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## Table of Contents Executive Summary ............................................................................................................. .......................... 1 Introduction .................................................................................................................. ................................ 2 Program Description and Background ............................................................................................ .......... 2 Data Desc ription .............................................................................................................. ......................... 3 Data Prep rocessi ng ............................................................................................................ ....................... 4 Research Question: Public Incentive Programs for Ecosys tem Services .................................................. 4 Section 1 – Descriptive Statistics ............................................................................................ ...................... 6 Initial Descriptive Statistics ................................................................................................ ....................... 6 Time Series Analysis .......................................................................................................... ........................ 7 Section 2 – Model Hy pothesis Testing .......................................................................................... .............. 13 Assumptions and Limitations ................................................................................................... ............... 13 Individual Model Te sting Results .............................................................................................. .............. 14 All Installation Types by Cost per Square Foot over Time .................................................................. 15 Cost per Square Foot by Land Use Type ......................................................................................... .... 15 Costs per Square Foot by Insta ll Type and Land Use Type ................................................................. 16 Costs per Square Foot for Large Installations (> 10,000 sq ft) ............................................................. 18 Labor Costs per Square Fo ot by Land Use Type .................................................................................. 18 Section 3 – Conclusions an d Future Recommendations ............................................................................ . 20 Works Ci ted ................................................................................................................... .............................. 22 Appendix: Technical Analyses .................................................................................................. ................... 24



## Table of Figures Figure 1: Housing Price Index and the Durati on of the Ecoroof In centive Program..................................... 3 Figure 2: Histogram of Installa tion Costs per Square Foot ..................................................................... ...... 6 Figure 3: Size of Installa tions by Land Use Type .............................................................................. ............. 7 Figure 4: Installation by La nd Use Type (Gro uped Types) ....................................................................... ..... 8 Figure 5: Cost per Square F oot by Project Over Time ........................................................................... ........ 9 Figure 6: Scatterplot of Installa tion Costs by Program Year ................................................................... .... 10 Figure 7: Box plot of instal l cost by type and year ........................................................................... ........... 11 Figure 8: Cost per Square Foot by Land Use Type ............................................................................... ....... 12 Figure 9: Scatterplot of Cost data and Robust Regression Model Plot ....................................................... 15Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services iii Figure 10: SFR Installation Scatterp lot and Robust Regr ession Plot ........................................................... 16 Figure 11: Cost Scatterplot for New Installs fo r All Land Uses and Robust Regression Plot ...................... 16 Figure 12: Cost Scatterplot for Retro Installations for All Land Use Types and Robust Regression Plot .... 17 Figure 13: Cost Scatterplot for Single Family Residenc e Installations not Using Tray Type Technology and Regression Plot ............................................................................................................... ............................ 17 Figure 14: Cost Scatterplot for Large Installations (>10,000 sq ft) and Robust Regression Plot ................ 18 Figure 15: SFR Labor Costs per Square Foot Scatterplot and Robust Regression Plot (Non

‐ Tray Type) .... 19



## Table of Tables Table 1: Basic Descriptive Statistics on Installation Costs per Square Foot .................................................. 6 Table 2: Count and Total Ar ea by Land Use Type ................................................................................ ......... 7 Table 3: Count of Installations by Land Use Type and Sum of Area ............................................................. 8 Table 4: Count of Installati ons by Land Us e and Year .......................................................................... ....... 11 Table 5: Median Cost per Squa re Foot by Land Use Type ......................................................................... . 11Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 1 

## Executive Summary The City of Portland Bureau of Environmental Servic es’ Ecoroof Program instituted an incentive that supported installations of ecoroofs for five years from 2009

‐ 2014. The program collected extensive data from the participants in the ecoroof incentive. On e goal for the program was to support the use of ecoroofs by increasing the extent and rate of installation. The program also had the goal of reducing the cost of ecoroof installation through economies of scale and maturation of the industry through increased adoption of the technology. This report sh ares the results of an analysis of these data to understand if there was a change in the per

‐ unit cost to install ecoroofs. We conclude that the data do not support a statically significant relationship between the ongoing incentives distributed during the program and the installation per unit costs. This relationship was evaluated through a variety of techniques. We concl ude that there is not a statistically significant relationship because either the relationship between the incentive and ecoroof costs is not direct or strong enough to affect a change, or that the data collected from participants in the program were not consistent enough to support statistical relationships. Despite these conclusions, we find that the prog ram dataset provides impo rtant information on the distribution of costs by installation type and land use. Descriptive statistics indicate that median installation costs range from approximately $6.00 per square foot for single

