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1. Introduction

Ocean health has become one of the major concerns facing humanity today. Many scientists feel

that the ocean’s health is in jeopardy and needs urgent attention (Halpern et al. 2012; Halpern et al. 2015;

Rojas-Rocha 2014). Coastal communities are apprehensive that the ocean waters are becoming more

polluted; the fish caught are smaller now than ever before and the amount of debris found in the oceans is

increasing at an alarming rate. What, then, is a healthy ocean? An acceptable definition of a healthy ocean

is one that has abundant unpolluted waters and delivers benefits to future generations (Rapport et al.

1998; Samhouri et al. 2011). Most of the existing definitions for ocean health are based on

assumptions about the intrinsic functional benefits that the ocean provides to a community

(Samhouri et al. 2011; McLeod and Leslie 2009). Hence, there is a need to quantitatively

evaluate the effects of certain factors influencing ocean health and set sustainable management

targets over time.

The health of the ocean can be treated like that of an enlarged household or community.

The broad physical, social, and economic factors that contribute to an individual’s health provide

an indication of the variables that influence ocean health. The ocean, like the household, exists

within a natural environment, and socioeconomic and anthropogenic behavior determines its

health position. The economics literature suggests that the health status of an individual or

community is the result of a production function process. In the ocean health process, physical

activities, human behavior, and socioeconomic factors influence health status in the short run

(Rosenzweig and Schultz 1983). In the long run, health status can be considered similar to

capital stock that can be used and reused over time, and there can be community investment and

divestment (Grossman 1972). The ocean health production function is comparable to those of

household and community health, as it uses inputs that affect health directly (food provision and

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natural products), and indirectly (regulating services, coastal protection, and cultural services),

along with central aspects of human well-being that flow from multiple services (Lowndes et al.,

2014). However, the measurement of ocean health remains a real problem.

Halpern and others (2012) and a group of 65 scientists created the Ocean Health Index

(OHI), which is a valuation tool that scientifically measures key elements from all dimensions of

the ocean’s health—biological, physical, economic, and social. The measures are selected to

reflect human and ecosystems sustainability, a systematic approach that evaluates the overall

condition of marine ecosystems and treats nature and people as integral parts of a healthy system

(Halpern et al. 2008). The health status index proposed by Halpern and others seems to be well

thought out and transparent. Though assessable and transparent measures are proposed, there is a

need to evaluate how these measures or goals influence ocean health (Samhouri et al. 2012). The

measurement of health status using an index, however, encounters statistical problems that result

in biased coefficient estimates (Austin et al. 2000).

2. Ocean Health Production Function and Model Specification

2.1. Conceptual Framework

The ocean provides a broad range of benefits, from food products to recreational benefits

that improve the livelihoods of coastal communities (Halpern et al. 2012). On the other hand, an

unhealthy ocean can have negative consequences for human health through consumption of

contaminated seafood, swimming in polluted water, and exposure to toxins from harmful algal

blooms (Knap et al. 2002; Dewailly et al. 2002; NRC 1999; Pew Oceans Commission 2003;

Stegeman et al. 2002; Tyson et al. 2004; Fleming and Laws 2006; Fleming et al. 2006; Tyson

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2012). The benefits derived from a healthy ocean are measured using the OHI. The index also

combines key services provided by the ocean.

A computed production function that includes services and outcomes of ocean health

benefits may produce much needed information for policy studies. In this paper, we employ

ocean health production functions based on a priori human and community health production

functions to evaluate how these can be used to generate information for policy decisions

(Sanglimsuwan 2012). The rest of the paper describes a theoretical framework, implicit and

explicit functions, methods, results, and discussion.

Any such health production function can be placed within a neoclassical framework of

utility maximization:

U=U(OH,Z:Ɵ) (1)

where U is the level of utility derived from the use of the ocean, OH is the ocean health

represented by an index, Zi is a composite of fish production and ocean services, and Ɵ is the

conditional parameter that is utility based on the time preference for health status that measures

the shape of the utility function. The utility is maximized subject to the ocean health production

function and its convexity and the country’s resource endowment. OH is based on the care we

provide for the ocean, by either sustainable or unsustainable use of its products (fish, natural

products, recreation, artisanal fisheries) and services.

The ocean faces a production function that is twice differentiable, continuous, and

convex. OHI is a vector of ocean health that depends on caregiving and is conditioned by

physical, environmental, and anthropogenic factors. The partial aptitude to prevent ocean

degradation and a low OHI score depends on the society’s capacity to minimize overfishing and

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pollution and maximize conservation of species. Second, the ocean faces resource constraints of

income and human resources in terms of level of education, life expectancy, and gross national

per capita income that are measured by HDI.

