Two approaches for estimating the kilowatthours used for lighting that are based upon data from the 1993 RECS were used in this report. The first approach used only bulb type and hours of usage data from the RECS Lighting Supplement. The second approach is a regression-based approach that uses the full RECS dataset. This appendix will provide more details concerning both of these methods.

The main purpose of the Lighting Supplement, which collected data from a subsample of the 1993 RECS respondents, was to develop a model of kilowatthours used for lighting as a function of variables obtained on the full RECS Household Questionnaire. The resulting model was used to create an index of lighting usage. This index was then used as a predictor variable in a regression analysis. The results of the regression analysis were used to disaggregate the total electricity usage into consumption by end use. One of these end uses is lighting.

The RECS Lighting Supplement (Form EIA-457H) is a short questionnaire completed by 474 of the 7,111 households that responded to the RECS Household Questionnaire (Form EIA-457A). The Lighting Supplement was not administered to all of the 1993 RECS respondents because of cost and respondent burden constraints. The Lighting Supplement provides detailed information on indoor lights used 15 minutes or more (up to a maximum of 15 lights) by type of bulb, hours used, and the room in which the light is located. If the respondents reported that there were more than 15 lights that met the criteria covered by the Lighting Supplement, only the number of additional bulbs was recorded.

Calculating Kilowatthours

Lights in the Lighting Supplement database were assigned a wattage amount based upon the bulb type reported. Similarly, the hours used for a light were inferred from the respondent's estimate of the number of hours the light was used.

Kilowatthours = (Wattage * Hours Used)/1000

The kilowatthours for each light equals the wattage times the hours, divided by 1,000. The kilowatthours for each respondent to the Lighting Supplement equal the sum of the estimated kilowatthours for all the lights for that respondent.

Assigning Wattage to Lights

Respondents categorized lights by type, such as incandescent, fluorescent, halogen, or other. The specific wattage was assigned to each type by using the values in Table B.1.

Wattage for Incandescent Lights

Incandescent lights in the Lighting Supplement database were assigned a wattage based upon the respondents' estimates of their wattage. Lighting fixtures with more than one bulb were counted as one light. The wattage for these fixtures was the total wattage of all bulbs in the fixture. The respondents were asked to categorize incandescent lights by their total wattage. Lights with total wattage less than 10 (night lights) were excluded from the Lighting Supplement. Incandescent lights with a total between 10 and 40 were coded as "low" incandescent. Those with wattage between 41 and 149 were coded as "medium" incandescent and those with 150 or more were coded as "high" incandescent. It is assumed that some of the lights coded as "medium" incandescent are actually fixtures with multiple bulbs. The same applies to "high" incandescent. Incandescent lights coded as "low" were assigned a wattage of 30, "medium" were assigned a wattage of 100, and "high" were assigned a wattage of 200. Incandescent lights for which the respondent did not provide a wattage estimate were assigned a wattage of 60.

Table B.1 Bulb Type and Wattage

Bulb Type	Assigned Wattage
Incandescent
Low	30
Medium	100
High	200
Unknown	60
Fluorescent
Short	17
Long	40
Compact	13
Unknown	40
Halogen	250
Other	60
Don't Know, No Answer	60
Lights Beyond 15 Listed	60

Source: Energy Information Administration, Office of Energy Markets and End Use, 1993 Residential Energy Consumption Survey.
Note: Wattage assignments for fluorescent lights are based on data from various lighting industry literature. Incandescent wattages are based on the Lighting Supplement Questionnaire.

Wattage for Fluorescent Lights

Fluorescent lights in the Lighting Supplement data base were assigned a wattage based upon the respondents' description of the lights. Lights categorized as "short" fluorescent were assigned a wattage of 17, "Long" fluorescent lights were assigned a wattage of 40, and "compact" fluorescent lights were assigned a wattage of 13. Fluorescent lights for which the type was coded as "unknown" were assumed to be long fluorescent and were assigned a wattage of 40.

Wattage for Halogen Lights

The Lighting Supplement did not distinguish between the different types of halogen lights. Halogen desk lights may have a low wattage (10 to 20), while halogen floor lights may have a high wattage (200 to 500). Only 24 out of the 4,196 lights in the Lighting Supplement data base are Halogen lights. All halogen lights were assigned a wattage of 250 as a compromise.

Wattage for Other Bulb Types

Lights in the Lighting Supplement data base that were not classified as incandescent, fluorescent, or halogen were assigned a wattage of 60. This category includes lights where the respondent classified the lights as "other," where the respondent did not know the type, and lights where no type was recorded because the limit of 15 lights for a respondent had been reached.