‐ family residences up to $15.55 per square foot for institutio nal installations. The program included over 330,000 square feet of ecoroof installations with a total private investment of over $6 million. The data collected through the incentive support se veral conclusions regarding the incorporation of ecoroof technology into the broader Portland communi ty. First, these data help to facilitate a public understanding of the types and variations of ecoroof installation costs in the Portland area which helps guide future technological development. Second, th e variation in cost data suggests other possible program tools may be more effective in increasing ecoroof adoption, such as credit and market based systems or reverse auctions. Finally, these data pr ovide a strong foundation and lessons learned for future cost evaluation projects.Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 2 

## Introduction The City of Portland’s ecoroof incentive was developed as a means to expand the City’s green stormwater management infrastructure by increasing the frequency and affordability of installing green roofs on private and public buildings within the City. Additionally, the City hoped that the incentive would promote the development of a small, local, in dustry of contractors and installers by decreasing installation costs while the industry developed. In an effort to asse ss the success of the incentive, the City collected data on the installation costs of ea ch participating project. This report presents an evaluation of these data and attempts to identify re lationships which suggest an installation cost benefit from the incentive. The primary benefit being assessed is a decreasing per

‐ unit cost to install these facilities over time. The main hypothesis being tested in this analysis is whether or not these data suggest that the incentives program has caused a change in the per

‐ unit cost over the duration of its implementation. Testing of this hypothesis includes time series analyses and requires some assumptions about the role of the City’s incentives in the larger market. 

### Program Description and Background The Ecoroof Program grew out of the Sustainable Stor mwater Management Division that was formed in 2001. Program activities were focused on demonstrat ion projects, technical a ssistance, and monitoring for stormwater performance. The Ecoroof Program was expanded in 2008 by the Grey to Green Initiative, wh ich provided a direct financial incentive of $5 per square foot to boost implementation. During this time, the Ecoroof Program hosted annual seminars and sympos ia to build awareness and connect willing property owners with ecoroof professionals. Leading researchers and poli cy makers from Portland, and around the globe, were invited to participate and share the most curre nt information on successful green roof technology. The incentive helped to fund 134 projec ts with $1.9 million over 5 years. In all, the ecoroof incentive allowed the program to leverage multiple partnerships, resources, and funding opportunities. The primary goal of the ince ntive was to reduce upfront costs so that more ecoroofs would be used in Portland and to jump start a forming industry. The Ecoroof Program provided the incentive during a unique period in the US housing market and for the economy as a whole. The Portland housing market increased steadily through, and out of, the short 2001 recession but beginning in 2004 the rate of home price increa sed quickly. Home prices, as measured in the Case

‐ Shiller Home Price Index, increased ov er 80% from 2000 to its peak in the beginning of 2008 when the Great Recession began. From this period forward home prices quickly fell. The Portland Ecoroof Incentive program data begins in 2009 and runs through 2014. Figure 1 shows the housing price data along with the duration of the Ec oroof data. As the index shows, housing prices go through a U

‐ shaped curve over this time window. This curv e may have influenced ecoroof costs and, if so, influenced them in two directions. This creates a challenge for analysis of the relationship between the real estate market and ecoroof costs.Figure 1: H o Through o roof. Gre e here. Fur t Intensive roofs hav e installati o 

### Data D e The data s and Sept e identifica t Commer c Size (sf), a which inc Barrier, D Materials which fur t the instal It is impo r Some we r 0 2 0 4 0 6 0 8 0 10 0 12 0 14 0 16 0 18 0 20 0Case‐ShillerPortlandHomePriceIndex

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o ut this docu m e n roof is a c o t her, there is installations e shallower s o ns are the ty


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is analysis co For each ins t s within the d nal, Mixed U s o n Date. Ad d e nts and inst a a in Channel, P o r, and Other e d the costs a ight be uniq u that the typ e e d “do

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nsists of cost t allation, add d ataset. Thes e s e, and Hosp i d itionally, a c o a llers were a s P rotection B o Costs. Addit ssociated wi t u e to a partic u

e and nature o u rself” install a200420052006

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o f Cost Analy s d, Bureau of r oof Incentive P p referred, bu t r ch literature , e nsive and e x b lic spaces, t r r bs, grasses o

data for 105 itional descri e data includ e i tal), Installat o st breakdo w s ked to repor t o ard, Growin g

ional notes w t h the ‘Other u lar install.