Z=HDI (2)

Hence the production function is represented by:

OHI= U(OH,Z:Ɵ)+ϕ(X3(X4,X5) (X7))+g (h(X8, X9))+ø( (k) (X17,X18))+€ (L)(X6 (X10(X11,X12))

+λ(X44)+ μ(X23). (3)

X3=food provision, X4=wild caught fish, X5=mariculture, X7=natural products, h=regulating

services, X8=carbon storage, X9=coastal protection, k=cultural services,X13=tourism and

recreation,X14 sense of place, X17= clean waters, X18=biodiversity, L =central aspects of human

well-being that flow from multiple services, X6=artisanal fishing opportunities, X10=Coastal

livelihoods and economies, X11=coastal livelihoods, X12=economies, X44=social, demographic,

conservation and climate change variables, X23=HDI.

Health status is often measured using utility indices that provide a score that reflects the

health situation of the individual (Austin et al. 2000). Measurement of health status can be

subjected to a ceiling or censoring, and these present problems resulting in inefficient and biased

coefficients. Hence, a major issue in interpreting a health status index is the meaning of extreme

values in the index and categorizing health status as healthy or unhealthy.

The Tobit model proposed by Tobin (1958) has been shown to be the most appropriate

tool to handle censored variables involved in the determination of health status. The Tobit model,

also called a censored regression model, is designed to estimate linear relationships between

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variables when there is either left- or right-censoring in the dependent variable (also known as

censoring from below and above, respectively). The Tobit model is used to a limited extent to

evaluate health status (Austin et al. 2000) because of its usefulness in modeling censored

variables with a ceiling in econometric studies. Censoring from above takes place when cases

with a value at or above some threshold all take on the value of that threshold, so that the true

value might be equal to the threshold, but it might also be higher. In the case of censoring from

below, those values that fall at or below some threshold are censored. In this approach, a

threshold is defined and those subjects above the threshold are considered healthy and those

below unhealthy. This is a more efficient and robust way of analyzing the data. However, one of

the pitfalls of this approach is the loss of statistical power in the analyses performed (Austin et al.

2000).

There has been a common consensus that the use of two-stage least squares generates, to

some extent, unbiased efficient parameter estimates. The two-stage method of regression is

commonly used when the first stage represents some measure or index of a country, nation, or

environment. Estimated dependent variable (EDV) regression models are the second stage in a

two-stage estimation process. Two-stage least squares using limited dependent variables as

regressors have been discussed by Heckman (1978), Amemiya (1978 1979), Newey

(1986,1987), and Angrist (2001).

The first stage uses observed data to estimate the values of the dependent variable; the

EDV model then regresses these values against one or more independent variables to generate

the ultimate coefficients of interest (Lewis and Linzer 2005). The use of accurate and relevant

methods such as the Tobit model and/or rank-based regression may help improve the reliability

of the statistical coefficients by uncovering nonlinear covariate effects and improving the

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performance of the models for decision making (Hastie and Tibshirani 1986). To determine the

factors that influence ocean health, we use a two-stage model with the Tobit model in the first

stage and rank regression in the second stage.

2.2. Implicit Model Development

2.2.1. Standard Tobit Model

In this analysis we consider the standard Tobit model (Tobin 1958):

y i¿=α+ X i β+ϵi , i=1,2 , … ,n (4)

where y i¿ is a latent response variable, X i is an observed 1×k vector of explanatory variables

(ocean index goals and other socioeconomic variables), and ϵ i∼ iid N (0 ,σ 2) and is independent

of X i. Instead of observing y i¿, we observe y i:

y i={y i¿ , if y i

¿>γ0 , if y i

¿≤ γ (5)

where γ is a nonstochastic constant. In other words, the value of y i¿ is missing when it is less than

or equal to γ .

The problem with the standard Tobit model is that γ is often not observed in economic

data and is often assumed to be zero in empirical applications. In our analysis, y i is the observed

OHI when the latter is greater than 50. The known censoring threshold, γ, is, in fact, not zero but

the value that separates the healthy and unhealthy ocean, as we have defined above. We choose

γ=50 for our analysis.