Assigning Hours of Usage

For each light listed in the Lighting Supplement, the respondents were asked:

"Think of a typical 24-hour November weekday. For each indoor light used in your home for at least 15 minutes, please identify the light, how long that light is on, and what type of bulb is in the light fixture. As we list each room, keep in mind all activities and times-of-day that the light is used."

The responses were either the number of hours, a category for the number of hours, or "don't know." If the respondent reported the number of hours, then the light was assigned the reported number of hours. If a category for the number of hours was given, but not the actual number, the light was assigned the midpoint of the category. The only exception was the lowest category (15 minutes to 1 hour). In this case, the light was assigned the value of .5. If the respondent did not give either an estimate of the number of hours or a category, the lights were assigned a value of 1 hour. Similarly, lights beyond the 15 listed were given a value of 1 hour.

Modeling Kilowatthours by Using Lighting Supplement Data

The regression analysis of the Lighting Supplement data was done in two steps. In both steps, a stepwise linear regression program was used and the dependent variable was the kilowatthour estimate for lighting obtained from the bulb type and hours data described above. In addition, both steps used the same set of independent variables. In the first step, all of the observations received the same weight. In the second step, the Lighting Supplement observations were given a weight equal to the inverse of the predicted kilowatthours obtained from the first step. This weighting was used to adjust for the higher variance of the error term for households that were projected to use more electricity for lighting.

The set of independent variables used in both regression steps were obtained from the full 1993 RECS data set. The variables used are as follows:

Full RECS lighting variables

X1: Number of lights on more than 12 hours
X2: Number of lights on between 4 and 12 hours
X3: Number of lights on between 1 and 4 hours
X4: Number of fluorescent lights on more than 12 hours
X5: Number of fluorescent lights on between 4 and 12 hours
X6: Number of fluorescent lights on between 1 and 4 hours

Functions of full RECS lighting variables

X7-X12: The square root of the above variables
X13: An indicator variable that equals 1 if at least one light was on more than 12 hours

Full RECS variables on the size of the dwelling

X14: Number of rooms
X15: Total square footage of housing units (heated and unheated)
X16: Heated square footage
X17: Number of Windows

Full RECS variables on number of household members

X18: Number of household members
X19: Square root of the number of household members
X20: Number of household members aged 13 to 65
X21: Square root of the number of household members aged 13 to 65
X22: Number of household members aged 6 to 65
X23: Square root of the number of household members aged 6 to 65

Type of housing unit

X24: Single-Family attached unit
X25: Mobile Home
X26: Apartment units in a building with 2 to 4 units
X27: Apartment units in a building with 5 or more units

Family-Income Level

X28: low (less than $20,000)
X29: Medium ($75,000 - $99,999)
X30: High ($100,000+)

Age of householder

X31: 75 or more
X32: 70 or more
X33: 65 or more
X34: 34 or less

Daytime use of home

X35: Operation of a home-based service or business
X36: Other activity requiring a lot of energy
X37: Someone home all day

Results

The second step produced the following model:

Kilowatthours= -90.7
+ 115.4 x X2
+ 44.3 x X3
+ 282.2 x X4
+ 0.0491 x X15
+ 184.7 x X19

Introduction

For each household that responded to the 1993 RECS, the annual amount of electricity used for five end­use categories-- space heating, water heating, air-conditioning, refrigerators, and general appliance usage--was estimated. The end­use amounts were not based on data produced by placing meters on individual appliances; rather, they were obtained by estimating how much of the total annual consumption for electricity can be attributed to each of the end­use categories for each household by using a regression technique. The data from the Lighting Supplement allowed us to estimate lighting as a subcomponent of the appliance end-use estimates for the first time in the RECS history.

The annual consumption attributed to each of the end­use categories can be estimated by use of regression equations. The regression equations are also used to impute electricity consumption when the billing data are missing or inadequate. The dependent variable was the annual electricity consumption for the 1993 calendar year. The desire to use a large number of independent variables without using a large number of interaction terms and the desire to adapt the regression procedures to account for heteroscedastic[17] error terms led to the use of a nonlinear regression technique. The use of linear regression would have greatly restricted the ability to adequately model household energy consumption.

This section of the appendix provides an overview of the methodology used for the 1993 RECS end-use estimation. The specific regression equations used are not presented here. (For more detailed information, please contact the person cited as the end-use estimation contact on the Contacts page at the beginning of this report.) The procedure used for the 1993 RECS is very similar to that used in the 1990 RECS. Detailed equations for the 1990 RECS were published in Appendix D, "End-Use Estimation Methodology," of Household Energy Consumption and Expenditures 1990 (Energy Information Administration, February 1993, DOE/EIA-0321(90)).