o f ecoroof in s a tions on pri v20072008

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Costs’ categ o

stallation va r v ate residenc e20092010

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t al Services e same as an e o are used int o of types (R o p substrates. ler vegetatio n

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a ta. e rEcoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 4 institutional installations that appr oached 30,000 square feet. The differe nces in costs, associated with these extreme variations, appear in the data and contribute to its var iability. Larger installations may have required cranes or other mechanical tools not ty pically used for smaller installations, and may have also used higher cost prevailing wage labor. The sm aller installations may have used volunteer labor and simple tools. These factors impacted the cost data, and our ability to assess change over time. 

### Data Preprocessing Throughout the initial cost analysis, several decisi ons were made which had impacts on how the final analysis would be conducted. While other options were explored, the following decisions resulted in the most appropriate application of these data to the co st analysis process. Firs t, the installation costs that were considered did not include the membra ne cost. When included, the membrane cost contributed significantly to the noise and outliers of the dataset, the removal of these costs provided the first step in normalizing the comparison between data. Second, the six land use categories were re

‐ evaluated and generalized into three new categories which were similar in design and installation criteria, but contained more sample points, which incr eased the potential to identify significant trends. The three new groups are Single Family Residence (SFR) containing 59 installations; Mixed

‐ use, Commercial, and multi

‐ family residence (MXDMFR) containing 36 in stallations; Institutional and Hospital (INST) containing 10 installations. While an init ial analysis was conducted which assessed the potential for trends in each of the land use categories through out the duration of the project, only the Residential category had sufficient samples during the initial analys is, across the entire timespan of the project, to support a potentially significant trend. Third, severa l outliers were identified and investigated, which resulted in the implementation of corrections to th e initial data collection or transcription process, further helping to support the analysis. These pre

‐ processing steps were necessary to provide the highest potential for identification of trends within the dataset. 

### Research Question: Public Incentive Programs for Ecosystem Services The management of stormwater, air and water pollutan ts, and urban heat island effect are three classes of environmental goods and services that ecor oofs provide (Rowe 2011). These environmental goods and services are supplied by the natural biophysica l system as ecosystem se rvices, until development occurs (Bolund and Hunhammar 1999; Hassan et al. 2005). With development, replacement of these services is required, normally this is accomplishe d through engineered solutions. In the context of impervious surfaces, new conveyance and treatmen t facilities are required for stormwater. Ecoroofs represent a hybridization of engineered and natural systems to replace services lost to development while retaining the benefits of urban development. Th is is a form of urban “d omestication” of natural systems to better serve human communities (Kareiva et al. 2007). The benefit of ecoroofs has been a growing object of empirical and modeled research. A recent meta

‐ analysis of existing research identified a wide suite of benefits from these green roof technologies (Rowe 2011). These benefits include the above mentioned st ormwater, air and water pollution filtration, and urban heat island effect reductions. For example, one square meter of green roof removes the same amount of particulate matter as that pro duced by the average automobile (Rowe 2011:2102).Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 5 Stormwater reductions can range from 50

‐ 100% depending on local climactic and design considerations (Rowe 2011:2104). Other benefits include reducing build ing heating and cooling energy requirements, urban noise, and reduced life

‐ cycle costs of roofing materials. Longer range modeling of green roof installation shows large reductions in lif e cycle costs. Using Washington, DC’s 20

‐ 20

‐ 20 initiative to develop 20 million square feet of green roofs, Niu et al. found that green roofs would be 30

‐ 40% less costly in net present value (2010). Based on this modeling, the br eak even for using green roofs over conventional roofing would occur after 7 years. Based on these findings, local jurisdictions are seek ing policy tools to expand the rate and extent of ecoroof adoption. For ecosystem services and enviro nmental programs there are several existing policy tools. These range from command type tools that require particular design standards, to voluntary subsidy or incentive programs and on to market ba sed solutions (Tietenberg 2006). Green roof programs have focused on the first two options, with more applying incentive programs (Carter and Fowler 2008; Mees et al. 2014). The City of Port land fits these models through its Ec oroof incentive. This leads to the basis of the research question, how effective can the incentive be at increasing the adoption of ecoroof technology? More specifically for this report, the hypoth esis is: The public in centive reduced the per

