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Modeling Social Equity in Energy Consumption Using Digital Twins
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13 September 2023
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Abstract
This research examines the impact of social equity on energy consumption. We constructed a digital twin for residential energy consumption by enriching the synthetic population with real-world surveys and feeding them with other environmental and appliance data to the energy modeling framework. We analyzed household hourly energy consumption data from Albemarle County and Charlottesville City in Virginia, USA, for the year 2019. We used clustering analysis to identify patterns in social equity and energy consumption. The results demonstrated the impact of different residential attributes on energy poverty. Statistical analyses, including ANOVA and Chi-Squared tests, were conducted to test for significant differences between racial groups in quantitative and categorical variables. The study found that race is significant in determining the location and quality of housing. People of color often live in areas with higher pollution and less access to green spaces. Additionally, income levels and the age of the house are influential factors in determining energy efficiency. Future work should focus on collecting and analyzing data at the country level and using qualitative data collection methods to gain a more comprehensive understanding of social equity issues concerning energy consumption. Overall, this study provides valuable insights into the relationship between different residential attributes and energy consumption, which can inform policy development to promote more equitable and sustainable communities.
Keywords:
Subject: Engineering - Other
I. INTRODUCTION
Climate change is an existential threat. Many countries have pledged to transition to green and sustainable energy by 2050. This step ensures the global temperature rise does not exceed 1.5 2.0-degree C. Among many factors contributing to climate change, carbon emissions account to 60% of humanity’s overall ecological footprint. In the United States, contributions from residential energy alone are projected at 17% of annual greenhouse gas emissions (GHG). Reducing energy demand in the residential sector is one of the crucial factors for achieving the goal of reducing GHG emissions. One of the ways of reducing residential consumption is retrofitting building stock.
Retrofitting building stock helps reduce energy consumption and provides a safe and healthy place for people to live. Many works have stressed the importance of retrofitting building stock to mitigate climate change, address energy poverty and inequity, and reach net-zero emissions [15]. Based on U.S. Energy Information Administration (EIA) [9], 1/3rd of the U.S. lives in energy poverty, and 11% keep home in unhealthy conditions just because they cannot afford to pay their electricity bills. Although we have federal policies and incentives for retrofitting, these numbers look scary.
The existing policies through federal grants and programs focus on extremely low-income households to reduce energy consumption. Other policies, such as sustainable energy loans, benefit higher-income households who can afford monthly mortgage payments. However, such strategies fail to identify and design policies for fairness and social equity. Researchers have emphasized the importance of social equity in residential energy [1,2,3]. Some of the demographic attributes suggested in these research works are race, income, and area type.
Although the importance of social equity is undeniable, federal programs struggle to develop policies based on insights due to a lack of understanding of residential energy consumption at a higher granular level. In addition, there is necessary to uncover social and economic demographic patterns in energy poverty at a larger scale. Combating these issues requires high-resolution data at the household-appliance level while addressing privacy concerns and confidentiality aspects. A digital twin is a one-stop solution to solve this problem [16]. A digital twin is a virtual model that can be used to understand the behavior of the real world. These models are developed using real and synthetic datasets spreading across spatial and temporal domains. Digital twins are used in various domains, such as the aviation industry, medical domain, and so on, to run simulations on a virtual platform instead of running them directly in the real world and causing havoc. Here, the synthetic population acts as a proxy for the real population.
Our contribution to this paper is as follows:
- A digital twin development of synthetic residential energy consumption data for Albemarle-Charlottesville region.
- Analysis and modelling of social equity constraints to understand the impact of equity in energy poverty through cluster analysis and statistical analysis.
Paper organization. First, we introduce our methodology in Section II. Second, we provide our results and insights in Section III. Next, we discuss our limitations and future work in Section IV. Finally, we pitch our discussion and conclude in Section V.
II. METHODS
Our methodology is divided into three steps: (i) Data Extraction, (ii) Cluster Analysis, and (iii) Statistical Analysis as in Figure 1.
