**6.2.1 Order logit model without socioeconomics variables**

For this part of the analysis, the Ordered Logit regression is utilized in the plumbing material estimation of preferences and is estimated at the aggregate response level. The aggregate level analysis implies that average value coefficients are estimated for the participating sample of respondents.

The analysis provides information on the preferences of homeowners for plumbing materials, and the attributes that drive their decision, when making purchasing decision with regards to the type of home plumbing system. Each respondent evaluated a set of two plumbing material portfolios at one time for a total of six portfolios using the valuation metrics 1-9 described earlier. Each of the plumbing materials has a set of attributes described in Table 1. Each material attribute level is employed as the independent variable in the material preference analysis. They are coded as dummy variables taking a value of 1 when that plumbing material characteristic is a part of the product portfolio and zero otherwise. Finally, the socioeconomic characteristics (reported in the first survey) are also included in the Ordered Logit model. These characteristics represent household home value (continuous variables), age of the house (continuous variable), plumbing material type (dummy variable), pinhole leak occurrences in the past (dummy variable), and respondent's previous cost of plumbing material repairs and replacement (continuous variable).3

The first step in evaluating the results of the Ordered Logit model is to review the model performance / fitting criteria. The model fitting information indicates the parameters for which the model-fit is calculated. There are four variables that evaluate the goodness of fit: Chi-square statistics4, p-value5, log-likelihood value6, and R-square7. The model fitting

<sup>3</sup> Variables for race, education level, and gender were not included in the model, as little variation in

these characteristics was observed for the sample of respondents. 4 Chi-square Test establishes whether or not an observed frequency distribution differs from a theoretical distribution (Aaron, 2005).

<sup>5</sup> P-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true (Aaron, 2005).

<sup>6</sup> Log-likelihood Test compares the fit of two models, one of which (the null model) is a special case of the other (the alternative model) (Aaron, 2005).

<sup>7</sup> R-square represents the proportion of variability in a data set that is accounted for by the statistical model (Aaron, 2005).

Households' Preferences for Plumbing Materials 437

Besides evaluating the directional impact of the independent variables on the preference level of the households, the impact of the statistically significant independent variables on the preference category is evaluated for all three plumbing materials. As the attribute levels describing each of the three hypothetical materials are known, the regression results can be organized by plumbing materials. For example, Material A is described by attribute level called 'corrosion proof' as well as 'installation takes around 4 days'. The coefficient estimates for the statistically significant attribute levels are employed to compute preference valuation categories for each material type. In case of the Material A (epoxy coating) computation of the preference valuation category called 'Moderately Preferred', the following represents the estimate computation: 1.315 - 0.654 - 0.559= 0.102, where 1.315 is the moderately preferred coefficient, 0.654 is 'the corrosion proof' coefficient, and 0.559 is 'the convenience of installation' coefficient; and the odds ratio

Threshold Values (For All Independent Variables Set to Zero) Not Preferred -0.096 0.108 0.790 0.374 Moderately Preferred 1.315 0.115 131.554 0.000 Strongly Preferred 2.289 0.125 333.413 0.000 Very Strongly Preferred 3.742 0.164 521.510 0.000 Independent Variables (Variables that Improve Overall Model Significance)e 1) Corrosion proof 0.654 0.143 20.943 0.000

aThe number of observations included in the model is 1086. Independent variables take form of dummy variables with value of one when the characteristic was present in the plumbing material profile and zero otherwise. To avoid a dummy variable trap, one of the attribute levels was excluded from the analysis. The omitted characteristics represent Material C (copper) descriptions. b Coefficient estimates show how much increase in the likelihood of being in a higher category results

e Model Statistics: Log-likelihood value is 182.641 with chi-square of 114.136 and p-value of 0.000;

plumbing material attributes (without socioeconomic variables))a.

Table 10. Ordered logit regression estimates with categorical answers (dependent variable represents the plumbing material valuation and the independent variables represent the

When further investigating the Ordered Logit results, the coefficient for each preference category in combination with the coefficients for each independent variable can be expressed as marginal probability estimates to provide a greater insight into the preferred plumbing material (Table 11). Based on the marginal distribution of the probability estimates, Material A

Standard Errorc Wald-

0.559 0.119 22.016 0.000

Statsd

P-Valued

computation: exp(0.102) = 1.107.

2) No need to tear into some sections of wall for installation. Installation takes around 4 days.