‐ unit installation costs for ecoroofs in the City of Portland while it wa s active. This hypothesis is based on an assumption that the incentive provides a price effect through ch anging demand, increasing quantities of installation, and developing benefits from economies of scale and industry maturity. This process assumes the following steps: First, the subsidy shifts the demand curve to the right where more quantities of goods are produced for the same price. Next, this shift in the demand curve is realized by consumers (or building owners) as a decrease in price per square foot. Finally, the increase in the quantity of installations then introduces econom ies of scale and maturation in the industry. Economies of scale and maturity are seen through increases in contractor firms, improvement of installation skills, and decreases in material and labor costs as the technology moves fr om an emerging technology to a common application. These assumptions are support ed by empirical data showing US costs of installation are higher in comparison to conventional roofs, while in Europe the two types are marginally similar (Blackhurst, Hendrickson, and Matthews 2010 :142). As the European market for ecoroofs predates that of the United States, this obse rvation suggests policy measures may close the gap between the two technology types. The following sections review descriptive statistics from the City’s program to understand the general trends and distributions of values in the dataset. The first section provides a basis for characterizing the cost of installations across multiple land use and installation types. While these data show some mixed results, they are informative for future program deve lopment. The next section seeks to test the above hypothesis using several different approaches. The st atistical models do not re ject the null hypothesis that there is no effect. Therefore we cannot settle the question of whether the incentive had an effect on installation costs. However these data provide in sight on possible progress in other policy tools. The final section concludes by reviewing what was learne d from the analyses and proposes several options for future research and policy development.

## Sectio n Initial D Followin g in these d phase of t around t h the entir e without i n 

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4 4,186Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 9 Table 3 provides a summary of the count, area and total cost for each land use grouping. 1 Of these installations, nine are 10,000 square feet or larger. Institutional large installations provide 44,621 square feet of green roof and multi

‐ family/MXD/commercial installations provide 151,595 square feet. These large installations comprise approximately 60% of the area installed through the incentive. Of all of the installations, 61 were new and 44 were retrofit.

Figure 5: Cost per Square Foot by Project Over Time A scatterplot of these data suggests that the SFR inst allations may show a slight decline. Figure 6 shows the distribution of installation costs for each year in a scatterplot and by land use type. Also included are simple regression lines to indicate any directionality – though not with a measure of significance.

1 Note that some totals vary slightly between figures as the analysis moves to the hypothesis testing. In the statistical analysis some cases were removed after review with City staff, others were removed based on outlier analysis. The data presented here ha s the larger dataset before excludin g any data for anal ytical purposes. $0.00 $2.00 $4.00 $6.00 $8.00 $10.00 $12.00 $14.00

2009 2010 2011 2012 2013CPSFw/oMembrane

Single Family Residence CPSF All Land Use CPSFFigure 6: Sc Another l o year of t h whiskers the dark l install, ca accompa n across th e

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o ok at these e program. T r each to the e ine in the mi d using just th e n ies Figure 7 e years of th e

r epared for C t allation Costs b data is prese T he box mea s e nd of the ra d dle of the b o e median to p a nd shows t h e incentive.

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2011

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12 rEcoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 13 

## Section 2
– Model Hypothesis Testing Assumptions and Limitations The starting hypothesis for this project is that the Ci ty incentives for ecoroof installation allowed for an increase in installations and a decrease in the per

‐ unit cost. Section 1 reviewed the descriptive statistics to begin exploring this hypothesis. The descriptive da ta revealed that for all installations there did not appear to be a decrease over time. There may be so me decreases over time, however, within subsets of installation based on the land use, size, and technolo gy used. The descriptive statistics also revealed some of the technical challenges for regression models with the installation data. Before discussing the models and techniques used in this report, the general challenges for statistical modeling need to be addressed. Once this background is established, the particular model choices can be explored in more detail. One of the most common regression techniques for this type of analysis is the ordinary least squares (OLS) (Burt and Barber 19 96). Regression techniques such as OLS are based on four primary assumptions: normal distribution of variables; a linear relationship between dependent and independent variables; low or no measurement e rror; and errors are homoscedastic (Osborne and Waters 2002). The first assumption means that the frequency of the variable observations centers on a mean value with equal increments of observations to the right and the left of the mean. The histogram in Figure 2 shows an example of examining a variable for normal ity. The figure shows a skewedness that must be addressed to perform an OLS regression. This can be accomplished with transformations. Transformations are the use of an equation to cha nge the value of each ob servation such that the frequency becomes normal. For example, by raising th e cost per square foot by 0.20, the distribution approximates normality, although this also makes interpretation of results more challenging as the coefficients from the regression model become relative , rather than absolute. As observed in Figure 2, normality in distributions is a challenge for these data . We try to address this in the models below with several techniques. Another related challenge to norm ality is the existence of outliers. Outliers have been a challenge in these data and we have remove d some and corrected others as identified by the project team. The second assumption (of a linear relationship) is a requirement based on the structure of OLS or multiple regression techniques. If the relationship is curvilinear it can be managed, but we did not detect this as a problem in these data. The third assumption (low or no measurement error) is a challenge in this project. As discovered with the City of Portland team, the self

