**4. Empirical analysis**

426 Corrosion Resistance

plastic, or epoxy coating), and positive or negative experiences with these materials could have influenced their responses. The questions included two stimuli, which are compared simultaneously. Each respondent rated each of the two alternatives on a scale from 1 to 9. The scale value of 1 indicates the plumbing material is not preferred, while 9 indicates an

> Material B (Plastica)

Same as material A

Same as material A

Need to tear into some sections of wall for installation. Installation takes 5-6 days.

Less than 20 years in the market

\$6,500 ~ 13,000 depending on the size of house

Warranty is 10 years for the material.

Corrosion proof Same as material A Some risk of corrosion

Material C (Coppera)

Compounds released from this material in drinking water plumbing may give a bitter or metallic taste or odor to the water.

Material meets EPA Standards. There is a very small chance that compounds from this plumbing material that are released into drinking water may cause vomiting, diarrhea, stomach cramps, and nausea.

Need to tear into the wall and/or floor to replace the existing system. 7-9 days required for installation.

More than 50 years in the market

\$9,000 ~ 16,000 depending on the size of house

A 50 year manufacturer's warranty applies. Some exceptions apply (e.g. warranty reduces to one year if compounds in water corrode pipes).

extremely preferred plumbing system. The material attributes are listed in Table 1.

Attributes Material A

Corrosion Resistance

> Taste / Odor

Health Effects

Convenience of Installation

Proven performance in market

> Cost (labor + material)

(Epoxy Coatinga)

Compounds released from this material in drinking water plumbing may give a chemical or solvent taste or odor to the water.

Material meets EPA Standards. There is a very small chance that compounds from this plumbing material that are released into drinking water may lead to microbial growth in water. Microbial growth may cause severe illness.

No need to tear into the wall and/or floor. Installation takes around 4 days.

Less than 10 years in the market

\$9,000 ~ 14,000 depending on the size of house

material.

aNames of the plumbing materials were not revealed to the study participants

Warranty Warranty is 15 years for the

Table 1. Description of plumbing materials.

The empirical analysis of the Southeastern Community home plumbing data includes several econometric and statistical techniques. The first survey data analysis uses simple descriptive statistics, such as mean (average values), percentages (percent distribution across all responses), and total sums, in order to provide a summary view of the home plumbing issues faced by the Southeastern Community. These issues include the frequency of pipe failure, the location of the failure in the plumbing system, the costs and time associated with fixing pipe failures, and the preventive measure taken to avoid incidences in the future. The analysis preferred plumbing materials concentrates on estimating the household preferences for plumbing types based on the follow-up survey of the Southeastern Community. The data estimation process employs the Ordered Logit regressions, based on which the household preferences for plumbing materials are derived. The paragraphs presented below describe the econometric models in more detail.

#### **4.1 Ordered logit model description**

The second Southeastern Community survey data analysis employs the Conjoint Analysis (CA) methodology to analyze the preferences for plumbing materials. This type of analysis includes eliciting the preferred good / service choices based on the presented information / stimuli. Utility Maximization Theory is usually employed to guide the process, design, and analysis of the CA studies, and involves making a choice that yields the greatest satisfaction to the respondents, otherwise known as utility, based on their available financial resources. As a result, the preference maximization problem is defined mathematically, as maximization of a utility function based on a specified financial resource constraint (Varian, 1992):

$$\text{Maximize utility function: } \mathbf{u}(\mathbf{x}) \tag{1}$$

$$\text{Subject to: } \text{px} \le \text{m}, \text{ where } \text{x is in } \text{X}\_{\prime} \tag{2}$$

where u(x) represents the utility function, and px ≤ m represents the financial resource constraint, with m being the fixed amount of money available to households (Champ et al., 2003).