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2.2.2 Rank-Based Model

Second, we use rank-based estimation, which is a more robust technique to investigate

the predicted dependent variable with other variables. The rank-based estimation technique is

defined as follows. For a given linear model:

Y=XT β+e (6)

We define the rank-based objective function as

Dn(β )=∥Y−Xβ ∥φ (7)

where ∥⋅∥φ is a pseudo-norm defined as

∥u∥φ=∑i=1

n

a(R(u i))ui , (8)

where R denotes the rank, a (t)=φ( tn+1

), and φ is a non-decreasing, square-integrable score

function defined on the interval (0,1). There are many other score functions, but we will consider

the most popular, known as the Wilcoxon score function, with score function satisfying

∫ φ(u)du=0 and ∫ φ2(u)du=1.

The rank-based estimator of β is therefore defined as:

βφ=Argmin∥Y−Xβ ∥φ (9)

This estimator is highly efficient and is robust in the Y -space: that is, it is not influenced by

strange outliers.

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For the rank-based estimation, we do not need any specific assumption about the error

terms other than the requirement that they are drawn from an absolutely continuous density

function.

3. Method

3.1. Explicit Model Development

The OHI is expressed as a function of a set of 10 generally accepted public goals (food

provision, artisanal fisheries, natural products, carbon storage, coastal protection, coastal

livelihoods and economies, tourism and recreation, sense of place, clean water, and biodiversity)

for the contributions they make to society, plus gross national income (GNI), life expectancy,

and the level of education of a country. Methods for calculating the OHI, and the conceptual

framework and rationale for how it is constructed, are detailed extensively by Halpern et al.

(2012). The index considers the relations between coastal human societies and ocean ecosystems

and their services. The OHI model is therefore represented as:

Y=f 3 ( X3 )+ f 6 ( X6 )+ f 7 ( X7 )+ f 8 ( X8 )+ f 9 ( X9 )+ f 10 ( X10 )+ f 13 ( X13 )+ f 14 ( X14 )+f 17 ( X17 )+ f 18 ( X18 )+f 22( X22)+f 23 ( X23 )+ f 24 ( X24 )+ f 25 ( X25 )+f 27( X27)

(10)

As with least squares, the goal of rank-based regression is to estimate the vector of

coefficients, B, of a general linear model of the form:

Ŷ=β0 1n+βX+e (11)

where Ŷ= [ y1, y2 ,⋯ , yn ]T is the n ×1vector of responses, X=[ x1 , x2 ,⋯ , xn ]T is the n× p

design matrix, β=[ β1 , β2 ,⋯ , βn ]T is the p×1 vector of parameter, and e=[ e1 , e2 ,⋯ , en ]T is the

n ×1vector of error terms. Here 1n represents an n ×1 vector with all 1s. The only assumption on

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the distribution of the errors is that it is continuous; hence the model is general. We also assume

without loss of generality that the design matrix of predictors (covariates) X is centered and has

full column rank, so that the dimension of the range of X , say , is p. Since we also want to

achieve robustness in data analysis, we employ the predicted value of the response from the

Tobit model to analyze a second stage of the data, but this time using the rank-based modeling

approach. In the second stage the EDV (Ŷ i ¿ is regressed on some added variables such as HDI

value, CO2 emissions, marine protected areas, nitrous oxide (NO2) emissions, and PM2.5 air

pollution.

Ŷ i= f 23 ( X 23 )+ f 27 ( X27 )+ f 29 ( X29 )+f 31 ( X31 )+f 32 ( X32 )+ f 34 ( X34 ) (12)

The Ocean Health Index (Y) is a global measure that generates information on ocean

health status based on the ocean’s capacity to deliver certain goods and services sustainably to

humans. OHI scores range from 0 to 100, and are derived from 10 internal human goals that

represent crucial ecological and socioeconomic benefits that a healthy ocean can generate

(Halpern et al. 2012) and external HDI goals that influence the OHI. The index, therefore,

recognizes linkages between human societies and ocean ecosystems, and that people are part of

coastal and ocean systems. A healthy ocean is characterized by an OHI score greater than 50 and

is scored 1, whereas an unhealthy ocean scores less than 50 and is given a value of 0. The

variables for the Tobit and rank models are defined below.

