FLOOD09697

• County: Statewide
• Community: Nationwide
• Basin: Statewide
• Title: Mathematical Modeling of a Sociological and Hydrologic Decision System
• Date: 6/1/1978
• Prepared By: Institute for Social Science Research on Natural Resources, Utah State Univ.
• Floodplain - Doc Type: Educational/Technical/Reference Information

vary from individual to individual and from group to
group. It. can be seen from this thai if the amount of
variance explained by Equation 5.2 is increased that
the absolute value of bO in Equation 5.1 can be de-
creased, provided Ihal the scales of the variables in
Equation 5.2 are such that their zero points are the
same as that of Y. If this is Ime, then the values of
the terms including the coefficients will be such thai
their effects will tend 10 make bO go to zero. This
occurs because the vaiue of a term with its sign will
then vary directly with I.he value of Y and because the
weightings given 10 each variable or combination of
variables in Equation 5.2 keep these values within rea.
sonable bounds. If there were no explanatory terms
in 5.2, bo and bo would be the same; it is the addilion
of these terms that parlially explains bo and conse.
quently can reduce boo As one adds additional signi.
ficanl factors to Equalion 5.2 this would be increas.
ingly true.

Anolher implication of the preceding is that the
model can be calibrated withoul knowing the values
of the variables contained only in terms of types I or
2. This could be done by using Equation 5.3 which
contains none of these terms.

Type m Terms are those in which a factor from
a proposed project and a faclor from Ihe population
or agency interacl in the same term, (bs - b8) in J?qua-
tion 5.1. The presence of the project factors means
Ihat these lerms reflect differences in characteristics
between flood control proposals. The z factors should
be measurable discriptors of perceived features of
flood conlrol proposals which make a difference in
the way individuals or groups react 10 the proposals.
The X faclors are values or attitudes which affect the
way people respond to Ihe z factors; in general, the
relaled attiludes are considered to be the imporlance
attached 10 the respective factors by the population.
For a given population or agency these are sel at a
particular time. The differences in reactions among
flood control proposals can be seen by inserting the
values for the different z faclors in the equalions.

Interaction terms containing both x and z are
called II Acceptance Functions." A minimum value
may have to be obtained for each of these (regardless
of the lota1 value of the equation) to achieve accept-
ance. The acceptance functions and related values
could also be graphed separalely (see Appendix G)
and should have value for the planner particularly
when the relationships between these terms are known;
these relationships could be determined from the
regression equation involving these terms.

The perceived characteristics of proposals are
multiplied respectively by the measures of impor-
tance factors in order to account for variations in the
weightings of the proposal elements by groups and

individuals and thereby allow Ihe developmenl of an
equation that may be applicable to different groups
and individuals. Weightings for each factor in the equa-
tion could be obtained for each respondenl by re-
gression analysis, bullhen the equation would need
to be recalibraled for each evaluator. Conceptually,
the method used is believed 10 be correct since the
effect of a factor is dependent on its imporlance which
varies within a group and from group to group. Em-
pirically, it also seems to be verified since the predicl-
ability of evalualions by an equation including accep-
tance functions is much _greater than when the factors
are included in an equation alone without Ihe impor-
tance factors or when Ihe importance factors and per-
ceived proposal characteristics are enlered separately
into an equation.

Ideally, the perceived factors should completely
describe all differences ill flood conlrol proposals
which make a difference in people's reactions 10 them.
For this research project, it was decided that the fac.
tors of effectiveness, cost, aesthetics, recreation, and
ecology would be used (Appendix B). Numerical
values for various flood control proposals for per-
ceived values of each of these five factors provide data
for use in equations of this Iype. Another way of des-
cribing the function of these proposal characteristics
is thai just as Ihe differences in reaction specific to a
proposal depends on the differences between popula-
tions, the differences in reaction of a particular popu-
lation depends on the differences between proposals.
Both types of differences must be described mathe-
matically to develop a model sensitive to proposal and
group variations. One can also for a given proposal
insert various X values in equations of type (5.1) to
determine differences in reaction to the same propos-
al by different populations.

Type IV Terms portray the interaction between
faclors describing the population and factors describ-
ing outside influence (X and V); Ihere can and prob-
ably will be more than one of these terms in equations
of the model. These terms represenllhe relationships
between the attitudes of a population or agency and
the opinioJls of "significant others" toward a proposal.
For example, a flood conlrol agency may favor or ap-
prove a proposal and, thereby, influence Ihe opinion
of the population or another agency toward the pro-
posal. The value for V 1 could be the dependenl vari.
able of another equation represenling the reaction for
that agency or group. The reactions of the parts of a
system are linked to its reaction as a whole, and vice-
versa.

A Type IV term Ihat includes a faclor Ihal may
change from proposal to proposal may be considered
an acceptance function. Such a situation occurs when
an evaluation of the proposal by one group influences
another group. Omission of significant terms of this
Iype would lead to serious errors of prediction.

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