In this chapter, a household faces a choice among three plumbing material alternatives. The utility (satisfaction) obtained from choosing a plumbing material, i, by the nth household is Uni. The decision maker chooses the option yielding the highest level of utility, which implies the following behavioral model: Uni > Unj , where i≠j. The level of utility is not observed by the researcher, but the attributes of the plumbing alternatives (xni) in the choice set are observed, as well as the socioeconomic characteristics of the decision maker (zn). Based on the known variables, a representative utility function can be specified as: Vni = V (xni, zn) for all alternatives (Train, 2003).

For this exercise, each respondent pair-wise rated the preferred plumbing material option. The rating scale ranges from 1 to 9, with 1 indicating a not preferred plumbing material option, and 9 indicating the most preferred option. The plumbing material rating exercise is based on the utility-maximizing behavior, as higher plumbing material rating results in an increased level of utility, and therefore, a higher preference level for a given alternative. The

Households' Preferences for Plumbing Materials 429

reported learning about pinhole problems through their own experience, 65% heard through a neighbor or friend, 48% heard about pinhole leaks through the media, and 42% reported

Two hundred twelve respondents (20%) reported incidents of pinhole leaks in drinking water pipes in their current homes; 780 respondents (74%) reported no incidents of pinhole leaks; and 32 respondents (3%) were not sure of any incidents. One hundred twenty eight respondents (60% percent of the respondents with leaks) had 1 or 2 leaks, 47 respondents (22%) had 3 or 4 leaks, 17 (8%) had 5 or 6 leaks, and 15 (7%) had 7 or more incidents. Over 90% of the leaks had occurred since the year 2000. Of 212 respondents with pinhole leaks, 151 (71%) stated that their first pinhole leak occurred since 2004, and 44 (21%) stated that

Respondents with pinhole leaks had somewhat older homes compared to respondents without leaks (Table 2). Fifty-three percent of respondents without leaks lived in homes built since 2000 compared to 4% of respondents with leaks. Five percent of respondents without leaks lived in homes built before 1990 compared to 23% of respondents with

Since 2000 441 53 9 4 1995 to 1999 240 29 76 36 1990 to 1994 102 12 75 36 Before 1990 39 5 49 23 Do not know 1 0 2 1

Total 835 100 212 100

Most respondents with leaks had leaks in horizontal pipes, while fewer had leaks in vertical pipes or pipe bends (Figure 1). Most leaks were in the finished or unfinished basement

Pinhole leaks occurred in cold water pipes in 138 cases, in both cold and hot water pipes in 14 of the cases, and in hot water pipes only in 33 cases (Table 3). Twenty respondents were

aPercent = number divided by total number of respondents without leaks (835). bPercent = number divided by total number of respondents with leaks (212).

followed by the crawl space and first floor, respectively.

not aware of the type of water pipes where leaks occurred.

Respondents without leaks Respondents with leaks

Number Percenta Number Percentb

12 1 1 0

hearing of the problem through the property management.

their first leak occurred between 2000 and 2003.

leaks.

Year house was built

Missing/not reported

Table 2. Year house was built.

rating scale questions require individuals to make judgements about the magnitude of utility associated with plumbing material profiles. These plumbing material evaluations directly transform utility levels into a rating scale. As a result, an employment of rating models in which the rating value for each profile is regressed on a vector of attribute levels is justified (Champ et al., 2003).

To analyze the CA data, an Ordered Logit regression is employed. The Ordered Logit is based upon the idea of the cumulative logit, which relies on the cumulative probability. The cumulative probability CP*nl* is the probability that the nth individual is in the lth or higher plumbing material valuation category:

$$\text{CP}\_{\text{nl}} = \text{probability (R} \le \text{I)} = \sum\_{\text{l}} \text{I} \text{--} 1 \text{ to 1} \text{[probability(R} = \text{L})\text{.} \tag{3}$$

The cumulative probability is transformed into the cumulative logit:

$$\text{logit CP}\_{\text{nl}} = \log(\text{CP}\_{\text{nl}}(\text{1-CP}\_{\text{nl}})).\tag{4}$$