A. Data Extraction
We begin by collecting the data for our analysis as in Figure 2. Here, we use the digital twin of the US population from the Network Systems Science and Advanced Computing (NSSAC) synthetic population [8]. The base population of the digital twin is developed using a 5% sample of complete records from Public Use Microdata Sample (PUMS) [11]. In this work [8], each person P from household H in a residential location RA is assigned an activity sequence A from the list of activities, where each activity has a type TA, start time s, duration d and activity location LA using two-stage fitted value method [5]. The activity model is constructed based on the National Household Travel Survey (NHTS) [12], the Multinational Time Use Study (MTUS) [6], and the American Time Use Survey (ATUS) [10]. We use the base population data of the household along with the activity information that captures the demographic attributes, household characteristic features, and in-house activity. This information also provides the occupancy patterns in the home.
Next is the enrichment step for energy information, where we map the attributes from the Residential Energy consumption survey (RECS) [9] to the synthetic population. This survey consists of real samples representing the US population for household characteristics and attributes, appliance information, and other energy-related information. The problem formulation for this mapping is given in Problem 1.
Problem 1: Let H be the set of households in the synthetic population. Let S and R be the set of RECS survey households. Let Aiv = {a1, a2. . . , ak} represent the common demographic and household attributes between S and R. The objective is to enrich S with appliance and residential at- tributes from R, Adv = {b1, b2. . . , bj} , where the distribution of Aiv closely matches between S and R.
The mapping between S and R helps to enrich S with appliance information and residential attributes from R, where the distribution of Aiv is similar between S and R. The common attributes Aiv are called the independent variables, and the mapped appliance information and residential at- tributes, Adv, are called the dependent variables. We enrich S by using multivariate conditional inference trees in R, where the conditional tree is built for multiple independent and dependent variables simultaneously. Conditional inference trees are developed by recursive binary partitioning where the node split is based on the statistical significance between the independent and dependent variables [13].
We modify the energy model by Swapna et al. [4] to develop high-resolution hourly energy consumption data for each household. The energy demand modeling framework consists of individual appliance models that simulate hourly energy use of different end-uses such as HVAC, lighting, refrigerator, hot water use, major appliances such as dishwasher, clothes washer, clothes dryer, and miscellaneous plug load. This model also takes in other information from other datasets such as (i) weather data, (ii) irradiance data, (iii) appliance rating and other information, (iv) insulation levels, (v) water temperature, and (vi) water usage data. Depending upon household occupancy and behavior, energy use is generated hourly for each household-level appliance.
B. Cluster Analysis
The problem formulation for the first set of analysis is given in Problem 2.
Problem 2: Let H be the set of households in the enriched synthetic population. Let E be the corresponding energy consumption values and let A = {a1, a2. . . , ak} represent the demographic and household attributes for H. The objective is to group H based on similarities in E and A to identify the set of attributes Ae, where Ae⊆A, that contribute to energy poverty.
To extract insights from the data, we explored various clustering algorithms, including K-prototype and HDBSCAN. Prior to clustering, an exploratory analysis was conducted with Principal Component Analysis (PCA) to see if there is enough merit in using Principal Components since the ratio of features (f = 33) to observations (n=58,283) is more than satisfactory in mitigating the curse of dimensionality. As there were no clear loadings on the principal components, we decided not to use principal components in reducing the dimensionality of the data as no additional value was added.
K-prototype was the clustering algorithm decided on due to its capability in handling numeric and categorical data. The algorithm is an extension of the popular K-means algorithm by utilizing a matching dissimilarity measure for categorical data.
Figure 2.
Framework to extract hourly residential energy consumption data at the household level. For any given county and date, the enriched synthetic population, along with environmental and appliance data, is fed to the energy model to produce highly granular synthetic residential energy consumption data.
Figure 2.
Framework to extract hourly residential energy consumption data at the household level. For any given county and date, the enriched synthetic population, along with environmental and appliance data, is fed to the energy model to produce highly granular synthetic residential energy consumption data.
We conducted the Elbow method and calculated the Calinski-Harabasz index as a clustering validation metric to determine the optimal number of clusters k. Repeated analysis of the original data and subsets of the data yielded optimal cluster values of 3 and 4. By clustering households based on their energy consumption and a set of household attributes, we can identify patterns and characteristics that contribute to energy poverty. The k-prototype algorithm is well-suited for this task as it allows us to capture the complex relationships between household attributes and energy consumption. The resulting clusters can provide insights into the key factors contributing to energy poverty.
This can be achieved by using the k-prototype clustering algorithm to identify the clusters and analyzing the attribute distributions within each cluster to identify the attributes that contribute to energy poverty.