Electricity Consumption Equation

Basic Equation

For electricity, the basic equation is:

Total Consumption = Space­Heating Component
+ Water­Heating Component
+ Air­Conditioning Component
+ Refrigerator Component
+ Appliance Component.
Discussions of each component of the general consumption equation will be followed by a discussion of the nonlinear regression technique.

General Space­Heating Component

The space­heating component was defined as all electricity used to generate heat by space­heating equipment. The equipment could be the main space­heating equipment or secondary space­heating equipment. Hence, a household could have had a positive amount of electricity assigned to the space­heating component even if the electricity source was not used as the main space­heating energy source.

For the electricity equation in the 1987 and subsequent RECS, the electricity associated with the operation of fans in any central forced-air heating equipment was assigned to the electricity appliance component and not to the space-heating component. [18]

General Water­Heating Component

The component for water heating was defined as all electricity used to heat water for hot running water, as well as water heated at point sources (such as stoves or auxiliary water­heating equipment) for bathing, cleaning and other noncooking applications of hot water. Electricity used at point sources to heat water for cooking and hot drinks was considered part of the general appliance component, as was electricity used to heat water for a swimming pool, hot tub, spa, or jacuzzi.

General Air­Conditioning Component

The electricity air­conditioning component was defined as all electricity associated with (1) electric air­conditioning equipment and (2) fans in any central air­conditioning equipment including natural gas air­conditioning equipment. The regression equations for electricity do not contain specific terms for whole-house fans, window fans, and evaporative (swamp) coolers, because the terms were only marginally significant. Hence, the consumption of electricity to operate these fans and evaporative coolers was not assigned to the air-conditioning component; it was included in the appliance component. The term for ceiling fans is in the electricity appliance component. [19]

In the 1993 RECS, the households that reported that they had air­conditioning equipment but did not use the equipment, were assigned a value of zero for their electricity air­conditioning component. In RECS prior to 1987, these households were assigned small but positive values for their electricity air­conditioning component.

General Refrigerator Component

The refrigerator component for electricity consisted of all electricity used to operate refrigerators. The electricity used to operate freezers that are not part of a refrigerator was assigned to a separate component under General Appliance.

General Appliance Component

The general appliance component consisted of all electricity not used specifically for any of the other end uses. For electricity, the general appliance component was split into six subcomponents: (1) Appliance Subcomponent, (2) Lighting Subcomponent, (3) Cooking Subcomponent, (4) Dishwasher Subcomponent, (5) Clothes Dryer Subcomponent, and (6) Freezer Subcomponent.

Electricity used in appliances during the winter will frequently help heat the housing unit. This secondary effect of the appliance consumption was not included in the estimation of the space­heating component. In addition, during the summer, energy used in general appliances may add to the load on the air­conditioning system. This was not included in the air­conditioning component.

Appliance Subcomponent. The appliance subcomponent consisted of all electricity not used for any of the other five subcomponents or the other four main components. This included electricity used to heat water beds, hot tubs and pools, and the electricity used to operate fans (including fans for forced-air, space-heating systems), evaporative coolers, water pumps, small kitchen appliances (such as toasters, mixers, and can openers), home entertainment equipment (such as radios, televisions, stereos, video cassette recorders, electronic games, and computers), and numerous other appliances and uses not covered elsewhere.

Lighting Subcomponent. This subcomponent consists of all electricity used for indoor and outdoor lighting.

Cooking Subcomponent. The cooking subcomponent was positive if the household reported that electricity was the main cooking fuel; otherwise, the subcomponent was zero. The definition of the subcomponent did not involve the type of cooking equipment that was used. Consequently, households with some electric cooking equipment (including microwave ovens) could have been assigned a zero value for the electricity cooking subcomponent if the household did not list electricity as a cooking fuel. The electricity used to operate the electric cooking equipment in households that did not list electricity as a cooking fuel was included in the appliance subcomponent. Similarly, electricity used to operate common kitchen appliances, such as toasters and mixers, was included in the appliance subcomponent.

Dishwasher Subcomponent. This subcomponent consisted of all electricity used to operate dishwashers.

Clothes Dryer Subcomponent. This subcomponent consists of all electricity used to operate clothes dryers.

Freezer Subcomponent. The freezer subcomponent for electricity consisted of all electricity used to operate freezers that were not part of a refrigerator.