Food provision (X3 ¿=¿ (X 4 , X5) is the greatest contribution of a healthy ocean to human

society (FAO 2012). The food provision goal measures the amount of seafood sustainably

harvested in a given Exclusive Economic Zone (EEZ) or region through any means for use in

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human consumption, and thus includes wild-caught commercial fisheries, mariculture, artisanal-

scale fisheries, and recreational fisheries. Food provision received the second lowest global

score: 33 over 100. The only goal receiving a lower score was natural products harvest, which

received a score of 31 (Cohen 2013). It is estimated that the world will need 70 percent more fish

to meet its target by the year 2050. Hence a positive relationship is expected between OHI and

the goal of food provision, (B3). Wild caught fish (X 4) represents fish caught sustainably from

the wild, and is designed to assess how much seafood is being provided in a renewable way for

local consumption or export, given the ecosystem’s productive potential. The measure of

minimum of the maximum sustainable yield reference point (mMSYR) provides a suitable point

of departure for sustainable extraction that is based on established concepts in fisheries biology

with known caveats and shortcomings (Pet-Soede et al. 1999; Kleisner et al. 2013).

Mariculture (X5) is defined as the strict production of marine species from both the

marine and brackish water FAO categories, excluding aquatic plants such as kelps and seaweeds,

which were assumed to contribute predominantly to medicinal and cosmetic uses rather than as a

source of food.

Artisanal fisheries (X6) refers to fisheries involving households, cooperatives, or small

firms (as opposed to large, commercial companies) that use relatively limited capital and energy,

employ small fishing vessels (if any), make relatively short fishing trips, and use fish mainly for

local consumption or trade. Over 400 million people in the poorest countries in Asia and South

Asia obtain at least half of their essential protein and mineral intake from catch in small-scale

fisheries (Dulvy and Allison 2009; Bell et al. 2009; Allison 2011). Artisanal fisheries employ 90

percent of the 35 million fishers worldwide and provide 90 million additional jobs in associated

sectors (Halpern et al. 2012; Teh and Sumaila 2013). A healthy ocean is necessary for artisanal

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fisheries to reach their target of supplying much needed food to the developing world. Hence a

positive relationship is expected between OHI and artisanal fisheries,(B6>0).

Natural products (X7) is the sustainable harvest of non-food natural products, important

to local economies and for international trade. Through this goal the community maximizes the

sustainable harvest of living marine resources, such as corals, shells, seaweeds, and fish for the

aquarium trade. It does not include nonliving resources such as oil, gas, and mining products that

are not sustainable when harvested on a large scale. It also does not include bioprospecting that

focuses on potential (largely unknowable and potentially infinite) value rather than current

realized value (Lam and Roy 2014). Globally, natural products generate 2.5 billion US dollars in

revenue. This provides jobs and economic support to communities around the world. A positive

relationship is expected between ocean health and natural products, (B7>0¿.

Carbon storage (B8) measures the ocean’s ability to store CO2 and prevent it from

escaping to increase the chances of global warming. The ocean represents the largest potential

sink for anthropogenic CO2. It already contains an estimated 40,000 GtC (billion metric tons of

carbon) compared with 750 GtC in the atmosphere and 2200 GtC in the terrestrial biosphere

(Herzog and Golomb 2004). The three main coastal habitats known to provide significant carbon

storage are mangroves, seagrass, and salt marshes. The physical-chemical mechanisms driving

the ocean sink are well understood but are not directly amenable to human management (Moore,

2008). Hence a positive relationship is expected between OHI and carbon storage,(B¿¿8>0). ¿

Coastal protection (X 9) measures the degree of protection offered by ocean habitats to

coastal areas that people value. Here, we hypothesize that all coastal areas have value (and equal

value) and consider the total area and condition of key habitats within each EEZ (without regard

for their precise location relative to coastal areas). The habitats that provide protection to coastal

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areas for which we have global data include mangroves, coral reefs, seagrasses, salt marshes, and

sea ice (Katona 2013). A positive relationship is expected between OHI and coastal protection, (

B9>0 ¿ .

Coastal livelihoods and economies (X10 ¿=¿ (X11 , X12) measure

the coastal livelihoods and economies provided by the ocean. The jobs and revenue

produced by marine-related industries are of immense value to many people, even those who do

not directly participate in the industries but value community identity, tax revenue, and indirect

economic and social impacts of a stable coastal economy,(B¿¿10>0) .¿

Tourism and recreation (X13) capture the value that people have for experiencing and

enjoying coastal areas (Halpern et al. 2015). Tourism and recreation are major components of

thriving coastal communities and measure how much people value ocean systems: i.e., by

traveling to coastal and ocean areas, people express their preference for visiting these places.