C. Statistical Analysis
Problem 3: Let H be the set of households in the enriched synthetic population. Let E be the corresponding energy consumption values and let A = {a1, a2. . . , ak} represent the demographic and household attributes for H. The objective is to find the statistical significance of a particular attribute ai with other attributes A\ai, for understanding social equity.
We conducted multiple statistical analyses to test for significance between race groups in terms of other variables to shed light on the importance of accounting for social equity moving forward. We included 4 quantitative variables, where we performed one-way ANOVA tests for each, and 6 categorical variables, where Chi-Sqaured tests were performed for each. All tests were followed by a post-hoc test to see where the statistical difference, if any, lie.
III. RESULTS AND INSIGHTS
A. Data Extraction
We collected daily residential energy consumption data using the framework as described in section II-A. We performed this simulation for 12 random days, one day from each month for Albemarle County (County code: 003) and Charlottesville City (County code: 540). We have ≈58, 000 households in this region. We then averaged energy consumption from these 12 days in our optimization models. This setup helps us capture the diversity in energy consumption due to seasonal differences.
The total energy consumption data from the energy model from section II-A is the sum of energy consumed by HVAC, refrigeration, water heater, dishwasher, clothes washer, clothes dryer, lighting, and some miscellaneous plug loads (cleaning, cooking, computer, television and so on). Output used for analysis and modelling is explained in Table 1.
The six major household attributes, along with their proportions in the collected data, are shown in Figure 3. These attributes, such as race, ownership of the house, dwelling type, household income, age of the constructed house, and square footage of the house, play a crucial role in developing social equity constraints. While 93.5% of the households are White alone and Black/African-American alone, 6.5% of the population in this region is constituted by races belonging to Asians, Native Hawaiian/Pacific Islander, American Indian/Native Alaskan, and multi-household races. The major contributors in house ownership and dwelling type include owned houses (66.2%) and five-plus apartment dwellings (64%), respectively. It is also important to note that 12.8% of households have income less than the Virginia area median indicator (AMI) of $60,000, and 32.7% of houses have a construction age greater than 50 years.
B. Clustering
We conducted clustering for the entire dataset with k=3 clusters where the second cluster emerged as the most energy burdened, as pictured in Table 2. The summary table for the clusters is composed of the mean values of the numeric features and the mode of the categorical features. The first cluster seems to be the most energy-burdened compared to the others as it has the lowest income bracket (<$20K), and older housing (20-29 years old). It also has less square footage yet about the same HVAC KWH. It should also be noted that the numeric values in Table 2 are scaled according to the minimum-maximum. However, moving forward, the other table on the later results will not be scaled for ease of interpretability.
It is difficult to extract more conclusive insights into energy- burdened households in the general clustering; thus, we intro- duce specifications for equity constraints.
- 1)
- (HouseAge > 20) ∧ (Income < 60k) ∧ (hhSize 2)
- 2)
- (HouseAge 20) ∧ (Income 60k) ∧ (hhSize 2)
- 3)
-
Apartments
- a)
- (HouseAge > 20) ∧ (Income < 60k)
- b)
- (HouseAge ≥ 20) ∧ (Income < 60k)
- 4)
-
Single-family Houses
- a)
- (HouseAge > 20) ∧ (Income < 60k)
- b)
- (HouseAge ≥ 20) ∧ (Income < 60k)
To investigate the extremes of the households in terms of house age and income levels, the first two specifications are drawn up. The first two specifications use 20 years as a bar for house age and $60K as a bar for income, where the extremes are greater or less than while constraining the household size to be greater or equal to 2. Specification 3 and 4 aims to investigate the lower-income households while comparing dwelling type (3-4) and house age (a-b). The specifications for equity constraints are used to create subsets of the original data for the cluster analysis to be performed on each subset of data that meets each specification.
Table 3 shows the clustering results concerning Specifi- cations 1 and 2, which provide further evidence of energy- burdened households. In Specification 1, the majority rent large apartments (5 plus units) with a mean income range of $6K to $52K. In comparison, most own single-family detached houses with a mean income range of $88K to $512K. The cluster with the lowest mean income bracket comprises a majority of Black or African-American (Specification 1). It also appears that as income increases, the square footage of the dwelling also increases.