Nagelkerke's R-square is 0.084.

Variable Name Coefficient

from a one unit increase in the independent variable. c Standard error represents the variation of the estimate. d Wald statistics and p-value represent the significance level.

Estimateb

information presents that the Chi-square statistic is 114.136 with a p-value of 0.000, and a log-likelihood value of 182.641, which implies the existence of a relationship between the independent variables (plumbing material attributes) and the dependent variable (plumbing material selection) is supported. The goodness-of-fit measure is also employed, and the Nagelkerke's R-square is 0.084, which implies that 8% of variation in the dependent variable is explained by the variation in the independent variables.

In evaluating the Ordered Logit model, threshold represents the response variable in the regression. A different intercept is provided for the different levels of the cumulative logit model. The beta coefficient of the independent variables does not change, and the value of each is subtracted from the intercept. Each threshold level indicates the logit of the odds of being equal to or less than the baseline category when all independent variables are zero (Aaron, 2005). The baseline group is set to 'Extremely Preferred'. The beta estimate represents that a one unit increase in the independent variable increases / decreases the logodds of being higher than a specific preferred valuation category. Because the beta coefficient is not indexed by each category, a one unit increase affects the log-odds the same regardless of which threshold value is considered (Aaron, 2005).

As represented in Table 10, the regression estimates reveal that when compared to the baseline category ('Extremely Preferred'), the categories 'Moderately Preferred', 'Strongly Preferred', and 'Very Strongly Preferred' have higher threshold estimates. A category 'Not Preferred' has a statistically insignificant negative coefficient estimate. Since the estimate is not statistically significant at the 95% confidence interval, it is not included in comparison analysis between the categories.

The threshold values are also evaluated. These values inform the expected cumulative distribution of categorical preference values for individuals with the independent variables set to zero (Aaron, 2005). This threshold represents a natural tendency for all the responses to all the scenarios presented to respondents when the independent variables are suppressed. When these coefficients are exponentiated, the cumulative odds for each category are obtained (Table 12). By employing the following equation, (odds /(1+odds)), the cumulative probabilities are computed (Aaron, 2005). Table 10 represents the odds ratios and cumulative probabilities (columns 3 and 4 in Table 10). For example, the 'Moderately Preferred" category is 3.7 times more likely to be selected by the respondent compared to the 'Extremely Preferred' category when all independent variables are set to zero.

The independent variable coefficient estimates are statistically significant only for two attribute levels: risk of corrosion variable represented by 'corrosion proof' attribute level and convenience of installation represented by 'no need to tear into the wall and/or floor. Installation takes around 4 days' (Table 10). Other independent variables were considered redundant in the model estimation. The independent variable coefficients represent how the log-odds of these thresholds increase / decrease with one unit of the independent variable. The positive value indicates that one unit of independent variable increases the odds of being in a higher category (Aaron, 2005). For example, the 'corrosion proof' attribute level increases the odds of choosing a higher preference category by 0.654 compared to the independent variable represented by 'some risk of corrosion' attribute level. 'Installation of plumbing material taking about 4 days' increases the odds of choosing a higher preference category by 0.559 compared to 'the installation taking between 7 and 9 days.'

information presents that the Chi-square statistic is 114.136 with a p-value of 0.000, and a log-likelihood value of 182.641, which implies the existence of a relationship between the independent variables (plumbing material attributes) and the dependent variable (plumbing material selection) is supported. The goodness-of-fit measure is also employed, and the Nagelkerke's R-square is 0.084, which implies that 8% of variation in the dependent variable

In evaluating the Ordered Logit model, threshold represents the response variable in the regression. A different intercept is provided for the different levels of the cumulative logit model. The beta coefficient of the independent variables does not change, and the value of each is subtracted from the intercept. Each threshold level indicates the logit of the odds of being equal to or less than the baseline category when all independent variables are zero (Aaron, 2005). The baseline group is set to 'Extremely Preferred'. The beta estimate represents that a one unit increase in the independent variable increases / decreases the logodds of being higher than a specific preferred valuation category. Because the beta coefficient is not indexed by each category, a one unit increase affects the log-odds the same

As represented in Table 10, the regression estimates reveal that when compared to the baseline category ('Extremely Preferred'), the categories 'Moderately Preferred', 'Strongly Preferred', and 'Very Strongly Preferred' have higher threshold estimates. A category 'Not Preferred' has a statistically insignificant negative coefficient estimate. Since the estimate is not statistically significant at the 95% confidence interval, it is not included in comparison

