Statistical Techniques

This study’s central thesis is that planners’ commitments and role orientations are associated with flood hazard mitigation features in development projects, both directly and indirectly. This study utilizes three sets of data analyses to examine the correlations between planner characteristics and flood hazard mitigation. First, descriptive statistics are used to report frequencies and measures of central tendency for variables under study. Second, bivariate regression analyses are used to examine relationships between variables when no other variables are controlled for. Third, multivariate path analysis is used to evaluate the strength, direction, and significance of hypothesized relationships between variables depicted in Figure 3.1. Path analysis is an appropriate technique because the conceptual model that is tested in this study includes variables that are expected to be indirectly associated with flood hazard mitigation features, mediated by site plan review process variables. Path analysis enables for these indirect effects to be estimated, along with the effects of variables that are directly associated with flood hazard mitigation features.

Paths between variables in the conceptual model are tested in multiple regression analyses, with the choice of regression techniques being based upon the manner in which the dependent variable in each regression model is measured. For regression models with dependent variables measured as dichotomies, binary logistic regression is used; for

regression models with dependent variables measured as counts, Poisson regression7 is used.

7_{Long (1997, p. 217) notes that treating count dependent variables as continuous variables and using ordinary}

4.3.1 Identifying Total, Direct, and Indirect Effects through Path Analysis

This study addresses the following four questions regarding the association of planners’ commitment and role orientations with flood hazard mitigation: (1) is planners’ commitment associated with flood hazard mitigation, (2) are planners’ role orientations associated with flood hazard mitigation, (3) are planners’ role orientations associated with public participation, and (4) does the association of planners’ commitment with flood hazard mitigation depend upon planners’ role orientations. Specific hypotheses that are developed in Chapter 3 to help answer each of these questions are displayed in graphic form in Figure 3.1. The basic premise behind the conceptual model is that flood hazard mitigation features in development projects are determined by land use planner characteristics, the site plan review process, community characteristics, and project characteristics. In order to assess all relationships between variables depicted in Figure 3.1, this study utilizes a path analysis approach that enables the identification of both direct and indirect associations of variables with flood hazard mitigation.

In order to calculate indirect effects, this study relies on a simple relationship between total effects, direct effects, and indirect effects, whereby the total effect of one variable (X) on another (Y) is equal to the indirect effect of X on Y added to the direct effect of X on Y. Given that this relationship is true by definition, it is also true that the indirect effect of X on Y is equal to the total effect less the direct effect. The total effect of X on Y is equal to the regression coefficient8 for X that is produced by regressing Y on X without including in the regression model the mediating variable(s) (i.e. the variable(s) through which X effects Y).

8 _{Unexponeniated coefficients (instead of odds-ratios or incidence rate ratios) are used to calculate total, direct,}

and indirect effects. Once the indirect effects have been calculated in this way, all effects can be exponentiated and transformed into either odds-ratios or incidence rate ratios, depending upon the nature of the particular regression analysis.

The direct effect of X on Y is equal to the regression coefficient for X that is produced by regressing Y on X while including in the regression model the mediating variable(s). Thus, the indirect effect of X on Y is equal to the total effect less the direct effect.

4.3.2 Testing for Interaction Effects

The regression analyses are used in part to test for the presence of interaction effects involving planners’ commitments and role orientations. Testing for interaction effects requires a model estimation approach that differs from that used for models without

interaction terms. For each dependent variable, a Main Effects model is estimated that does not include interaction terms. Next, an Interaction model (with interaction terms) may or may not be tested, depending upon the results of the Main Effects model. The model

estimation process for each dependent variable in the remainder of this chapter proceeded as follows:

1. Estimate Main Effects model (without interaction terms)

a. If significant effects are not observed for commitment, do not estimate Interaction model, and use Main Effects model as final model

b. If significant effects are observed for commitment, estimate Interaction model (with interaction terms)

i. If significant effects are observed for all four interaction terms, keep interaction terms in model and use Interaction model as final model

ii. If significant effects are observed for one, two, or three interaction terms, drop non-significant interaction terms and re-estimate model. Repeat process until model includes only those interaction terms that are found to have significant effects, and use as final model

iii. If significant effects are not observed for any interaction terms, drop interaction terms from model and use Main Effects model as final model