Through Specifications 3a-b and 4a-b, we consider the lower-income households (less than $60K) and older dwellings (> 20 years) while comparing dwelling types (apartments and single-family houses). A composite metric of the ratio of annual energy consumption to square footage (RAE) was created to evaluate the level of energy consumption better, as shown in Formula 1. In comparing 3a (Single-Family Houses) and 4a (Apartments), the average RAE was 3.163 and 5.131, respectively. The lowest income cluster (in 4a) comprises Black or African-American and White with a mean income of $5K but is also found to have the highest total daily energy consumption. At the same time, the second lowest income cluster is found in 3a with a mean income of $8K. It comprises mainly of Black or African-American and Native American or Alaskan Native, respectively.
The final set of specifications considers the lower-income households (less than $60K) and newer dwellings (≤20 years) while comparing dwelling types (apartments and single-family houses). In comparing 3b (Single-Family Houses) and 4b (Apartments), the average RAE was 4.039 and 6.613, respectively. The lowest income cluster (in 4b) comprises White and Black or African-Americans with a mean income of $3K, which is even lower than that of 4a. In all four specifications, 3a-b and 4a-b, this cluster has the lowest income and the highest RAE of 8.225. Regardless of age, the RAE is higher for apartments than single-family houses, but newer dwellings (b) tend to have a higher RAE. The low-income clusters with comparable or higher RAE to the higher-income clusters indicate those clusters as energy-burdened.
RAE = (totalDailyKWH ∗ 365)/sqft
C. Statistical Analysis
- 1)
- ANOVAs: Four one-way ANOVAs were conducted to test for significant difference between race groups in terms of 4 numeric variables: (1) energy consumption, (2) income, (3) home age, and (4) area. Results show significant differences between race and each of these variables with a p-value<0.001 for all variables.
Tukey’s Post-Hoc test was conducted after every ANOVA to test between which races, does the significance lie for a particular variable. Table 4 summarizes the results of the four post-hoc tests conducted. Results show that there is a positive significant difference in all variables 1, 2, 3, and 4 when compared to all other racial groups. This means that people who were identified as white have a high amount of income, larger houses, higher house ages, and they consume more energy than all other races.
- 2)
- Chi-Squared Tests: Six Chi-Squared Tests were con- ducted to test for significant differences between racial groups in terms of 6 categorical variables which are (5) Own/rent, (6) Dwelling Type, (7) Old Dishwasher, (8) Old CD, (9) Old CW, and (10) Old Insulation. Results show significant differences between race and each of these variables with a p-value<0.001 for all variables.
Post-Hoc tests were also conducted after every Chi-Squared test to test between which races, does the significance lie for a particular variable. Table 5 summarizes the results of the six post-hoc tests conducted. Results show that White and Native Hawaiian or Other Pacific Islander have the highest percentage of homeownership (70.5% and 68.3% respectively), while Black/African American and Asian have the lowest (54.8% and 53.4% respectively). Moreover, Black/African American have the highest percentage of renters (45.8%), while White have the highest percentage of type 2 dwellings (68%). White have the highest percentage of no old insulation (83.%), while Black/African American have the lowest (77.1%).
IV. LIMITATIONS & FUTURE WORK
One limitation to this study is that the data analyzed in this study is limited to 2019, which may not reflect changes that have occurred since the COVID-19 pandemic. Moreover, the COVID-19 pandemic has caused significant disruptions to energy consumption patterns, making the data analyzed during this time period unstable. Future work should consider these changes and analyze post-COVID data when it becomes available.
Additionally, the analysis in this study was based on per-day average, which may obscure important patterns that emerge over longer time periods. Therefore, future work should focus on collecting and analyzing data from all days of each month to better understand social equity trends. Moreover, future work should include annual data to identify longer-term trends in social equity and energy consumption patterns.
This study focused on time series analysis of energy data to understand trends of social inequity. While this approach is useful, future work should also consider qualitative data collection methods, such as interviews or surveys, to gain a more nuanced understanding of social equity issues in relation to energy consumption.
Finally, policymakers should develop policies with specifications that follow equity constraints. This approach would ensure that all households have access to high-quality, energy- efficient housing regardless of their race, income, or age of the house. Such policies could include programs to help low-income households upgrade their homes, incentives for developers to build more energy-efficient housing, and regulations to ensure that all new buildings meet energy efficiency standards. By addressing the impact of race, income, and age of the house on residential attributes and energy consumption, we can work towards a more equitable and sustainable future.