The threshold values are also evaluated. These values inform the expected cumulative distribution of categorical preference values for individuals with the independent variables set to zero (Aaron, 2005). This threshold represents a natural tendency for all the responses to all the scenarios presented to respondents when the independent variables are suppressed. When these coefficients are exponentiated, the cumulative odds for each category are obtained (Table 12). By employing the following equation, (odds /(1+odds)), the cumulative probabilities are computed (Aaron, 2005). Table 10 represents the odds ratios and cumulative probabilities (columns 3 and 4 in Table 10). For example, the 'Moderately Preferred" category is 3.7 times more likely to be selected by the respondent compared to

The independent variable coefficient estimates are statistically significant only for two attribute levels: risk of corrosion variable represented by 'corrosion proof' attribute level and convenience of installation represented by 'no need to tear into the wall and/or floor. Installation takes around 4 days' (Table 10). Other independent variables were considered redundant in the model estimation. The independent variable coefficients represent how the log-odds of these thresholds increase / decrease with one unit of the independent variable. The positive value indicates that one unit of independent variable increases the odds of being in a higher category (Aaron, 2005). For example, the 'corrosion proof' attribute level increases the odds of choosing a higher preference category by 0.654 compared to the independent variable represented by 'some risk of corrosion' attribute level. 'Installation of plumbing material taking about 4 days' increases the odds of choosing a higher preference

the 'Extremely Preferred' category when all independent variables are set to zero.

category by 0.559 compared to 'the installation taking between 7 and 9 days.'

is explained by the variation in the independent variables.

regardless of which threshold value is considered (Aaron, 2005).

analysis between the categories.

Besides evaluating the directional impact of the independent variables on the preference level of the households, the impact of the statistically significant independent variables on the preference category is evaluated for all three plumbing materials. As the attribute levels describing each of the three hypothetical materials are known, the regression results can be organized by plumbing materials. For example, Material A is described by attribute level called 'corrosion proof' as well as 'installation takes around 4 days'. The coefficient estimates for the statistically significant attribute levels are employed to compute preference valuation categories for each material type. In case of the Material A (epoxy coating) computation of the preference valuation category called 'Moderately Preferred', the following represents the estimate computation: 1.315 - 0.654 - 0.559= 0.102, where 1.315 is the moderately preferred coefficient, 0.654 is 'the corrosion proof' coefficient, and 0.559 is 'the convenience of installation' coefficient; and the odds ratio computation: exp(0.102) = 1.107.


aThe number of observations included in the model is 1086. Independent variables take form of dummy variables with value of one when the characteristic was present in the plumbing material profile and zero otherwise. To avoid a dummy variable trap, one of the attribute levels was excluded from the

analysis. The omitted characteristics represent Material C (copper) descriptions. b Coefficient estimates show how much increase in the likelihood of being in a higher category results from a one unit increase in the independent variable.

c Standard error represents the variation of the estimate.

d Wald statistics and p-value represent the significance level.

e Model Statistics: Log-likelihood value is 182.641 with chi-square of 114.136 and p-value of 0.000; Nagelkerke's R-square is 0.084.

Table 10. Ordered logit regression estimates with categorical answers (dependent variable represents the plumbing material valuation and the independent variables represent the plumbing material attributes (without socioeconomic variables))a.

When further investigating the Ordered Logit results, the coefficient for each preference category in combination with the coefficients for each independent variable can be expressed as marginal probability estimates to provide a greater insight into the preferred plumbing material (Table 11). Based on the marginal distribution of the probability estimates, Material A

Households' Preferences for Plumbing Materials 439

characteristics on the plumbing material preferences. The statistically significant interaction

When the socioeconomic variables were entered in the Ordered Logit model one at a time, 'corrosion proof' as well as 'installation takes about 4 days' were the two attribute levels appearing statistically significant in many of the model specifications. The coefficient value for corrosion attribute varied from 0.651 to 1.450, and the convenience of installation coefficient varied from 0.554 to 0.754. The only statistically significant interaction effect was observed between attribute level of 'corrosion proof' and respondent's 'previous cost of plumbing materials repairs or replacement' (coefficient estimate = 0.00001; standard error = 0.00000; Wald-statistic8 = 15.773; p-value = 0.000). This interaction effect was entered into the