Tourism and recreation might have an indeterminate effect on OHI. In the first case, preparation

for tourism and recreation might force coastal communities to improve OHI, but in the second

case, an overabundance of tourism and recreation may damage the fauna and flora of the ocean

bed and have a negative effect on OHI, (B¿¿13>0∨¿0).¿

Sense of place (X14) captures the aspects of coastal and marine systems that people value

as part of their cultural identity. This definition includes people living in all proximity to the

oceans. The goal is divided into two sub-goals—iconic species and lasting special places—and

an assigned equal weight is attributed when combining them to create a single goal score,

(B¿¿14>0) .¿ The iconic species¿¿) sub-goal focuses on those species seen as iconic whose

existence has cultural, spiritual, or aesthetic value. Lasting special places¿¿), the other sub-goal,

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refers to places that provide intangible but significant resources that sustain economic

opportunities.

Clean water (X17) measures the degree of clean water that people enjoy from the ocean.

People value marine waters that are free of pollution and debris for aesthetic and health reasons.

Contamination of waters comes from oil spills, chemicals, eutrophication, algal blooms, disease

pathogens (e.g., fecal coliform bacteria, viruses, and parasites from sewage outflow), floating

trash, and mass kills of organisms due to pollution. People are sensitive to these phenomena

occurring in areas that they access for recreation or other purposes, as well as to simply knowing

that clean waters exist. This goal scores highest when the contamination level is zero. It is

expected that(B¿¿17>0)¿.

Biodiversity (X18) estimates the diverse number of species existent around the world and

how well they are being maintained. The risk of species extinction generates great emotional and

moral concern for many people. As such, this goal assesses the conservation status of species

based on the best available global data through two sub-goals: species¿) and habitats ¿¿). We

also assess habitats as part of this goal in that they support a broad array of species,(B¿¿18>0) .¿

The Human Development Index (HDI) (X23) is a composite measure of average

achievement in three basic dimensions of human development: life expectancy, education, and

per capita income. The index is used to rank countries into tiers of human development.

Lowndes et al. (2014) found that HDI is the greatest predictor of OHI. The HDI is expected to

have a positive effect on OHI,(B¿¿23>0) .¿

Gross national income (GNI) (X27) represents the standard of living per capita, expressed

in constant 2011 international dollars converted using purchasing power parity (PPP) rates. GNI

expresses the income accrued to residents of a country, including international flows such as

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remittances and aid, and excluding income generated in the country but repatriated abroad. Thus,

GNI is a more accurate measure of a country’s economic welfare than GDP. The GNI coefficient

is expected to have a positive effect on the OHI.

CO2 emission(B¿¿29<0)¿ in metric tons per capita 2011 to 2015 (World Bank 2015)

represents the largest potential sink for anthropogenic CO2 measured in the air. Experts have

stated that oceans are heating, losing oxygen, and becoming more acidic because of CO2, and are

at risk of irreversible damage if these conditions continue (Gray et al., 2002), (B¿¿29<0) .¿

Marine Protected Areas (MPAs) (B¿¿31>0)¿ as a percentage of territorial waters 2011

to 2015 (World Bank 2015) are protected areas for the preservation of species that are likely to

be lost to habitat fragmentation (Ovaskainen 2012), which is a sound strategy to expand

biodiversity. MPAs help reduce overexploitation of vulnerable species, and therefore, are

supported by many nations and international bodies as a means of improving biodiversity. Bio-

economic modeling of commercial fishing, recreational fishing, and tourism shows that the

economic and biological benefits of well-managed MPAs far outweigh the cost of implementing

MPAs (Reimer et al. 2015; Sala et al. 2013). The establishment and management of MPAs can

be executed by local coastal communities at a low cost(B¿¿31>0)¿.

Nitrous oxide (N2O) in thousand metric tons CO2 equivalent (B¿¿32<0)¿ is emitted

during agricultural and industrial activities as well as during the burning of fossil fuels and solid

wastes. N2O, like other greenhouse gases, is supposed to have a positive effect on global

warming and may increase fish mortality (B¿¿32<0) .¿

PM2.5 air pollution (B¿¿34<0)¿ is the mean annual exposure (micrograms per cubic

meter, 2013) of direct emissions of particulate matter and secondary particle formation caused by

oxidation of sulfur dioxide, nitrogen dioxide, and aerosol organic carbon. Levels of airborne

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particles affect natural ecosystems through reduced productivity, disruption of nutrient cycles,

and massive summer fish kills, as observed in the Chesapeake Bay and Long Island Sound this

decade (Pascale et al. 2016).