V. DISCUSSION & CONCLUSION
The focus of this research is to investigate the influence of race on residential features and energy consumption. The impact of race and income on residential attributes and energy consumption is a critical issue that requires attention. Studies have shown that race plays a significant role in determining the location and quality of housing, with people of color often living in areas with higher pollution and less access to green spaces. The statistical analyses presented examine the relationship between race and various variables, including energy consumption, income, homeownership, dwelling type, and the presence of old infrastructure in the home. The results suggest that significant differences exist between different racial groups with respect to these variables. The analysis finds that White and Native Hawaiian or Other Pacific Islander individuals have the highest rates of homeownership, while Black/African American and Asian individuals have the lowest. This finding may reflect differences in income, wealth, or access to credit, among other factors, which could affect the ability of individuals from different racial groups to purchase a home. The analysis also examines the presence of old infrastructure in the home, including old dwelling and insulation. The results indicate that White individuals have the highest percentage of homes without old infrastructure in all categories, where Black/African American individuals have the lowest percentage. This finding suggests that individuals from different racial groups may have differing levels of access to and quality of housing infrastructure. Furthermore, income levels play a crucial role in deciding the type of dwelling and ownership of the house, which can have implications for energy consumption. Lower-income households are more likely to live in older, less energy-efficient homes, which can result in higher energy bills and increased carbon emissions. Moreover, the age of the house is also an important factor in determining energy efficiency. Older appliances and insulation are more common in houses that are around 15 years old, which can lead to higher energy usage. However, it is worth noting that many older buildings are refurbished to meet building standards, which can help to improve energy efficiency. Taken together, these results highlight the ongoing importance of addressing disparities in housing access and quality among individuals from different racial groups. Policies aimed at reducing income and wealth inequality, increasing access to credit, and promoting equitable distribution of housing re- sources may be important steps in addressing these disparities. Through our analysis, we have demonstrated the necessity of considering social equity constraints in developing federal initiatives and policies to support households in energy poverty. These policies not only help the community to have a safer and healthier place to live but also has a greater good of reducing CO2 emissions. We have provided insights on race’s significant impact on residential attributes, energy consumption, and income level. The current policies and initiatives by Federal and state governments to support clean and sustainable green energy are focused on energy-burdened low-income households. One example is by the government to advance building codes and standards [14] for climate resilience and lower utility bills. These initiatives are intended to support building projects through federal funding opportunities, provide incentives for communities for retrofitting, and deploy bipartisan infrastructure law to implement building standards. Another one is the Weatherization Assistance Pro- gram (WAP) initiated by the Department of Energy (DOE), where households below the poverty of 200% are eligible to participate in retrofitting programs. While these policies focus on one of the attributes, the income of households, we need more policies that take care of diverged attributes, including race, income level, dwelling type, house age and ownership of houses.
In conclusion, while this study provides valuable insights into the relationship between social equity and energy consumption patterns, there are limitations that must be addressed in future work. By addressing these limitations, future studies can provide a more comprehensive understanding of social equity issues and develop more effective policies to address them.
References
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Figure 1.
Hourly residential energy consumption data at the household level is used to develop insights on social equity constraints through cluster analysis and statistical analysis.
Figure 1.
Hourly residential energy consumption data at the household level is used to develop insights on social equity constraints through cluster analysis and statistical analysis.
Figure 3.
Data distribution in the Albemarle-Charlottesville region for the household attributes such as race, house ownership, dwelling type, household income, house age, and square footage. These attributes are major contributors to consider for social equity constraints. While the first five attributes are demonstrated in a pie chart, the area square footage of the household is shown in a histogram.
Figure 3.
Data distribution in the Albemarle-Charlottesville region for the household attributes such as race, house ownership, dwelling type, household income, house age, and square footage. These attributes are major contributors to consider for social equity constraints. While the first five attributes are demonstrated in a pie chart, the area square footage of the household is shown in a histogram.
Table 1.