The threshold values, which inform the expected cumulative distribution of categorical preference values for individuals with the independent variables set to zero, are evaluated (Aaron, 2005). Table 12 represents the odds ratios and probabilities. For example, the 'Moderately Preferred" category is 3.67 times more likely to be selected by the respondent than the 'Extremely Preferred' category when all independent variables are set to zero. On the other hand, the 'Not Preferred' category is only 0.86 times as likely to occur compared to

Based on Table 12, the independent variable coefficient estimates are statistically significant only for two attribute levels: 'corrosion proof' and 'installation takes about 4 days'. For example, the 'corrosion proof' variable increases the odds by 1.145 of choosing a higher preference category compared to the variable set at 'some risk of corrosion'. 'Installation of plumbing material taking about 4 days' increases the odds of choosing a higher preference category by 0.575 compared to 'the installation taking between 7 and 9 days'. The only socioeconomic variable entered into the regression is the respondent's previous cost of plumbing repairs and/or material fixing or replacement and is statistically significant when interacted with corrosion proof attribute level. The joint coefficient is 1.197 (1.145+0.0001\*\$5229) and is statistically significant at 5% significance level10. This coefficient value further implies that the interaction variable increases the odds by 1.197 of choosing a higher preference category compared to the variable set at 'some risk of corrosion'. This finding can be explained as households, who have accrued cost of plumbing material repairs in the past, value the 'corrosion proof' attribute level more compared to the 'some risk of corrosion' attribute level. Plumbing material with low corrosion risk would imply

As in the previous version of the Ordered Logit model, effects of statistically significant independent variables on the preference category for all three plumbing materials are evaluated. The statistically significant attribute levels were computed together with the thresholds levels by plumbing material into odds ratios and probability values. As attribute levels describing each of the three hypothetical materials are known, the regression results can be organized by plumbing materials. For example, Material A is described by attribute

8 Wald Test is used to test the true value of the parameter based on the sample estimate (Aaron, 2005). 9 \$522 is the mean cost value of the previous cost spent on plumbing material repairs and replacement. 10Cost of Plumbing Material Fixing or Replacement \* Corrosion Proof: Wald statistic = 5.684 and p-value

variables were then included in the final model estimation.

final model estimation alongside of other plumbing material attributes.

the baseline category when no independent variables are considered.

decrease in the future costs of plumbing material repairs.

= 0.020.

has a larger probability estimate for 'Strongly Preferred' to 'Extremely Preferred' category preference. On the other hand, Material C has a higher probability estimates for categories 'Not Preferred' and 'Moderately Preferred'. All three materials have the highest frequency of estimates falling into 'Not Preferred' and 'Moderately Preferred' categories. Based on the overall results, Material A (epoxy coating) is the most preferred material followed by Material B (plastic). Material C (copper) is the least preferred plumbing material.


aCoefficient estimates are built up from the statistically significant estimates for the attribute levels and threshold values. Coefficients are compared to the base "Extremely Preferred" level.

Table 11. Ordered logit regression results' analysis by plumbing material type (dependent variable represents the plumbing material valuation and the independent variables represent the plumbing material attributes (no socioeconomic variables)).

## **6.2.2 Order logit model with socioeconomics variables**

The second specification of the Ordered Logit model includes the socioeconomic variables alongside of the attributes for plumbing material. As the socioeconomic characteristics do not vary for a given respondent, they should be interacted with the attributes levels of each attribute. As the total number of respondents is rather small (230), there are not enough degrees of freedom to include all interaction variables between the attribute levels and the household characteristics. As a result, the Ordered Logit model was first estimated with socioeconomic variables entering one at a time to measure the impact of household

has a larger probability estimate for 'Strongly Preferred' to 'Extremely Preferred' category preference. On the other hand, Material C has a higher probability estimates for categories 'Not Preferred' and 'Moderately Preferred'. All three materials have the highest frequency of estimates falling into 'Not Preferred' and 'Moderately Preferred' categories. Based on the overall results, Material A (epoxy coating) is the most preferred material followed by Material

Coefficient Estimatesa

Odds Ratio Estimates

Marginal Probability Estimates Distribution

aCoefficient estimates are built up from the statistically significant estimates for the attribute levels and

Table 11. Ordered logit regression results' analysis by plumbing material type (dependent variable represents the plumbing material valuation and the independent variables

The second specification of the Ordered Logit model includes the socioeconomic variables alongside of the attributes for plumbing material. As the socioeconomic characteristics do not vary for a given respondent, they should be interacted with the attributes levels of each attribute. As the total number of respondents is rather small (230), there are not enough degrees of freedom to include all interaction variables between the attribute levels and the household characteristics. As a result, the Ordered Logit model was first estimated with socioeconomic variables entering one at a time to measure the impact of household

Material A Material B Material C

B (plastic). Material C (copper) is the least preferred plumbing material.

