justified by substantive and theoretical
considerations.
4Although it is tempting to think of this profile as monotonically
increasing with time, this need not be the case. Trends in knowledge and
practice can diverge in the short if not in the long run because of such
factors as changes in the political climate.
ith appropriate assumptions about the errors, equations (1.16) and
(2.1) form a mixed model. Of particular relevance here is that the
l-term can be thought of either as arising from uncertainty in the
specification of (2.1) (see, e.g., Lindley and Smith, 1972), or as random
error occasioned by the sampling of countries from a super-population.
For the purposes of the present discussion of substantive, theoretical
hypotheses about the systematic effects of macro variables, the distinc-
tion is not critical. It does matter for estimation. Due to limitations
of time, funding, the pace of statistical developments, and availability
of appropriate computer programs, the estimation results to be presented
later in this chapter are by no means optimal with respect to either view
of macro error. Future research on this subject will take advantage of
some estimation progress for mixed models of the type this chapter rests
on (Wong and Mason, forthcoming).
6Note the connection between our hypothesis about the lack of systematic
setting variability in the SES and AFB effects on EF, and the hypothesis
developed here about setting variability in the EF intercept. If the
former hypothesis is wrong, this should be most clearly and meaningfully
demonstrable for S. given the validity of what we have argued about the
strategies of family planning programs in the Third World. For this
reason, we examine the macro data for a potential relationship between
the micro socioeconomic coefficients of the EF equation and level of
socioeconomic development (for which Table 2.2 contains the only zero
entry) .
7The abbreviations used in this chapter appear in the Glossary.
8This is not necessarily the most extreme contrast. Its use is
nonetheless valid and appropriate for present purposes, if not optimal.
This is addressed further in subsequent discussion.
9Tables 2.6 to 2.8 deliberately do not include standard errors of
regression coefficients, although they report three levels of p-values.
The reasons for this are as follows. First, most of the socioeconomic
explanatory variables are polytomous, and the standard errors would refer
to contrasts. The contrasts in this instance would be those between the
included categories of a polytomy and the category excluded for purposes
of estimation (see, e.g., Johnston, 1972:1781. Standard errors for these

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particular contrasts are not necessarily relevant for present substantive
purposes. Instead of presenting such standard errors, Tables 2.6 to 2.8
report the results of logically prior global tests of the null hypothesis
that all coefficients for a polytomy are simultaneously zero, against the
alternative that at least one of them differs from zero. A second reason
for not reporting standard errors is that there is no cross-country or
within-country inference we wish to make which depends crucially on
reporting point estimates of standard errors. A third reason for not
presenting standard errors is that efficient estimates of them are not
currently available base Wbng and Mason, forthoom~), given that our
purview is ultimately that of the mixed (hyperparameter} model. A fourth
reason for not reporting standard errors is specif i ~ to Table 2 ~ 8 ~ which
contains interactions involving polytomies. In this instance, the stan-
dard errorsto£ specific contrasts are of little value because it is the
entire pattern of interaction that must be apprehended, and not whether
one particular coefficient differs "significantly. from zero--i.e., from
the effect of being in the omitted category.
10Purging the intercept for Korea of its religion component is
essentially the first step in renormalizing the religion coefficients
into the form of weighted deviations from the grand mean. Since it would
be confusing to present the coefficients for religion or ethnicity in
this normalization while maintaining the coefficients for other variables
in the dummy coding normalization, we do not show the religion or
ethnicity coefficients. Tn any case, these are nuisance parameters for
immediate purposes, and are insignificant in the AFB, EF, and LF
regressions for Korea.
11TO illustrate the potential relevance of other macro variables, it
may be noted that Peru does appear to have shorter average breastfeeding
than Korea; this difference could account for the difference in EF
intercepts between the countries (World Fertility Survey, 1979, 1980~.
12Th is result may be due to imperfect control for the pace of fertility
and may arise, in effect, from an omitted variable. A better specifica-
tion might well produce the expected results, and our later analyses will
address this issue.
13The term "conditional coef f ic lent" may be new to some readers; the
following example may help to clarify it. The regressions presented in
Table 2.8 specify that EF interacts with both WED and HOCC. This means
that there is an EF coeff icient for each cell in the cross-classif ication
of WED by HOCC. Each of these coeff icients is a conditional coeff icient.
14That the cell sizes are small for occupational categories, given that
EF = 0, can be seen by noting that the standard deviation for EF is 1.3 4 .
Thus EF = 0 is more than two standard deviations from the mean of EF.
15Sharp diminution of socioeconomic effects on fertility was found in
Taiwan for the parents of couples interviewed in the early 1970s. This
is compatible with our expectations of cohort differences in a society

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moving from the more traditional to the more transitional end of the
setting continuum. See Hermalin et al. {1982:262, fin. 17~.
Although it is possible and desirable to indicate the magnitudes of
the standard errors of the estimated coefficients as part of these plots,
this has not been done due to software, time, and funding limitations.
Future research will present such information, and will do so for
coefficients estimated using more efficient procedures than were
available when the work reported here was in progress.
17Mauldin et al. (1978) report this correlation to be .58, computed
over many more countries.
The bivariate distribution of countries is:
Prouram Strength
Strong Other
Social Setting High
Social Setting Other
6
4
3
2
The association between these two dichotomized variables in the Mauldin
et al. (1978) data is, however, positive.