CODE TABLE FOR THE SELECTED OUTPUT COLUMNS USED FOR ANALYSIS.
| Variable | Variable description | Response set and explanation |
|---|---|---|
| race | Householder race | 1- White Alone 2—Black or African/American Alone 3—American Indian or Alaska Native Alone 4—Asian Alone 5—Native Hawaiian or Other Pacific Islander Alone 6—Some Other Race Alone 7—2 or More Races Selected |
| areatype | Census area type | R—Rural U—Urban |
| ownRent | Owned/rented house | 1. - Own 2. - Rent |
| dwellingType | Type of housing unit | 1—Mobile home 2—Single-family detached house 3—Single-family attached house 4—Apartment in a building with 2 to 4 units 5—Apartment in a building with 5 or more units |
| hasElectricH2oHeater | Has electric water heater | 1. - Yes 2. - No |
| hasElectricHeat | Has electric heater | 1. - Yes 2. - No |
| hasAC | Has air conditioner | 1. - Yes 2. - No |
| hasCw | Has clothes washer | 1. - Yes 2. - No |
| hasCd | Has clothes dryer | 1. - Yes 2. - No |
| hasDW | Has dishwasher | 1. - Yes 2. - No |
| oldInsulation | poor or not adequately insulated | 1. - Yes 2. - No |
| OldDW | dishwasher ≥ 10 years | 1. - Yes 2. - No |
| OldCW | clothes washer ≥ 10 years | 1. - Yes 2. - No |
| OldCD | clothes dryer ≥ 10 years | 1. - Yes 2. - No |
| totalDailyKWH | total daily energy consumption in kWh | float values |
| hvacDailyKWH | hvac energy consumption in kWh | float values |
| refrigeratorDailyKWH | refrigerator energy consumption in kWh | float values |
| dwDailyKWH | dish washer energy consumption in kWh | float values |
| washerDailyKWH | clothes washer energy consumption in kWh | float values |
| dryerDailyKWH | clothes dryer energy consumption in kWh | float values |
| hhSize | household size | numeric value |
| income | household income | numeric value in dollars |
| houseAge | construction age of house | numeric value |
| sqft | House square footage | numeric value |
Table 2.
CLUSTER ANALYSIS OF THE ENTIRE DATASET WITH k=3 CLUSTERS.
| Segment | First | Second | Third |
|---|---|---|---|
| Count | 21229 | 24183 | 12871 |
| race | 1 | 1 | 1 |
| areatype | U | U | U |
| ownRent | rent | own | own |
| dwellingType | 5 | 2 | 2 |
| hasElectricH2oHeater | Yes | No | Yes |
| hasElectricHeat | Yes | No | No |
| hasAC | Yes | Yes | Yes |
| hasCw | No | No | Yes |
| hasCd | No | No | Yes |
| hasDw | No | No | Yes |
| oldInsulation | No | No | No |
| OldDW | No | No | No |
| OldCW | No | No | No |
| OldCD | No | No | No |
| income cat | <20K | >140K | >140K |
| houseAge cat | 20-29 | <10 | <10 |
| totalDailyKWH | 0.067 | 0.098 | 0.125 |
| hvacDailyKWH | 0.116 | 0.112 | 0.125 |
| refrigeratorDailyKWH | 0.807 | 0.818 | 0.818 |
| lightsDailyKWH | 0.172 | 0.377 | 0.382 |
| dwDailyKWH | 0.062 | 0.134 | 0.256 |
| washerDailyKWH | 0.021 | 0.003 | 0.517 |
| dryerDailyKWH | 0.015 | 0.002 | 0.4 |
| cookDailyKWH | 0.127 | 0.215 | 0.28 |
| tvDailyKWH | 0.136 | 0.222 | 0.271 |
| computerDailyKWH | 0.028 | 0.041 | 0.058 |
| cleanDailyKWH | 0.086 | 0.112 | 0.208 |
| dailyHotWaterKWH | 0.024 | 0.036 | 0.05 |
| hhSize | 0.068 | 0.156 | 0.189 |
| adultNum | 0.128 | 0.179 | 0.201 |
| sqft | 0.114 | 0.313 | 0.292 |
Table 3.