Very Strongly

Very Strongly

Very Strongly

Extremely Preferred

Extremely Preferred

Not Preferred -1.309 -0.750 -0.096 Moderately Preferred 0.102 0.661 1.315 Strongly Preferred 1.076 1.635 2.289

Preferred 2.529 3.088 3.742

Not Preferred 0.270 0.472 0.908 Moderately Preferred 1.107 1.937 3.725 Strongly Preferred 2.933 5.129 9.865

Preferred 12.541 21.933 42.182

Not Preferred 0.213 0.321 0.476 Moderately Preferred 0.313 0.339 0.312 Strongly Preferred 0.220 0.177 0.120

Preferred 0.180 0.120 0.069 Extremely Preferred 0.074 0.044 0.023

threshold values. Coefficients are compared to the base "Extremely Preferred" level.

represent the plumbing material attributes (no socioeconomic variables)).

**6.2.2 Order logit model with socioeconomics variables** 

characteristics on the plumbing material preferences. The statistically significant interaction variables were then included in the final model estimation.

When the socioeconomic variables were entered in the Ordered Logit model one at a time, 'corrosion proof' as well as 'installation takes about 4 days' were the two attribute levels appearing statistically significant in many of the model specifications. The coefficient value for corrosion attribute varied from 0.651 to 1.450, and the convenience of installation coefficient varied from 0.554 to 0.754. The only statistically significant interaction effect was observed between attribute level of 'corrosion proof' and respondent's 'previous cost of plumbing materials repairs or replacement' (coefficient estimate = 0.00001; standard error = 0.00000; Wald-statistic8 = 15.773; p-value = 0.000). This interaction effect was entered into the final model estimation alongside of other plumbing material attributes.

The threshold values, which inform the expected cumulative distribution of categorical preference values for individuals with the independent variables set to zero, are evaluated (Aaron, 2005). Table 12 represents the odds ratios and probabilities. For example, the 'Moderately Preferred" category is 3.67 times more likely to be selected by the respondent than the 'Extremely Preferred' category when all independent variables are set to zero. On the other hand, the 'Not Preferred' category is only 0.86 times as likely to occur compared to the baseline category when no independent variables are considered.

Based on Table 12, the independent variable coefficient estimates are statistically significant only for two attribute levels: 'corrosion proof' and 'installation takes about 4 days'. For example, the 'corrosion proof' variable increases the odds by 1.145 of choosing a higher preference category compared to the variable set at 'some risk of corrosion'. 'Installation of plumbing material taking about 4 days' increases the odds of choosing a higher preference category by 0.575 compared to 'the installation taking between 7 and 9 days'. The only socioeconomic variable entered into the regression is the respondent's previous cost of plumbing repairs and/or material fixing or replacement and is statistically significant when interacted with corrosion proof attribute level. The joint coefficient is 1.197 (1.145+0.0001\*\$5229) and is statistically significant at 5% significance level10. This coefficient value further implies that the interaction variable increases the odds by 1.197 of choosing a higher preference category compared to the variable set at 'some risk of corrosion'. This finding can be explained as households, who have accrued cost of plumbing material repairs in the past, value the 'corrosion proof' attribute level more compared to the 'some risk of corrosion' attribute level. Plumbing material with low corrosion risk would imply decrease in the future costs of plumbing material repairs.

As in the previous version of the Ordered Logit model, effects of statistically significant independent variables on the preference category for all three plumbing materials are evaluated. The statistically significant attribute levels were computed together with the thresholds levels by plumbing material into odds ratios and probability values. As attribute levels describing each of the three hypothetical materials are known, the regression results can be organized by plumbing materials. For example, Material A is described by attribute

<sup>8</sup> Wald Test is used to test the true value of the parameter based on the sample estimate (Aaron, 2005).

<sup>9 \$522</sup> is the mean cost value of the previous cost spent on plumbing material repairs and replacement.