The ordered logit simply models the cumulative logit as a linear function of independent variables:

$$\text{logit } \mathbf{CP}\_{\text{nl}} = \mathbf{c}\_{\text{l}} - \mathbf{f} \mathbf{x}\_{\text{n}}.\tag{5}$$

There is a different intercept for each level of the cumulative logit, but **β** remains constant across rating categories. In addition, the product of **β** and the independent variable, **xn**, is subtracted rather than added in the model. As a result, each αl indicates the logit of the odds of being equal to or less than category l for the baseline group (when all independent variables are zero). The **β** represents the increase in the log-odds of being higher than category l as the independent variable increases by one-unit (Edner, 2005).

The empirical Ordered Logit model is represented by the following regression:

$$\mathbf{R} = \mathbf{c}\_{\text{I}} \mathbf{-} \sum\_{\text{kin}=1...N} \sum\_{\text{f} \in \text{CR}} [\sum\_{\text{k}=1 \text{ to } K} \beta\_{\text{k}} \mathbf{x}\_{\text{jkn}} + \beta\_{\text{p}} \mathbf{p}\_{\text{jkn}}] + \mathbf{e} \tag{6}$$

where R represents the ordered rating scale (1-9), where βk is the preference parameter associated with the plumbing material attributes , xjkn are the plumbing material attributes in profile j for individual n, βp is the parameter on profile cost, pjkn is the cost attribute for profile j and e is the error term (Champ et al., 2003).

Although attributes of the plumbing materials vary over alternatives; the characteristics of each household do not differ over the alternatives. As a result, the socioeconomic variables need to enter the model estimation to leverage and explain the differences in utility levels between corrosion preventive options. These characteristics can enter the model through interaction with the plumbing material attributes (Train, 2003).

#### **5. Home plumbing corrosion issues**

#### **5.1 Pinhole leak awareness and Incidents**

A total of 1,047 survey responses were received, a 65% response rate. Seventy-six percent of respondents reported being very aware of pinhole leaks, 21% said they were somewhat aware of the problem, and 2% said they were unaware of the problem. Nineteen percent

rating scale questions require individuals to make judgements about the magnitude of utility associated with plumbing material profiles. These plumbing material evaluations directly transform utility levels into a rating scale. As a result, an employment of rating models in which the rating value for each profile is regressed on a vector of attribute levels

To analyze the CA data, an Ordered Logit regression is employed. The Ordered Logit is based upon the idea of the cumulative logit, which relies on the cumulative probability. The cumulative probability CP*nl* is the probability that the nth individual is in the lth or higher

CPnl= probability (Rl ≤ l) = ∑(l=1 to L)probability(Rl =L). (3)

 logit CPnl = log(CPnl(1- CPnl)). (4) The ordered logit simply models the cumulative logit as a linear function of independent

 logit CPnl = αl – **βxn**. (5) There is a different intercept for each level of the cumulative logit, but **β** remains constant across rating categories. In addition, the product of **β** and the independent variable, **xn**, is subtracted rather than added in the model. As a result, each αl indicates the logit of the odds of being equal to or less than category l for the baseline group (when all independent variables are zero). The **β** represents the increase in the log-odds of being higher than

 R = αl - ∑(n=1…N)∑(iЄR)[∑(k=1 to K)βkxjkn+βppjkn] + e (6) where R represents the ordered rating scale (1-9), where βk is the preference parameter associated with the plumbing material attributes , xjkn are the plumbing material attributes in profile j for individual n, βp is the parameter on profile cost, pjkn is the cost attribute for

Although attributes of the plumbing materials vary over alternatives; the characteristics of each household do not differ over the alternatives. As a result, the socioeconomic variables need to enter the model estimation to leverage and explain the differences in utility levels between corrosion preventive options. These characteristics can enter the model through

A total of 1,047 survey responses were received, a 65% response rate. Seventy-six percent of respondents reported being very aware of pinhole leaks, 21% said they were somewhat aware of the problem, and 2% said they were unaware of the problem. Nineteen percent

The cumulative probability is transformed into the cumulative logit:

category l as the independent variable increases by one-unit (Edner, 2005).

profile j and e is the error term (Champ et al., 2003).