‐ reporting of data appears to be a large and uneven source of error in the data. There is no technique to address this except to try and subset these data into categories where at least the error might be standardiz ed. However, this is a large limitati on of this study and needs to be kept in mind as the results are reviewed.Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 14 The final assumption on error homoscedasticity appe ars not to be a challenge in the models presented below. This assumption is based on the idea that the distribution of error is consistent across the analysis and would be violated if there were time windows in which the distribution was significantly tighter than others. We do explore the distribu tions of error as we evaluate various model and regression techniques. While we have identified some tools to correct thes e data to meet the four assumptions, some of the distributional issues are being managed through tr ansformation techniques. Alternatively there is a family of regression techniques known as robust regression. Robust regression methods have been developed to address the problems of outliers and to some degree issues of distributions (Andersen 2008). Several techniques are available for robust regression, based on th e challenges faced in this study we have used M

‐ estimator as the primary technique and this is supported by empirical research as a good fit for the data challenges present in this study. Several models were crafted based on the subset of data used as well as the management of these data through transformations to address distributions and outliers. The following models were tested:

 All installation types, cost per square foot over program

 Cost per square foot over program by land use type

 Cost per square foot over program by land use type and installation type

 Cost per square foot over program for large installations (>10,000 square feet)

 Labor costs per square foot for all installation types

 Labor costs per square foot by land use type The goals for each of these models are to explore a re fined subset of the data in an attempt to address the limitations discussed above. Th e subsets allow for testing that co ntrols for some error types, or provide subsets which show better distributions. However this can also introduce new problems. By creating subsets of these data, the number of observations are reduced which can introduce new sources of error which represent a limitation for the analysis. As found in the descriptive statistics, the single family residence installations provide the mo st observations and thus allow for subsets on multiple variables. Other land use types do not have a large enough set of observations to address multiple variables. This strategy has allowed us to detect some new possible trends in these data. 

### Individual Model Testing Results For all of the following models, we were not able to reject the null hypo thesis. We present these findings to show how we tested these data. But the conc lusion overall in these statistical tests is that we cannot claim the program’s hypothesis of reducing per

‐ unit costs can be supported or rejected. The Appendix provides detailed regression tables for the models tested.All Insta l Initial OL S significan t positive c means th a tested hy

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## Section 3
– Conclusions and Future Recommendations This section briefly reviews the analytical results from Section 2, the interpretation of these results, and then shifts to understand what info rmation these data do provide. Th is section also presents several data, program, and policy recommendations. The results of the various models were not found to be statistically significant. Therefore the null hypothesis cannot be rejected. This means these data do not support the conclusion that the incentive decreased costs over time. There are several reasons why the hypotheses may not be supported. First is the possible lack of a causal relationship in the economic dynamics behind the cost of ecoroof installations. These costs may not be affected by the City’s incentive. As discussed in the first section, the proposed causal relati onship was based on seeing increased ec onomies of scale and maturity in the ecoroof industry. While over 300,000 new square feet were supported with this program, 60% of that area was accomplished with 9 large projects. This may have limited the ability of economies of scale to be realized across the diverse set of installations. It is also possible that the underlying costs benefited from economies of scale but these benefits did not influence much of the total costs. We tested for the maturation of the industry by using labor costs as a measure of possible efficiencies. Unfortunately, thes e metrics also failed to support a statistically significant relationship. One limitation for this analys is was that the labor data was not complete across the entire dataset. Another reason for the possible lack of a relationship is that the set of projects included in the data collection are a unique sample of all projects installe d in Portland. It is possible that property owners who chose to participate in the program were skewed by the available incentive, leading to a sample of projects with unique or non