3.2. Data Sources and Analytical Procedure

The Ocean Health Index and 10 measured goals for 151 selected countries for 2013 were

extracted from the Excel spreadsheet for 2014. The index recognizes linkages between human

societies and ocean ecosystems, and that people are part of coastal and ocean systems within a

country’s EEZ. HDI data were taken from the United Nations Development Program (2013) and

from the World Bank (2015) Environment Bank database.

The researchers estimated scores for each area from data around the world. Globally, the

ocean’s health was scored at 60 out of 100. Scores for individual countries ranged from 33.3 to

86, with most scoring below 70. Scores for developed countries were generally higher than those

for developing countries. In Europe, Germany scored highly at 73 and Poland scored poorly at

42. Similar total scores could be achieved through different routes. For instance, while the UK

scored 62 with high scores for natural products and food provision, the US scored 63 with high

scores for coastal protection and coastal livelihoods and economies. Haiti, on the other hand, had

an overall score of 44.24 with a food provision index of 1.01, while Nicaragua had an overall

score of 45.05 with a food provision index of 37.31.

3.3. Scatterplot Matrix

We examine how well our model fits the data. We start with plots of the residuals to

assess their absolute as well as relative (Pearson) values and assumptions such as normality and

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homogeneity of variance. We present the estimation techniques, check the required assumptions

together with a table of correlation coefficients and descriptive statistics, and then present the

results and a detailed interpretation.

First of all, the log-likelihood of -147.7078 on 290 degrees of freedom suggests a small

p-value. Thus our model will compete when compared to any nested models. We recall that for

the Tobit model, degrees of freedom are computed as follow: df =2 n−γ−2, where γ represent

the number of predictors considered in the model.

The three plots on the first row in Figure 1 in the appendix from absolute as well as

relative (Pearson) residuals are used to check the homogeneity of variance. Since neither of those

plots shows a particular pattern, we suspect a non-violation of the homogeneity of variance.

{PLACE FIGURE I IN APPENDIX HERE}

The first two plots on the second row of Figure 2 in appendix, known as the quantile-

quantile plot of the residuals, are used to check the normality. Since the two plots suggest a

moderate linear association, we can say that the residuals come from an approximate or fairly

normal distribution. To confirm this we performed the Shapiro–Wilk test which utilizes the null-

hypothesis principle to check whether a sample X1 , X2 ,⋯ , Xn ,came from a normally distributed

population. The test provided a p-value= 0.1534554 which is greater than the significance level α

= 0.05. Thus we do have enough evidence to say that the sample residuals come indeed from a

normally distributed population.

The graphs at the bottom right in appendix figure 2 show the predicted, or fitted values

plotted against the actual. This can be particularly useful to investigate how accurately our model

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fits the data. We also calculated the correlation between these two, as well as the squared

correlation, to get a sense of how accurately our model predicts the data and how much of the

variance in the outcome is accounted for by the model.

The correlation between the predicted and observed values of Ocean Health Index (OHI)

is 0.9967. If we square this value, we get the multiple squared correlation; this indicates that

predicted values share 99.34 percent of their variance with OHI, which is of course variance

accounted for.

To this end, we adopt a combination of the Tobit regression model and a rank-based

modeling approach. In fact, there are long lists of analytical methods we may have encountered

or performed. Some of the methods listed are reasonable, while others have fallen out of favor or

have limitations.

3.4. Importance of Model Influence of Predictors

Table 1 in the appendix presents the relative influence of the predictor variables. The

relative variable influence on ocean health shows that biodiversity received the highest rank,

with a score of 17.15 percent; in second place is coastal protection with a score of 11.55 percent,

and in third place is clean water with 10.99 percent. The variable, wild caught fisheries, was in

fourth place, with a score of 10.12 percent. The choice of variables in our final model is partly

based on the relative influence score considering OHI as the dependent variable.

{PLACE TABLE I IN APPENDIX HERE}

4. Results

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The descriptive statistics in Table 1 for a sample of 151 countries for which data were

available indicate that the mean OHI is 62.70, with a standard deviation (SD) of 9.38, a

minimum value of 43.72, and a maximum of 82.55. The food provision index was 54.57, with

the lowest value being 1.01 and with a maximum of 98.00. Biodiversity had the highest mean

value, 83.85, with a minimum of 64.67 and a maximum of 98.26. HDI had an average of 0.70

with a median of 0.72, while MPA had a mean of 12.1 with a median of 5.8. Figure 1 shows that

there is a positive relationship between HDI and OHI, with those countries with an HDI greater

than 50 or a score of 1 having a higher OHI throughout. A similar relationship exists between

MPAs and OHI, where those countries with an OHI greater than 50 have higher MPAs (Figure

2).

