Case 3: Regression analysis on visual air quality

 (A classic study by Professor Tom Stewart, Director of the Center for Policy Research at the University at Albany, and colleagues in Colorado, done almost twenty years ago.)

Background

The establishment of a visibility standard was an important step in developing a comprehensive air quality control program for the Denver metropolitan area. A visibility standard setting program was undertaking by the Colorado Department of Health in the summer of 1989. A standard based on citizen judgments of visual air quality (VAQ) was recommended to the Colorado Air Quality Control Commission in time to meet a statutory deadline for adoption by January 1990. This assignment is based on the data collected to help determine the Colorado visibility standard.

Method

The method is based on studies conducted by the National Park Service (NPS) and National Center for Atmospheric Research (NCAR). Those studies focused on determining the validity and reliability of VAQ judgments as well as the appropriateness of using photographs as a surrogate for field observations of human judgment of VAQ. Results of the NPS and NCAR studies have shown that judgments of VAQ are reliable and valid, the judgments from one person or group to the next are highly correlated, and judgments made in the field are highly related to judgments made later from slides taken during the original field judgment. The NCAR studies in Denver also showed that judgments made in different locations by different people around the city were strongly associated.

The slides used in the study were taken from the Colorado Air Pollution Control Division's (CAPCD) Thornton visibility camera site between November 1, 1987 and January 31, 1988; the period of the 1987-88 Metro Denver Brown Cloud Study. This is a "sensitive" view and any haze present in the area is almost always perceptible from this location. It is representative of other views that offer a sweeping vista of the Denver basin with mountains in the background and is readily recognizable to residents of the area as a "typical" Denver view. At the same time the slides were taken, direct measurements of atmospheric extinction were being made in the brown cloud with an Optec LPV-2 long-path transmissometer. It monitored a site path of approximately 1.5 miles between the roof of a downtown building and an apartment to the southeast. The instrument was approximately 240 feet above the ground. Extinction is an objective measure of visibility. Clear air has an extinction value near zero because light easily passes through it. On the worst days in Denver, the extinction value is high.

Because of resource and methodological constraints, a true random sample of residents of the Denver metropolitan area was not practical. Therefore, diverse groups were recruited to view the slides. These were intact groups, that is, people who were meeting for other reasons and were asked if they would allow the Department of Health to have some time on their agenda to conduct the study. Demographic information was collected on each individual who participated.

Seventeen groups (totaling 214 people) viewed the slides and rated them on answer sheets. Two sets of 25 slides were used. Each group rated only one set. Totals for each slide set were 116 and 98 people respectively.

An instruction set was read so that each time the slides were shown the procedure for eliciting judgments would be the same. Each group was shown the slides twice in the same order: Once to judge the slides for VAQ on a 1-7 scale (1=very poor, 7=excellent) to familiarize the participants with rating slides for visibility and to show them the entire range of visibility conditions. Then additional instructions were read and each slide was judged again as to whether it would violate an urban visibility standard. Prior to each set of judgments, 7 warm-up slides were judged. The instructions read before the standard violation (SV) judgments asked each participant to consider whether a particular slide would violate an urban visibility standard and to base decisions on three elements:

1) The view is in an urban area with approximately 1.5 million people. The standard is for an urban area and not a pristine mountain area, such as Rocky Mountain National Park, where standards might be more strict.

2) Standard violations should be VAQ that is unreasonable, objectionable, and unacceptable visually. Participants were asked to discern "how much haze was too much" and not to indicate standard violations whenever any amount of haze was detectable unless any amount of haze was more than they could accept.

3) The violation judgments should be for visibility only and to the extent possible participants were asked not to consider any imagined health impacts of haze.

Variables

Data

The data for this assignment are on the web page Visual Air Quality Case Data. When you click on this link, the JMP file called VAQ.jmp should be downloaded to your computer. You ought to be able to double click on the file to open it in JMP. (Or open JMP, search for the file, and tell JMP to open it.) If you have trouble getting the file, please contact me.

Assignment

There are essentially three steps in this applied research effort to establish a visible air quality standard.

• The first is to make a connection between people's visual perceptions of air quality and their subjective views of acceptable and unacceptable levels of perceived air pollution.
• The second is to establish a connection between technical measures of light extinction and people's visual perceptions of air quality.
• Finally, we must put those two links together to create a scientifically measurable, politically acceptable standard for air quality.

The tasks in this assignment mirror these three steps.

(1) Create a scatterplot of PCTVIOL versus the perceived VAQ. Use JMP's Graph Builder for this. Note that PCTVIOL is an interpretation based on perception of visual air quality, so VAQ should be the explanatory variable and PCTVIOL should be the response variable. The smooth curve that JMP draws in the Graph Builder plot is your claim about the relation between VAQ and PCTVIOL in the population this sample represents. [You should not do a linear regression with Fit Y by X here. Can you see why?]

Use your political sense to decide how much political support you'll need for the VAQ standard, and use the smooth curve in your Graph Builder plot to identify a dividing line between politically acceptable visual air quality and politically unacceptable. Draw a horizontal line on your Graph Builder plot showing the level of political support you think you'll need, and a vertical line showing the corresponding VAQ.

(2) Derive a regression equation for predicting VAQ from Extinction. [You will use JMP's Fit Y by X command.] Note that VAQ is a subjective interpretation of visual air quality, and Extinction is a repeatable measurement from a piece of optical equipment. So Extinction should be the explanatory variable (the x-axis variable) and VAQ should be the response variable (the y-axis variable).

Use your regression equation to compute the Extinction reading that corresponds to the level of political support and VAQ you found in step 1.

(3) Pull the analyses in steps (1) and (2) together. Identify a politically acceptable Extinction level that you would propose as the scientifically measurable dividing line between acceptable and unacceptable air quality.

Write up your results in a Policy Memo with two Technical Appendices.

Policy memo: A policy memo to the Colorado Air Quality in which you state your visible air quality standard phrased in terms of the Extinction value that can be measured reliably by the Optic LPV-2 device. Explain in nontechnical terms how you determined that politically acceptable Extinction standard, referring to the two technical memos you include as appendices. It is here you will bring together the results of your two technical analyses in a form you think the Colorado Air Quality folks would want to read.

Technical Appendix #1: Show all the details of your scatterplot/smooth curve analysis in step (1) above, explaining why you did what you did and what you concluded. (It is in these technical memos where you will present the work that the Commission's technical staff will need to verify you've done these analyses to their technical satisfaction.)

Technical Appendix #2: Show all the details of your regression analysis in step (2) above, explaining what you did, what it all means, and how you used the regression equation to derive the Extinction standard.