**5. Home plumbing corrosion issues 5.1 Pinhole leak awareness and Incidents** 

interaction with the plumbing material attributes (Train, 2003).

The empirical Ordered Logit model is represented by the following regression:

is justified (Champ et al., 2003).

variables:

plumbing material valuation category:

reported learning about pinhole problems through their own experience, 65% heard through a neighbor or friend, 48% heard about pinhole leaks through the media, and 42% reported hearing of the problem through the property management.

Two hundred twelve respondents (20%) reported incidents of pinhole leaks in drinking water pipes in their current homes; 780 respondents (74%) reported no incidents of pinhole leaks; and 32 respondents (3%) were not sure of any incidents. One hundred twenty eight respondents (60% percent of the respondents with leaks) had 1 or 2 leaks, 47 respondents (22%) had 3 or 4 leaks, 17 (8%) had 5 or 6 leaks, and 15 (7%) had 7 or more incidents. Over 90% of the leaks had occurred since the year 2000. Of 212 respondents with pinhole leaks, 151 (71%) stated that their first pinhole leak occurred since 2004, and 44 (21%) stated that their first leak occurred between 2000 and 2003.

Respondents with pinhole leaks had somewhat older homes compared to respondents without leaks (Table 2). Fifty-three percent of respondents without leaks lived in homes built since 2000 compared to 4% of respondents with leaks. Five percent of respondents without leaks lived in homes built before 1990 compared to 23% of respondents with leaks.


aPercent = number divided by total number of respondents without leaks (835). bPercent = number divided by total number of respondents with leaks (212).

Table 2. Year house was built.

Most respondents with leaks had leaks in horizontal pipes, while fewer had leaks in vertical pipes or pipe bends (Figure 1). Most leaks were in the finished or unfinished basement followed by the crawl space and first floor, respectively.

Pinhole leaks occurred in cold water pipes in 138 cases, in both cold and hot water pipes in 14 of the cases, and in hot water pipes only in 33 cases (Table 3). Twenty respondents were not aware of the type of water pipes where leaks occurred.

Households' Preferences for Plumbing Materials 431

Twenty-nine percent of respondents with leaks reported that the expense of repairing pinhole leaks was less than \$100; while 30% reported expenses between \$100 and \$500; and 37% reported more than \$500 in expenses for pinhole leak repairs (Table 5). Seven

Replaced leaking pipe section with copper 75 35 Replaced leaking pipe section with CPVC 5 2 Replaced leaking pipe section with PEX 7 3 Replaced leaking pipe section-material not specified 46 22 Applied epoxy coating to all plumbing 9 4

Repair method Number of observations Percenta

Clamp over leak 77 7

Replumbed with copper 5 2 Replumbed with CPVC 4 2 Replumbed with PEX 32 15

Other 7 1 Don't know 3 1 Total 279 129

Replumbed-material not specified 9 4

aMultiple choices per respondent were accepted. Percent = number reported divided by the total

Amount Number of observations Percenta

Total 212 99

Less than \$100 61 29 \$100 to \$500 64 30 \$501 to \$1,000 14 7 \$1,001 to \$3,000 11 5 \$3,001 to \$5,000 20 9 \$5,001 to \$10,000 28 13 \$10,001 to \$20,000 6 3 More than \$20,000 1 0 Do not know 3 1 Missing/not reported 4 2

respondents reported more than \$10,000 in costs of repairs.

number of respondents with leaks (212).

aNumbers do not sum to 100 due to rounding. Table 5. Costs of repairing pinhole leaks.

Table 4. Method of leak repair.

aMultiple choices per respondent were accepted. Percent = number reported divided by the total number of respondents with leaks (212).

Fig. 1. Pinhole leaks by type of pipe.