{PLACE TABLE I HERE}

We first recall that for the Tobit model the linear effect is on the uncensored latent

variable, not the observed outcome. See McDonald and Moffitt (1980) for more details. The

correlation between the predicted and the observed values of OHI is 0.997. If we square this

value, the Tobit model has an R2 of 0.993, which means that 99.3 percent of the variation in the

dependent variable is accounted for by the variation in the independent variables. The likelihood

ratio is -148 with 290 degrees of freedom with an AIC of 319. Hence, we can say the Tobit

model is acceptable for measuring the factors that influence OHI. For example, for a 1-unit

increase in food provision, there is a 0.103 increase in the predicted OHI value. Also, for a 1-unit

increase in natural products, there is a 0.105 increase in the predicted OHI value (Table 2). The

same interpretation can be carried out for the rest of the predictors or variables that contribute to

the OHI via the Tobit model. The ancillary statistic of -0.331808 can be compared with the SD

of the response OHI, which was 9.378793, a substantial reduction. This implies that all

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predictors positively contribute to the predicted value of the OHI.

{PLACE TABLE II HERE}

The overall Wald test of the rank regression is 90 at a p-value of 0, which indicates a

significant association between the response and the predictor variables. The rank regression

showed that HDI and MPAs significantly influenced the predicted value of the OHI. A 1 percent

increase in HDI will result in a 0.32 percent increase in OHI, while a 1 percent increase in MPAs

results in a 0.03 percent increase in OHI.

{PLACE FIGURE I HERE}

5. Discussion and Conclusion

The scatterplot and the diagnostic statistics suggest that the two-stage model is

appropriate. The influence factors show that biodiversity received the highest rank, and in second

and third places are coastal protection and clean water. In fourth place are natural products. For

the Tobit model, the variable biodiversity has a major effect on ocean health and contributes

succinctly to the variation in OHI. This is understandable, since the other variables interact to

foster a biodiverse environment that may influence OHI. There may also be trade-offs (Selig et

al. 2015) among goals as countries attempt to improve one goal, biodiversity, at the expense of

another, coastal habitat for species. Expansion of biodiversity should be considered by policy

makers as the first effort to improve ocean health; this includes habitat management and

encouragement of the proliferation of diverse species. Development of the habitat and species

20

sub-goals is essential for the enhancement of OHI through the reduction of habitat devastation,

which poses the greatest threat to biodiversity (Ovaskainen 2012).

Other goals that affect OHI are livelihoods and economies, sense of place, clean water,

and artisanal fisheries. The evaluation of each factor separately helps one to develop an

understanding of goal substitution. However, increasing livelihoods and economies may have a

negative effect on OHI if the level of exploitation is too intensive, and may negatively affect the

coastal habitat and species biodiversity. The transfer of power to local communities so that they

can exert control over their lives and create local institutional structures that link sustainable

livelihood approaches to habitat and species preservation is essential to the successful

improvement of livelihoods and economies. Hence, coastal communities can adopt a

participatory approach to decision making through a process of co-management to improve

ocean health (Divakarannair 2007).

{PLACE FIGURE II HERE}

Sense of place is important in terms of cultural symbolism. People and communities

place intangible value on places and iconic species and are likely to make an effort to preserve

those (Selig et al. 2015). However, some countries only place value on a limited number of

places, and therefore, receive a low total score for this variable. The identification of a sense of

place and the reassurance of cultural preservation is a sound strategy to encourage the expansion

of biodiversity, and hence the improvement of OHI.

Clean water influences OHI and can be controlled by communities at a reasonable cost.

Reducing non-point source pollution, protecting water from pollution by defending the Clean

Water Act, and establishing new pollution limits can be done through legislation, enforcement,

21

and increasing water efficiency strategies to decrease the amount of waste water entering the

ocean. Polluted beaches that make swimmers sick may result in economic losses to coastal

communities in terms of loss of jobs and revenue. Clean water can be achieved by raising

community awareness and reducing the amounts of debris and trash dumped in the ocean.

Education is an important element in the advancement of clean ocean waters and hence a healthy

ocean.