‐ representative costs. While the descript ive data does not suggest a per unit skewedness, there is a possibility of selection bias base d on the incentive. To adjust for this, future data collection would need to randomly sa mple installations not participating in the incentive program to survey for similar cost data. The last challenge for the analysis is data quality. As the descriptive statistics review was developed with City staff it was acknowledged that the reporting of the data from participating installers was not consistent. There was variation in how costs were in cluded or excluded in the reporting, as well as how costs were categorized. We suspect this variation had a powerful impact on the data. It increased outliers and skewed data distributions. We attempte d to control for this by subsetting data into categories where the error may have been more uniform, however these methods were also unsuccessful in the identification of statistically si gnificant relationships. These efforts also created subsets of data with fewer cases and thus, further complicated developing statistical tests. These two issues do not mean the data is not of some value for the City in evaluating the program. The data collected around these insta llations provides a valuable snapsh ot of the economics of ecoroof installation. This is a useful tool for future pr ogram development and policy adoption. Based on our review of the data we offer the followi ng conclusions and their implications.Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 21 Conclusion 1: Data from Program Supports Better Policy and Public Information Environmental programs to incent landowners or developers are often hampered by “information asymmetry” (Ferraro 2008). Information asymmetry is the situation where landowners or developers better understand the financial impacts of proposed regulations on their practices than regulating entities. This higher quality information allows for more successful negotiation to reduce costs for regulation as the agency often does not know the true “cost of doing business.” By collecting these data, the City has a better understanding of how costs are distributed through the city, and can more appropriately compare these to othe r conventional costs. These conclu sions have the same caveats as noted above in the data quality discussion. But we be lieve these data to be insightful at this level. Further, this first phase of data collection can be seen as a pilot for further data collection. A key role for government in speeding innovation and adoption of new environmental technology is to reduce information costs and make the findings from data a public good for all parties to use (Jaffe, Newell, and Stavins 2005). Findings from this program should be sh ared with the public and participating contractors to grow the body of knowledge among practitioners. Conclusion 2: Cost Data is Highly Variable Within and Across Installation Types The descriptive statistics show that installation costs vary considerably . This is true within, and across, land use types. We also did not see that variability de clined over time. This difference means that some building owners have very low cost installations (typ ically single family) and others have higher costs (larger installations and institutional land uses). When large differences in cost are known to exist, one policy tool that can be effect ive is market based systems (Carter and Fowler 2008:154). Conclusion 3: Data Collection Improvements Can Expand Usefulness of Program As the previous two conclusions have shown, usin g the incentive to collect cost information from contractors is itself a public benefit. Further deve loping the cost data collection protocols can improve the quality and extent of the data for future evaluations. While this research did not directly review data collection practices, the team did discuss ch allenges experienced through the program. Self

‐ reported data requires more protocols to guide the respondents. This is especially true for data that varies greatly on how the technology is used. For example the tray

‐ type installations appeared to embed costs differently than other technologies. Another challe nge was making sure that data was completed and checked for accuracy. Labor data, membrane costs, a nd other components were inconsistently reported or were missing from the data. Developing more in volved protocols or instructional materials may improve data quality. Random selections of reports sh ould be reviewed by staff over the phone or in person to assess data quality as well. This rando m calling would also provide an opportunity for qualitative data collection. A survey could be developed to allow for open

‐ ended questions to explore drivers in costs or installation challenges. The resu lts of these surveys and interviews could change how data is collected to better capture the information needed.Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 22 

## Works Cited Alma, Özlem Gürünlü. 2011. “Comparison of Robust Regression Methods in Linear Regression.” International Journal of Contemporary Mathematical Sciences 6(9):409–21. Andersen, Robert. 2008. Modern Methods for Robust Regression . Los Angeles: Sage Publications. Blackhurst, Michael, Chris Hendricks on, and H. Scott Matthews. 2010. “Cost