Table 3. Pinhole leaks occurring in cold or hot water pipes.

#### **5.2 Pinhole leak repairs and repair costs**

Seventy-seven respondents repaired the leak using a clamp (Table 4). In some cases, a clamp was used initially while the leaking section or all plumbing was replaced for later leaks. One hundred thirty-three respondents repaired the leak by replacing the leaking pipe section. Copper was most often used for repairing leaking sections. Fifty respondents repaired the leak by replumbing the entire house. PEX was most often used for replumbing. Nine respondents applied epoxy coating to their existing plumbing systems.

More than 60% of respondents with leaks spent less than 20 hours dealing with pinhole leaks while more than 30% spent 21 or more hours. Twenty percent spent more than 40 hours dealing with pinhole leaks.

aMultiple choices per respondent were accepted. Percent = number reported divided by the total

Seventy-seven respondents repaired the leak using a clamp (Table 4). In some cases, a clamp was used initially while the leaking section or all plumbing was replaced for later leaks. One hundred thirty-three respondents repaired the leak by replacing the leaking pipe section. Copper was most often used for repairing leaking sections. Fifty respondents repaired the leak by replumbing the entire house. PEX was most often used for replumbing. Nine

More than 60% of respondents with leaks spent less than 20 hours dealing with pinhole leaks while more than 30% spent 21 or more hours. Twenty percent spent more than 40

Type of pipe Number of observations Percent

Cold water pipes 138 65 Hot water pipes 33 16 Both 14 7 Do not know 20 9 Missing/not reported 7 3 Total 212 100

Table 3. Pinhole leaks occurring in cold or hot water pipes.

respondents applied epoxy coating to their existing plumbing systems.

**5.2 Pinhole leak repairs and repair costs** 

hours dealing with pinhole leaks.

number of respondents with leaks (212). Fig. 1. Pinhole leaks by type of pipe. Horizontal pipe Vertical pipes Pipe bend Do not know

Twenty-nine percent of respondents with leaks reported that the expense of repairing pinhole leaks was less than \$100; while 30% reported expenses between \$100 and \$500; and 37% reported more than \$500 in expenses for pinhole leak repairs (Table 5). Seven respondents reported more than \$10,000 in costs of repairs.


aMultiple choices per respondent were accepted. Percent = number reported divided by the total number of respondents with leaks (212).

Table 4. Method of leak repair.


aNumbers do not sum to 100 due to rounding.

Table 5. Costs of repairing pinhole leaks.

Households' Preferences for Plumbing Materials 433

aMultiple choices per respondent were accepted. Percent = number reported divided by the total

Table 7. Use of water treatment for purposes other than corrosion prevention.

number of respondents (1,047).

aTotals do not sum to 100 due to rounding.

**6.1 Summary of descriptive results** 

Fig. 2. Satisfaction with home drinking water quality.

**6. Household preferences for plumbing material** 

Every respondent to the first Southeastern Community survey was asked to participate in the follow-up survey. Three hundred sixty three respondents agreed to participate, and 245 responded to the follow-up survey. Each respondent evaluated three Conjoint Analysis

Filter for entire home 133 16 Refrigerator filter 523 63 Water softener/water conditioner 66 8 Pitcher or bottle to filter water 136 16 Purchased drinking water 265 32 Filter on faucet or under kitchen sink 117 14 Ultra violet (UV) system 2 0 Other 25 3 None used 249 30 Missing/not reported 19 2 Total 1,535 184

Number Percenta

Very satisfied

Somewhat satisfied Somewhat dissatisfied Not at all satisfied Missing/not reported

In addition to the expense of repairing leaks, 92% of respondents with leaks reported having to repair property damage caused by leaks. Forty percent of respondents with damage reported less than \$100 of damage, while 49% had over \$100 in damage. Twelve respondents had over \$5,000 in property damage. Thirty-six percent of respondents reporting leaks found the experience of pinhole leaks very stressful, and 46% found it somewhat stressful. Thirteen percent experienced little or no stress.