<sup>10</sup>Cost of Plumbing Material Fixing or Replacement \* Corrosion Proof: Wald statistic = 5.684 and p-value = 0.020.

Households' Preferences for Plumbing Materials 441

Material C has the highest values of odds ratios for each preference category while Material A has the lowest. The odds ratios that present the likelihood of a preference category being selected are compared to the base category. For example, the category 'Strongly Preferred' is 10.145 times as likely to be selected as the base category for Material C while for Material A it is only 1.724 times as likely. A lower odds ratio for each preference category is more preferred, as it implies that the 'Extremely Preferred' category has a higher chance of being chosen relative to other categories. This finding implies that Material A is a more preferred

Following further analysis of the marginal distribution probability estimates, Material A has a larger probability estimate for 'Strongly Preferred' to 'Extremely Preferred' category preference. On the other hand, Material C has higher probability estimates for category 'Not Preferred'. Based on these results, Material A (epoxy coating) is again the most preferred material followed by Material B (plastic). Material C (copper) as previously found is the

Not Preferred -1.919 -1.344 -0.147 Moderately Preferred -0.472 0.103 1.300 Strongly Preferred 0.545 1.120 2.317

Preferred 2.018 2.593 3.790

Not Preferred 0.147 0.261 0.863 Moderately Preferred 0.624 1.108 3.669 Strongly Preferred 1.724 3.064 10.145

Preferred 7.522 13.367 44.256

Not Preferred 0.128 0.207 0.463 Moderately Preferred 0.256 0.319 0.323 Strongly Preferred 0.249 0.228 0.124

Preferred 0.250 0.176 0.068 Extremely Preferred 0.117 0.070 0.022

threshold values. Coefficients are compared to the base "Extremely Preferred" level.

aCoefficient estimates are built up from the statistically significant estimates for the attribute levels and

Table 13. Ordered logit regression results' analysis by plumbing material type (dependent variable represents the plumbing material valuation and the independent variables represent the plumbing material attributes and the socioeconomic characteristics).

Odds Ratio Estimates

Distribution Estimates

Material A Material B Material C

home plumbing choice for households.

least preferred plumbing material.

Coefficient Estimatesa

Extremely Preferred

Very Strongly

Very Strongly

Very Strongly

Extremely Preferred

level called 'corrosion proof' and 'installation takes about 4 days'. The coefficient estimates for the statistically significant attribute levels are employed in the material based preference category computation. In case of Material A (epoxy coating) the computation for preference valuation category of 'Moderately Preferred', the following represents the estimate computation: 1.300- 1.145- 0.575 -0.0001\*\$522 = -0.472; and the odds ratio computation: exp(- 0.472) = 0.624 (Table 15).


a The number of observations included in the model is 1072. Independent variables take form of dummy variables with value of one when the characteristic was present in the plumbing material profile and zero otherwise. To avoid a dummy variable trap, one of the attribute levels was excluded from the analysis. The omitted characteristics represent Material C (copper) descriptions. b Coefficient estimates show how much increase in the likelihood of being in a higher category results

from a one unit increase in the independent variable.

c Standard error represents the variation of the estimate.

d Wald statistics and p-value represent the significance level.

e Model Statistics: Log-likelihood value is 1565.522 with chi-square of 119.384 and p-value of 0.000; Nagelkerke's R-square is 0.101.

Table 12. Ordered logit regression estimates with categorical answers (dependent variable represents the plumbing material valuation and the independent variables represent the plumbing material attributes and socioeconomic variables interacted with attribute levels)a.

As presented in Table 13, Material A has the lowest values of estimates for all preference categories, compared to Materials B and C. Material C has the highest values of preference valuation. Threshold values with smaller absolute values imply smaller differences between preference valuation categories and the base category in the likelihood of that preference category being selected. For example, Material B has a smaller absolute threshold value compared to Material A for the "Not Preferred" category, implying a smaller difference between 'Not Preferred' and 'Extremely Preferred' for Material B (-1.344) compared to Material A (-1.919).

level called 'corrosion proof' and 'installation takes about 4 days'. The coefficient estimates for the statistically significant attribute levels are employed in the material based preference category computation. In case of Material A (epoxy coating) the computation for preference valuation category of 'Moderately Preferred', the following represents the estimate computation: 1.300- 1.145- 0.575 -0.0001\*\$522 = -0.472; and the odds ratio computation: exp(-