‐ Effectiveness of Green Roofs.” Journal of Architectural Engineering 16(4):136–43. Bolund, Per and Sven Hunhammar. 1999. “Ecosystem Services in Urban Areas.” Ecological Economics 29(2):293–301. Burt, James E. and Gerald M. Barber. 1996. Elementary Statistics for Geographers. New York: Guilford Press. Carter, Timothy and Laurie Fowler. 2008. “Estab lishing Green Roof Infrastructure Through Environmental Policy Instruments.” Environmental Management 42(1):151–64. Ferraro, Paul J. 2008. “Asymmetric Information and Contract Design for Payments for Environmental Services.” Ecological Economics 65(4):810–21. Hassan, Rashid M., R. J. Scholes, Neville Ash, and Millennium Ecosystem Assessment (Program). Condition and Trends Working Group. 2005. Ecosystems and Human Well

‐ Being : Current State and Trends : Findings of the Condition and Trends Working Group of the Millennium Ecosystem Assessment . Washington, DC: Island Press. Jaffe, Adam B., Richard G. Newell, and Robert N. Stavins. 2005. “A Tale of Two Market Failures: Technology and Environmental Policy.” Ecological Economics 54(2–3):164–74. Kareiva, Peter, Sean Watts, Robert McDonald, and Tim Boucher. 2007. “Domest icated Nature: Shaping Landscapes and Ecosystems for Human Welfare.” Science 316(5833):1866–69. Krzywinski, Martin and Naomi Altman. 2014. “Points of Significance: Visualizing Samples with Box Plots.” Nature Methods 11(2):119–20. Mees, Heleen LP et al. 2014. “A Method for the Deliberate and Deliberative Selection of Policy Instrument Mixes for Clim ate Change Adaptation.” Ecology and Society 19(2):58. Niu, Hao, Corrie Clark, Jiti Zhou, and Peter Adriae ns. 2010. “Scaling of Economic Benefits from Green Roof Implementation in Washington, DC.” Environmental Science & Technology 44(11):4302–8. Osborne, Jason and Elaine Waters. 2002. “Four Assumptions of Multiple Regression That Researchers Should Always Test.” Practical Assessment, Research & Evaluation 8(2):1–9.
R Core Team. 2012. R: A Language and Environment of Statistical Computing . Vienna, Austria: R Foundation for Statistical Com puting. Retrieved (http://www.R

‐ project.org/).Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 23 Rowe, D. Bradley. 2011. “Green Roofs as a Means of Pollution Abatement.” Environmental Pollution 159(8):2100–2110. Tietenberg, Thomas H. 2006. Environmental Economics and Policy . 5th ed. Boston: Pearson/Addison Wesley.Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 24 

## Appendix: Technical Analyses Following the evaluation of the descriptive statis tics, the analysis team was concerned that the distribution of the variables and the change of th e mean over time would not support a significant finding. We chose to explore thes e concerns through several OLS mode ls and robust regression models (M

‐ estimator). Due to the number of observations and the distributions we focused our models on single family residences where the assumptions of cost error estimation might be more similar, reducing measurement error effects. The following tables work though the several models we have developed to explore these data. The first set of regression tables are the OLS results for three models with cost per square foot without membrane as the dependent variable: a univariate model with the program month; a multivariate model with program month and size of the installation in square feet, and a multivariate model adding a dummy variable for installation type to the previo us model. The data was examined and identified skewedness in the dependent variable. Using the Box

‐ Cox technique a power transformation was applied. Initial plots identified outliers that were reasonable to remove. Based on these analyses we are not confident that the program duration and the incentives provided during it resulted in a change in co st per square foot for installation s. As discussed in the conclusion there are a number of ways to understand this. Following are the resultant tables for the three models using this single family residence data from the ecoroof master dataset:
MODEL 1: Univariate CPSF and Program Month
=============================================== Dependent variable:

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ cpsf_wo_memb0.2

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ progmo ‐ 0.0004 (0.002) Constant 1.475*** (0.061)

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Observations 55 R2 0.001 Adjusted R2

‐ 0.017 Residual Std. Error 0.186 (df = 53) F Statistic 0.073 (df = 1; 53)
=============================================== Note: *p<0.1; **p<0.05; ***p<0.01Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 25 MODEL 2: CPSF by Size and Program Month
=============================================== Dependent variable:

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ cpsf_wo_memb0.2

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ progmo 0.002 (0.002) sizesf

‐ 0.0001** (0.0001) Constant 1.479*** (0.058)

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Observations 55 R2 0.109 Adjusted R2 0.075 Residual Std. Error 0.178 (df = 52) F Statistic 3.188** (df = 2; 52)
=============================================== Note: *p<0.1; **p<0.05; ***p<0.01Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 26 MODEL 3: CPSF by Size, Program Month and Install Type =============================================== Dependent variable:

