Attitudinal Factors and Personal Characteristics Influence Support for Shellfish Aquaculture in Rhode Island (US) Coastal Waters

Abstract

This study explores public interests associated with shellfish aquaculture development in coastal waters of Rhode Island (US). Specifically, we examine (1) the levels of public support for (or opposition to) shellfish aquaculture development and (2) factors driving the levels of support, using survey data and ordinal logistic regressions. Results of the analysis identify several key attitudinal factors affecting individual’s support for shellfish aquaculture in Rhode Island (RI). The level of support is positively associated with attitudes related to shellfish aquaculture’s benefits to the local economy and its role as a nutritional food option, and negatively influenced by attitudes related to aquaculture farms’ effects on aesthetic quality and their interference with other uses. Findings highlight that support for (or opposition to) aquaculture in RI is driven more by attitudes associated with social impacts than by those associated with environmental impacts. The level of support is also affected by personal characteristics related to an individual’s participation in recreational activities. For instance, bicycle riders tend to be supportive of shellfish aquaculture while respondents who participate in sailing and birding are less supportive. By identifying the broader public’s interests in shellfish aquaculture, findings from this study and others like it can be used to address public concerns, incorporate public perceptions and attitudes into permitting decisions, and develop outreach targeted at specific stakeholder groups.

Appendix

Ordinal Logistic Regression Model

The model is outlined in the context of this study as follows: let y^* be a continuous variable representing a respondent’s level of support for shellfish aquaculture in RI coastal waters. We do not have specific information on y^*. The level of support is classified into 5 levels. As a result, y^*is a latent variable, i.e.,

$$y^ \ast = {\mathbf{\beta}}^\prime {\mathbf{x}} + \varepsilon$$

(1)

where x is the set of independent variables, β is a vector of parameter coefficients to be estimated, and ε is the error term. Although we do not observe y^*, we do observe the ordinal response variable y which is positively related to actual level of support for aquaculture y^*. As mentioned above, in the survey data set, y has five entries.

We have

$$y = \left\{\begin{array}{lll}1 & {\mathrm{if}} & y^ \ast \le \mu _1,\\ 2 & {\mathrm{if}} & \mu _1 < y^ \ast \le \mu _2,\\ \vdots & {} & \\ 5 & {\mathrm{if}} & \mu_4 < y^ \ast.\end{array}\right.$$

(2)

where μ _i (i = 1,2,…,4) are threshold parameters that distinguish the levels of support.

Let π _i (x) = P(y = i|x), the probability of y = i, for i = 1,2,…,5. The cumulative probabilities for y ≤ i are

$$P\left( {y \le i\left| {\mathbf{x}} \right.} \right) = \pi _1\left( {\mathbf{x}} \right) + \ldots + \pi _i\left( {\mathbf{x}} \right),\,i = 1, \ldots ,5.$$

(3)

The cumulative logits (i.e., log odds) are defined as (Agresti 2002)

$$\begin{array}{*{20}{l}}{\mathrm{logit}}\left[ {P\left( {y \le i\left| {\mathbf{x}} \right.} \right)} \right] & = \log \frac{{P\left( {y \le i\left| {\mathbf{x}} \right.} \right)}}{{1 - P\left( {y \le i\left| {\mathbf{x}} \right.} \right)}}\hfill \\ & = {\mathrm{log}}\frac{{\pi _1\left( {\mathbf{x}} \right) + \ldots + \pi _i\left( {\mathbf{x}} \right)}}{{\pi _{i + 1}\left( {\mathbf{x}} \right) + \ldots + \pi _N\left( {\mathbf{x}} \right)}},\,i = 1, \ldots ,4.\\ \end{array}$$

(4)

The proportional odds model simultaneously uses all cumulative logits is

$${\mathrm{logit}}\left[ {P\left( {y \le i\left| {\mathbf{x}} \right.} \right)} \right] = \alpha_{i} + {\mathbf{\beta }}^\prime {\mathbf{x}},\,i = 1, \ldots ,4.$$

(5)

Each cumulative logit has its own intercept (α _i ) which is increasing in i.

Predicted probabilities are computed as (Long and Freese 2001):

$$\begin{array}{l}P\left( {y = 1\left| {\mathbf{x}} \right.} \right) = \frac{{\exp \left( {\alpha _1 + {\mathbf{\beta }}^\prime {\mathbf{x}}} \right)}}{{1 + \exp \left( {\alpha _1 + {\mathbf{\beta }}^\prime {\mathbf{x}}} \right)}}\\ P\left( {y = i\left| {\mathbf{x}} \right.} \right) = \frac{{\exp \left( {\alpha _i + {\mathbf{\beta }}^\prime {\mathbf{x}}} \right)}}{{1 + \exp \left( {\alpha _i + {\mathbf{\beta }}^\prime {\mathbf{x}}} \right)}} - \frac{{\exp \left( {\alpha _{i - 1} + {\mathbf{\beta }}^\prime {\mathbf{x}}} \right)}}{{1 + \exp \left( {\alpha _{i - 1} + {\mathbf{\beta }}^\prime {\mathbf{x}}} \right)}},\,i{\mathrm{ = }}2, \ldots ,4\\ P\left( {y = 5\left| {\mathbf{x}} \right.} \right) = 1 - \frac{{\exp \left( {\alpha _4{\mathbf{ + \beta }}^\prime {\mathbf{x}}} \right)}}{{1 + \exp \left( {\alpha _4 + {\mathbf{\beta }}^\prime {\mathbf{x}}} \right)}} \cdot \end{array}$$

(6)

Since the probabilities modeled are cumulated over the lower ordered values (Eq. (3)), the probability of, say, y = 2 is

$$P\left( {y{\mathrm{ = }}2\left| {\mathbf{x}} \right.} \right) = P\left( {y \le 2\left| {\mathbf{x}} \right.} \right) - P\left( {y \le 1\left| {\mathbf{x}} \right.} \right).$$

(7)

Results of Odds Ratio Estimates

Table 5 presents the proportional odds ratios, which are the coefficients in Table 2 exponentiated, and the corresponding 95% confidence intervals. We see that for a one-unit increase in economy, the odds of high support versus the combined middle and low categories are 9.15 greater (Model I), given that all of the other variables in the model are held constant. Likewise, the odds of the combined middle and high categories versus low is 9.15 times greater. For respondent who participates in bicycle riding, the odds of the high category of support versus the low and middle categories of support are 2.22 times greater (Model I), given that the other variables in the model are held constant. The same increase, 2.22 times, is found between low support and the combined categories of middle and high support due to the proportional odds assumption.

Table 5

Table 5 Odds ratio estimates