Nonlinear Regression Technique

The nonlinear regression technique was used to produce electricity end­use estimates for each household. The end­use estimates were normalized so that the sum of the end­use estimates was equal to the actual or imputed yearly electricity consumption used by the household. The individual household end­use estimates were used to estimate averages and totals for end­use consumption over selected household categories. Following is an overview of the basic nonlinear equations. (To obtain the detailed equations and individual coefficients, please see the Contacts page at the beginning of this report for the end use estimation contact person.) [20]

General Regression Equation

The general regression equation splits estimated electricity consumption into its end-use components. The result is:

YCOM = SPHTCOM + WTHTCOM + AIRCCOM + RFRGCOM + APPLCOM,

where:

YCOM is the estimated annual consumption,
SPHTCOM is the estimated space­heating component,
WTHTCOM is the estimated water­heating component,
AIRCCOM is the estimated air­conditioning component,
RFRGCOM is the estimated refrigerator component, and
APPLCOM is the estimated appliance component.

Electricity Regression Equation

The regression equation for electricity splits estimated consumption for the appliance component into six additional subcomponents:

YCOM = SPHTCOM + WTHTCOM + AIRCCOM + RFRGCOM
+ FZZRCOM
+ DISHCOM
+ COOKCOM
+ LITECOM
+ DRYRCOM
+ APPSCOM,

where:

FZZRCOM is the estimated freezer subcomponent,
DISHCOM is the estimated dishwasher subcomponent,
COOKCOM is the estimated cooking subcomponent,
LITECOM is the estimated lighting subcomponent,
DRYRCOM is the estimated clothes dryer subcomponent, and
APPSCOM is the estimated other appliances subcomponent.

The actual annual consumption is called Y. The unit of measure for Y and YCOM is thousands of Btu. The typical regression error term is as follows:

e₁ = Y ­ YCOM .

Unfortunately, the variance of e₁ tends to increase as YCOM increases. Furthermore, the distribution of e₁ is skewed in the positive direction. These two facts violate the assumptions associated with linear least­squares regression. On the other hand, the distribution of

e₂ = (Y) ^¼ ­ (YCOM) ^¼

is closer to being normally distributed with a constant variance. Hence, a nonlinear least­squares regression procedure that minimizes the sum of squares of e₂ was used.

The dependent variable was the household's electricity consumption as reported on the RECS Suppliers Survey in thousands of Btu. Most of the independent variables are derived from information reported by the individual households on the Household Survey. The end-use components consisted of sums or products of terms that themselves may have been sums or products of the independent variables. The overall methodology may seem complex at first glance, but there was a common structure. In general, the components consisted of an overall term multiplied by various adjustments. This format allowed the components to be adjusted by many factors. The relative size of the adjustments was easy to determine.

The disadvantage of the format was that it yields a basic equation that is intrinsically nonlinear. As a result, standard multivariate linear regression techniques could not be used to estimate the parameters. A nonlinear technique was used instead. The parameters were estimated by using the nonlinear regression procedure (PROC NLIN) contained in the statistical computer package, SAS. [21]

Details of Lighting Component

The lighting component covers the consumption of electricity for both indoor and outdoor lighting. The indoor lighting is modeled by using the equation (converted to thousand Btu) developed from the Lighting Supplement as an independent variable. Outdoor lighting is modeled by using variables that describe the presence and use of outdoor lights. As with all components, the lighting component is multiplied times common adjustment terms. These terms are functions of the price of electricity, presence of household members during the day, family income, age of dwelling, housing unit type, and demographic characteristics of the house holder.

The resulting equation for the lighting component is given below:

Lighting component = 0.82710 x Y1
+ 1,016.05323 x Y2
+ 1,124.08710 x Y3
+ 1,773.86255 x Y4
+ 339.23403 x Y5
+ 734.26589 x Y6
+ 791.90744 x Y7

where

Y1 = 3.412 x kWh estimate from second step of Lighting Supplement regression (p 58)

Y2 = Indicator function for presence of outdoor light on all night

Y3 = Indicator function for presence of outdoor light on all night and the light is 150 watts or more

Y4 = Indicator function for presence of outdoor light controlled by a timer but there is not an outdoor light on all night

Y5 = Indicator function for presence of outdoor light (150 watts or more) controlled by a timer but there is not an outdoor light on all night

Y6 = Indicator function for presence of outdoor light on during the evening but there is not an outdoor light on all night or one controlled by a timer

Y7 = Indicator function for presence of outdoor light on during the evening (150 Watts or more) but there is not an outdoor light on all night or one controlled by a timer.

Go to Appendix C

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