Threshold Values (For All Independent Variables Set to Zero)

Independent Variables for Model Specification with Socioeconomic Variable Interactionse and f Corrosion Proof 1.145 0.502 5.190 0.023

a The number of observations included in the model is 1072. Independent variables take form of dummy variables with value of one when the characteristic was present in the plumbing material profile and zero otherwise. To avoid a dummy variable trap, one of the attribute levels was excluded from the analysis. The omitted characteristics represent Material C (copper) descriptions. b Coefficient estimates show how much increase in the likelihood of being in a higher category results

e Model Statistics: Log-likelihood value is 1565.522 with chi-square of 119.384 and p-value of 0.000;

Table 12. Ordered logit regression estimates with categorical answers (dependent variable represents the plumbing material valuation and the independent variables represent the plumbing material attributes and socioeconomic variables interacted with attribute levels)a.

As presented in Table 13, Material A has the lowest values of estimates for all preference categories, compared to Materials B and C. Material C has the highest values of preference valuation. Threshold values with smaller absolute values imply smaller differences between preference valuation categories and the base category in the likelihood of that preference category being selected. For example, Material B has a smaller absolute threshold value compared to Material A for the "Not Preferred" category, implying a smaller difference between 'Not Preferred' and 'Extremely Preferred' for Material B (-1.344) compared to

Not Preferred -0.147 0.089 2.705 0.100 Moderately Preferred 1.300 0.098 176.801 0.000 Strongly Preferred 2.317 0.114 415.544 0.000 Very Strongly Preferred 3.790 0.164 532.389 0.000

Standard Errorc Wald-

0.575 0.134 18.331 0.000

0.0001 0.00006 4.644 0.031

Statsd

P-Valued

0.472) = 0.624 (Table 15).

Need to tear into some sections of wall for installation. Installation takes around 4 days.

Respondent's previous cost of plumbing repairs and/or replacement \* Corrosion Proof

Nagelkerke's R-square is 0.101.

Material A (-1.919).

Variable Name Coefficient

from a one unit increase in the independent variable. c Standard error represents the variation of the estimate. d Wald statistics and p-value represent the significance level.

Estimateb

Material C has the highest values of odds ratios for each preference category while Material A has the lowest. The odds ratios that present the likelihood of a preference category being selected are compared to the base category. For example, the category 'Strongly Preferred' is 10.145 times as likely to be selected as the base category for Material C while for Material A it is only 1.724 times as likely. A lower odds ratio for each preference category is more preferred, as it implies that the 'Extremely Preferred' category has a higher chance of being chosen relative to other categories. This finding implies that Material A is a more preferred home plumbing choice for households.

Following further analysis of the marginal distribution probability estimates, Material A has a larger probability estimate for 'Strongly Preferred' to 'Extremely Preferred' category preference. On the other hand, Material C has higher probability estimates for category 'Not Preferred'. Based on these results, Material A (epoxy coating) is again the most preferred material followed by Material B (plastic). Material C (copper) as previously found is the least preferred plumbing material.


aCoefficient estimates are built up from the statistically significant estimates for the attribute levels and threshold values. Coefficients are compared to the base "Extremely Preferred" level.

Table 13. Ordered logit regression results' analysis by plumbing material type (dependent variable represents the plumbing material valuation and the independent variables represent the plumbing material attributes and the socioeconomic characteristics).

Households' Preferences for Plumbing Materials 443

acquire information on plumbing material attributes such as price, health impact, longevity, and corrosion resistance in order to make informed investment decisions about plumbing systems for their homes. Information on consumer preferences for drinking water plumbing attributes can be useful not only to individual households, but also to policymakers, program managers, water utilities, and firms with interests in drinking

This chapter addressed the issues of household plumbing material decisions. The information was elicited by two surveys of residents residing in a Southeastern Community in the U.S. The first survey elicited information on the prevalence of pinhole leaks and other plumbing material failures, households' experiences with plumbing material failures, the cost of repairs and property damages due to the material failures, and household preferences for corrosion preventive measures. The follow-up survey, sent only to those residents who agreed to participate in future studies related to the plumbing material issues, elicited information on households' preferences for a set of hypothetical