CLUSTER ANALYSIS FOR SPECIFICATION 1 AND SPECIFICATION 2.
| Specification 1 | Specification 2 | |||||||
| Segment | First | Second | Third | Fourth | First | Second | Third | Fourth |
| Count | 1832 | 2532 | 2652 | 2436 | 1658 | 3924 | 5694 | 638 |
| race | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| ownRent | Rent | Own | Rent | Rent | Own | Own | Own | Own |
| dwellingType | 5 | 2 | 2 | 2 | 3 | 2 | 2 | 2 |
| oldInsulation | No | No | No | No | No | No | No | No |
| OldDW | No | No | No | No | No | No | Yes | No |
| OldCW | No | No | No | No | No | Yes | Yes | Yes |
| OldCD | No | No | No | No | No | Yes | Yes | Yes |
| totalDailyKWH | 18.669 | 18.848 | 18.844 | 20.275 | 23.876 | 25.228 | 25.771 | 24.168 |
| hvacDailyKWH | 3.018 | 3.538 | 3.942 | 4.047 | 4.876 | 5.708 | 6.579 | 5.111 |
| refrigeratorDailyKWH | 2.466 | 2.457 | 2.461 | 2.462 | 2.491 | 2.489 | 2.489 | 2.49 |
| dwDailyKWH | 0.357 | 0.377 | 0.369 | 0.427 | 0.756 | 0.732 | 0.723 | 0.899 |
| washerDailyKWH | 0.08 | 0.099 | 0.106 | 0.115 | 0.144 | 0.139 | 0.131 | 0.174 |
| dryerDailyKWH | 0.458 | 0.584 | 0.637 | 0.691 | 0.901 | 0.878 | 0.834 | 1.103 |
| hhSize | 2.927 | 2.74 | 2.715 | 2.61 | 3.019 | 3.075 | 2.901 | 3.293 |
| income | 6366.96 | 22541.617 | 38253.898 | 52843.805 | 264532.432 | 151225.389 | 88375.719 | 512357.68 |
| houseAge | 47.525 | 48.116 | 49.235 | 48.779 | 12.754 | 12.816 | 13.156 | 12.859 |
| sqft | 1181.878 | 1449.487 | 1639.064 | 1743.115 | 3505.091 | 3428.464 | 2661.76 | 3638.34 |
Table 4.
TUKEY’S POST-HOC TEST RESULTS.
| Race | White | Black or American |
African | American Indian or Alaska Native |
Asian | Native Hawaiian or Other Pacific Is- lander |
2 or More Races Selected |
|||
|---|---|---|---|---|---|---|---|---|---|---|
| White | + sig. difference in variables 1,2,3, and 4 |
+ sig. difference in variables 1,2,3, and 4 |
+ sig. difference variables 1,3,4 |
in | + sig. difference in variables 1,2,3 |
+ sig. difference variables 1,2,3 |
in | |||
| Black or African American | + sig. difference in variable 3 only |
+ sig. difference variable 4 - sig. difference variables 2,3 |
in in |
- sig. difference in variable 3 |
+ sig. difference variable 4 - sig. difference variables |
in in |
||||
| American Indian or Alaska Native |
+ sig. difference variable 4 - sig. difference variable 2 |
in in |
No Significant Differences | + sig. difference variable 3 |
in | |||||
| Asian | + sig. difference in variable 2 - sig. difference in variable 4 |
+ sig. difference variable 2,3 - sig. difference variable 4 |
in in |
|||||||
| Native Hawaiian or Other Pacific Islander |
- sig. difference variable 1 |
in | ||||||||
Table 5.
RESULTS OF THE CATEGORICAL VARIABLES.
| Race/Variable | Own/Rent | Dwelling Type | Old DW | Old CD | Old CW | Old Insulation |
|---|---|---|---|---|---|---|
| White | Own: 70.5% | 68% type 2 | No: 76.6% | No: 75.7% | No: 79.3% | No: 83.7% |
| Black/African American |
Rent: 54.8% | 45.8% type 2 | No: 78.8% | No: 78.3% | No: 81.4% | No: 77.1% |
| American Indian or Alaska Native |
Own: 57.7% | 64.1% type 2 | No: 77.6% | No: 74.8% | No: 78.2% | No: 80.1% |
| Asian | Own: 53.4% | 44.5% type 2 | No: 77.1% | No: 77.6% | No: 80.9% | No: 83.2% |
| Native Hawaiian or Other Pacific Is- lander |
Own: 68.3% | 50.4% type 2 | No: 81.3% | No: 74.8% | No: 74.8% | No: 78% |
| 2 or More Races Selected |
Own: 66.2% | 47.7% type 2 | No: 79.4% | No: 77.4% | No: 80.6% | No: 80.3% |
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