### **5.3 Pinhole prevention and water treatment devices**

Thirty-five percent of respondents with leaks and 20% of respondents without leaks use some type of pinhole leak prevention strategy (Table 6). The most common strategy among those with leaks is preventive replumbing, which was used by 13% of those with leaks. Water softener / conditioner was the most common strategy used by those without leaks, which was used by 9% of those respondents.

Sixty-seven percent of respondents use some type of water treatment for purposes other than pinhole leak prevention (Table 7). The most common treatment was a refrigerator filter, used by 63%. Thirty-two percent of respondents reported that they purchase drinking water. The most common reasons given for using water treatment devices are to improve taste or smell of drinking water (mentioned by 45% of respondents), and to improve safety of drinking water (mentioned by 33% of respondents).


aMultiple choices per respondent were accepted. Percent = number reported divided by the total number of respondents with leaks (212).

bPercent = number reported divided by the total number of respondents without leaks (835).

Table 6. Use of pinhole leak prevention devices.

#### **5.4 Concerns about water safety and quality**

Eighty-two percent of respondents were somewhat or very satisfied with home drinking water quality (Figure 2). Only 5% of respondents were not at all satisfied with water quality. Problems with water quality most frequently mentioned were related to taste particularly chlorine. Respondents varied in concern about future pinhole leaks. Forty percent were somewhat or very concerned, while 55% were not very or not at all concerned.

In addition to the expense of repairing leaks, 92% of respondents with leaks reported having to repair property damage caused by leaks. Forty percent of respondents with damage reported less than \$100 of damage, while 49% had over \$100 in damage. Twelve respondents had over \$5,000 in property damage. Thirty-six percent of respondents reporting leaks found the experience of pinhole leaks very stressful, and 46% found it

Thirty-five percent of respondents with leaks and 20% of respondents without leaks use some type of pinhole leak prevention strategy (Table 6). The most common strategy among those with leaks is preventive replumbing, which was used by 13% of those with leaks. Water softener / conditioner was the most common strategy used by those without leaks,

Sixty-seven percent of respondents use some type of water treatment for purposes other than pinhole leak prevention (Table 7). The most common treatment was a refrigerator filter, used by 63%. Thirty-two percent of respondents reported that they purchase drinking water. The most common reasons given for using water treatment devices are to improve taste or smell of drinking water (mentioned by 45% of respondents), and to improve safety of

> Respondents with pinhole leaksa

Preventive replumbing 28 13 16 2 Preventive epoxy injection 8 4 4 0 Phosphate injection 12 6 26 3 Water softener/water conditioner 11 5 79 9 Copper Knight 5 2 12 1 Other 19 9 64 8 None used 134 63 644 77 Missing/not reported 4 2 29 3 Total 295 139 874 105 aMultiple choices per respondent were accepted. Percent = number reported divided by the total

bPercent = number reported divided by the total number of respondents without leaks (835).

somewhat or very concerned, while 55% were not very or not at all concerned.

Eighty-two percent of respondents were somewhat or very satisfied with home drinking water quality (Figure 2). Only 5% of respondents were not at all satisfied with water quality. Problems with water quality most frequently mentioned were related to taste particularly chlorine. Respondents varied in concern about future pinhole leaks. Forty percent were

Respondents without

pinhole leaksb

Number Percent Number Percent

somewhat stressful. Thirteen percent experienced little or no stress.

**5.3 Pinhole prevention and water treatment devices** 

which was used by 9% of those respondents.

drinking water (mentioned by 33% of respondents).

number of respondents with leaks (212).

Table 6. Use of pinhole leak prevention devices.

**5.4 Concerns about water safety and quality** 


aMultiple choices per respondent were accepted. Percent = number reported divided by the total number of respondents (1,047).

Table 7. Use of water treatment for purposes other than corrosion prevention.

aTotals do not sum to 100 due to rounding.

Fig. 2. Satisfaction with home drinking water quality.