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ cpsf_wo_memb0.2

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ progmo 0.002 (0.002) sizesf

‐ 0.0001** (0.0001) newdummy

‐ 0.002 (0.050) Constant 1.480*** (0.062)

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Observations 55 R2 0.109 Adjusted R2 0.057 Residual Std. Error 0.179 (df = 51) F Statistic 2.085 (df = 3; 51)
=============================================== Note: *p<0.1; **p<0.05; ***p<0.01Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 27 In addition to the OLS models we attempted robust techniques to both examine outliers and leverage points as well as to assess the co efficients and standard errors under these methods. Due to the small dataset we chose M

‐ Estimator as the most appropriate method (Alma 2011). The results are similar to OLS in that coefficients are very close to 0, thus suggesting the null hypothesis cannot be rejected. The power transformation should reduce this number as the transformation would approach a zero slope further to the right, on higher dependent values. Regardless, the low coefficient is still too low.
MODEL 4: Robust (M
‐ Estimator) CPSF by Program Month
=============================================== Dependent variable:

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ cpsf_wo_memb0.2)

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ progmo ‐ 0.001 (0.002) Constant 1.469*** (0.070)

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Observations 58 Residual Std. Error 0.243 (df = 56)
=============================================== Note: *p<0.1; **p<0.05; ***p<0.01
MODEL 5: Robust (M
‐ Estimator) CPSF by Program Month and Size
=============================================== Dependent variable:

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ cpsf_wo_memb0.2

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ progmo 0.002 (0.002) sizesf

‐ 0.0001*** (0.0001) Constant 1.466*** (0.058)

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Observations 55 Residual Std. Error 0.186 (df = 52)
=============================================== Note: *p<0.1; **p<0.05; ***p<0.01Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 28 MODEL 6: Robust (M
‐ Estimator) CPSF by Program Month, Size and Install Type =============================================== Dependent variable:

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ cpsf_wo_memb0.2

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ progmo 0.002 (0.002) sizesf

‐ 0.0001** (0.0001) newdummy 0.006 (0.050) Constant 1.463*** (0.062)

‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Observations 55 Residual Std. Error 0.183 (df = 51)
=============================================== Note: *p<0.1; **p<0.05; ***p<0.01
The analysis for this project was conducted in the R statistical scripting and analysis language using R Studio for a user interface (R Core Team 2012). The MASS and ggplot2 packages were used to support this analysis as well. The following code was used to generate these analyses from Section 2. Data was subsetted to new dataframes as needed for these anal yses. The primary subsetting is listed below with dataframe name in parentheses:
 Observations with SFR Land Use Type (cleandataSFR)
 Large Installations => 10,000 sq ft (largeinstalldata)
 New installations (cleandata.allnewinstall)
 Retro installations (cleandata.allretroinstall)
 Tray type installations (traydata) Regression Analyses: Figure 9: Scatterplot of Cost data and Robust Regression Model Plot rlm((cleandata$cpsf_wo_memb^.2)~cleandata$progmo) Figure 10: SFR Installation Scatterplot and Robust Regression Plot rlm((cleandataSFR$cpsf_wo_memb^.2)~cleandataSFR$progmo) Figure 11: Cost Scatterplot for New Installs for All Land Uses and Robust Regression Plot rlm(sfr.notray$laborsf^.18 ~ sfr.notray$progmo)Ecoroof Cost Analysis Prepared for City of Portland, Bureau of Environmental Services 29 Figure 12: Cost Scatterplot for Retro Installations for All Land Use Types and Robust Regression Plot rlm((cleandata.allretroinstall$cpsf_wo_me mb^.2)~cleandata.allretroinstall$progmo) Figure 13: Cost Scatterplot for Single Family Residenc e Installations not Using Tray Type Technology and Regression Plot rlm(sfr.notray$cpsf_wo_memb^.18 ~ sfr.notray$progmo) Figure 14: Cost Scatterplot for Large Installation s (>10,000 sq ft) and Robust Regression Plot rlm((largeinstalldata$cpsf_wo_me mb^.5)~largeinstalldata$progmo) Figure 15: SFR Labor Costs per Square Foot Scatterplot and Robust Regression Plot (Non

‐ Tray Type) rlm((cleandataSFR$laborsf^.2)~cleandataSFR$progmo)