The artisanal fisheries goal indicates how individuals in a community access fishing

opportunities to support their livelihoods. Fish harvesting is usually done by a large number of

limited-resource fishermen and a few larger fishing businesses. There is a belief that the

involvement of large numbers of limited-resource poor fishers may have serious consequences

for food provision and human well-being, but on the other hand, the extraction of abusive

quantities of fish might undermine progress in biodiversity improvement and have a deleterious

effect on OHI.

In the second model, HDI and MPAs significantly influenced OHI. HDI is positively

related to OHI: countries with high HDI, like many European countries and the US, also have

high OHI. Lowndes et al. (2014) found that HDI is the greatest predictor of OHI. Expansion of

marine protected areas (MPAs) for the preservation of species that are likely to be lost to habitat

fragmentation (Ovaskainen 2012) is also a sound strategy to expand biodiversity. MPAs assist in

the reduction of overexploitation of vulnerable species, and therefore, have the support of many

nations and international bodies as a means of improving biodiversity.

Policy makers should note that biodiversity increases may have the greatest effect on

OHI, and its improvement may be within the reach of even the poorest country. Countries with

22

varying levels of resource endowment may choose different techniques to improve OHI, but the

implementation of MPAs should be a priority for all, since they have a major effect on OHI. A

policy of international assistance from countries with high OHI to those with low HDI is

opportune at this moment. The assistance may be in the form of awareness creation or education

about the need to put in place systems to improve the global OHI.

23

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Table 1: Descriptive statistics of the variables

Variables N Mean Sd Median Min Max Se

Wild Caught Fisheries (X 4 ) 151 56.01 24.40 61.56 1.01 98.00 1.99

Mariculture (X5) 151 35.98 31.25 26.97 0.01 100.00 2.54AF Opportunities (X6) 151 61/51 12.24 61.45 41.42 100.00 1.00Natural Products (X7) 151 63.31 26.12 62.66 0.06 100.00 2.13Carbon Storage (X 8) 151 68.09 21.33 62.66 5.53 100.00 1.74

Coastal Protection (X 9) 151 56.98 25.85 62.66 5.46 100.00 2.10Livelihoods (X11) 151 77.54 23.04 83.63 0.17 100.00 1.87Tourism, Recreation (X13) 151 36.54 26.56 28.91 2.54 100.00 2.16Iconic Species (X15) 151 56.72 7.03 56.03 37.13 78.29 0.57Lasting Special Places (X16) 151 66.57 34.10 74.42 0.12 100.00 2.78Clean Water (X17) 151 65.50 11.09 64.47 34.74 93.92 0.90Species (X19) 151 81.97 4.70 81.07 73.32 96.52 0.38Habitat (X20) 151 85.73 13.36 90.13 50.48 100.00 1.09Mean Years of Schooling (X25)

151 9.89 10.21 8.50 1.60 62.66 0.83

GNI/capita (X27) 151 19042.54 27492.45 11477.00 62.66 267711.00 2237.3

Ocean Health Index (X2)Food Provision (X3)Livelihood & Economies (X10)Sense of Place (X14)Biodiversity (X18)Human Dev. Index (X23)Marine Protected Areas(X31)

151151151

151151151151

62.7054.5783.2

57.9983.850.7012.10

9.3824.1616.5

21.917.360.1516.9

62.7060.1184.5

64.4685.360.725.80

43.721.013.5

18.7964.670.340.0

82.5598.00100

10098.260.949.5

0.761.971.3

1.780.600.011.4

31

Table 2: Results of the two stage equation with Tobit at stage one and the rank regression as stage two

32

Figure 1: OHI plotted against HDI for countries with an OHI greater than 50. The regression equation for the line through the points is: OHI=39.30+33.21 HDI

33

Figure 2: OHI plotted against MPA for countries with an OHI greater than 50. The regression equation for the line through the points is:OHI=60.0332+0.2175 MPAs

34

Appendix Table1: Importance of variables in the model using relative influence ranks

Variables Relative influence

Biodiversity (X18) 17.154614Coastal Protection(X 9) 11.547042Clean Water(X17) 10.991649Wild Caught Fisheries(X 4) 10.117793Natural Products(X7) 8.845601Iconic Species(X14) 7.863998Tourism, Recreation(X13 ) 7.086078Livelihoods and Economies(X10) 6.851335HDI value (X 23) 6.024677AF Opportunities(X 6) 5.668185Carbon Storage(X 8) 4.142504GNI/capita 2011(X 27) 2.176117Mariculture(X5) 1.530407GNI/capita 2011 Squared 0.000000

35

Appendix Figure 1: Checking Assumptions model and diagnostics for the Tobit Model