Overall, the Southeastern Community survey revealed high level of awareness of pinhole leak problem among residents of the community. Twenty percent of the households reported actual pinhole leak incidents. The percent of pinhole leak reports was on par with other hotspot areas of corrosion in the U.S., but above the rate of pinhole leak occurrences in non-hotspots (Scardina et al., 2007). The pinhole leak problem was more prevalent in houses built before the 1990s with copper pipes installed as the plumbing system. This finding is in an agreement with a Maryland Pinhole Leak Survey conducted by Kleczyk and Bosch in

The total repair expenses due to the pinhole leaks varied between \$100 and \$5,000 with several reports of more than \$5,000 in repairs. Similar results were found by Kleczyk et al. (2006) of selected communities in the East, Southeast, Midwest, and West regions. Over 50% of surveyed respondents spent more than \$100 on repairs with estimates as high as \$12,000. In comparison, in their Maryland Pinhole Leak Survey, Kleczyk and Bosch (2008) found costs from the plumbing material failure repairs as high as \$25,000. Unlike the present survey, however, the study by Kleczyk and Bosch (2008) did not separate the costs associated with pipe failure and property damage. This Southeastern Community survey accounted for this factor, which might have resulted in the differences between the two studies. Furthermore, many households in the Southeastern Community cited using a preventive measure against corrosion, including whole house re-plumbing and installation of water softeners. Over 80% of residents of the Southeastern Community were satisfied

The follow-up survey data of residents in the Southeastern Community revealed that among three hypothetical plumbing materials (A, B, and C), the households preferred Material A (epoxy coating) followed by Material B (plastic). Material C (copper) was the least preferred material in the set. This result was derived based on each of the respondents' preference evaluation of the different plumbing material groupings. The preference ranking of the materials was the same across both Ordered Logit model specifications (with and without socioeconomics variables). Furthermore, the results were

water infrastructure.

plumbing materials.

with the water quality in their homes.

2004.

As in the previous model specifications, Material A is the most preferred plumbing material when the CA data is estimated, employing an Ordered Logit Model with and without socioeconomic characteristics. Material C is the least preferred plumbing material. Two plumbing material attributes are important in making the decision on type of pipes to be installed in a house: 'plumbing material installation time' and 'corrosion risk'. The regression coefficients as well as the computed odds ratios and probability estimates differ between the model specification with and without the socioeconomic variables.

For example, for Material A, the odds ratios are lower for all preference categories in the case of model specification with socioeconomic variables, category 'Very Strongly Preferred' has odds ratios ranging from 9.034 to 14.083 for model without socioeconomic variables and 7.522 for model including socioeconomic variables. This finding implies that the socioeconomic variables impact the discrimination level between the plumbing material preference valuations. For example, if a household has experienced previous cost of plumbing repairs and/or replacement, their preference valuation level is lower for a more corrosion prone plumbing material compared to material with an attribute level of 'corrosion proof'.

The marginal distribution of probability estimates (Table 13) has higher values for lower preference categories for Material C in the case of model specification without socioeconomic variables. For example, for Material C, 'Not Preferred' has probability distribution estimate ranging between 0.476 compared to 0.463 (with socioeconomic variables). The marginal distribution estimates for higher preference valuation categories are lower for Material A and B for model without socioeconomic variables. For example, for Material A, 'Extremely Preferred' has a probability distribution estimate ranging from 0.074 (without socioeconomic) compared to 0.117 (with socioeconomic variables). As a result, the inclusion of socioeconomic variables raises the level of preference for Materials A and B, while it decreases the level of preference for Material C.

In conclusion, although the inclusion of socioeconomic variables does not change the final preference ranking of the plumbing materials, it increases the estimated level of preference for Material A (epoxy coating) and Material B (plastic) by increasing the marginal probability distribution of estimates for the higher preference categories (i.e. 'Strongly Preferred'). The increase is the most pronounced in the case of Material A (model with socioeconomic variables) for which the 'Extremely Preferred' category has a probability distribution estimate almost twice as large compared to the model specification without socioeconomic variables (0.117 vs. 0.074). The respondent's previous cost of plumbing material repairs and replacement impacts positively the preference level for plumbing materials described by 'corrosion proof' attribute level. This finding implies that Materials A and B are more highly preferred when socioeconomic factors are taken into consideration. Households experiencing high costs of fixing corrosion related damage in the past are more likely to prefer and choose materials with lower corrosion levels. The decreased corrosion level implies lower future plumbing material failures, and therefore, lower costs associated with repairs of water-related damage.
