Using structural equation modeling to construct calibration equations relating PM2.5 mass concentration samplers to the federal reference method sampler

Abstract

h i g h l i g h t sCollocated PM 2.5 mass concentration samplers were calibrated using linked structural equation models (SEMs). Bias and imprecision were determined for FRM, TEOM, SFS, SASS, and IMPROVE samplers. SEMs were stratified to describe the temperature dependency of TEOM samplers. TEOM bias relative to FRM followed a well-defined sigmoidal temperature dependency. FRM was most precise while TEOM imprecision decreased with increasing temperature. a b s t r a c tThe objective of this study was to remove systematic bias among fine particulate matter (PM 2.5 ) mass concentration measurements made by different types of samplers used in the Pittsburgh Aerosol Research and Inhalation Epidemiology Study (PARIES). PARIES is a retrospective epidemiology study that aims to provide a comprehensive analysis of the associations between air quality and human health effects in the Pittsburgh, Pennsylvania, region from 1999 to 2008. Calibration was needed in order to minimize the amount of systematic error in PM 2.5 exposure estimation as a result of including data from 97 different PM 2.5 samplers at 47 monitoring sites. Ordinary regression often has been used for calibrating air quality measurements from pairs of measurement devices; however, this is only appropriate when one of the two devices (the "independent" variable) is free from random error, which is rarely the case. A group of methods known as "errors-in-variables" (e.g., Deming regression, reduced major axis regression) has been developed to handle calibration between two devices when both are subject to random error, but these methods require information on the relative sizes of the random errors for each device, which typically cannot be obtained from the observed data. When data from more than two devices (or repeats of the same device) are available, the additional information is not used to inform the calibration. A more general approach that often has been overlooked is the use of a measurement error structural equation model (SEM) that allows the simultaneous comparison of three or more devices (or repeats). The theoretical underpinnings of all of these approaches to calibration are described, and the pros and cons of each are discussed. In particular, it is shown that both ordinary regression (when used for calibration) and Deming regression are particular examples of SEMs but with substantial deficiencies. To illustrate the use of SEMs, the 7865 daily average PM 2.5 mass concentration measurements made by seven collocated samplers at an urban monitoring site in Pittsburgh, Pennsylvania, were used. These samplers, which included three federal reference method (FRM) samplers, three speciation samplers, and a tapered element oscillating microbalance (TEOM), operated at various times during the 10-year PARIES study period. Because TEOM measurements are known to depend on temperature, the constructed SEM provided calibration equations relating the TEOM to the FRM and speciation samplers as a function of ambient temperature. It was shown that TEOM imprecis...

Calibration of PM2.5 mass concentrations used in the Pittsburgh Aerosol Research and Inhalation Epidemiology Study

“…As shown in more detail in our previous study (Bilonick et al, 2015), the relationship between any pair of devices can be derived. By taking expectations (averaging out the random error using expected values), the calibration equations can be determined.…”

“…(The relative biases and differences in imprecision among the various models of FRM samplers are assumed to be negligible).This basic design is then used as a building block to handle a more complex analysis. For example, in our previous work (Bilonick et al, 2015), the classic model was extended, using stratification, to account for the nonlinear effect of temperature on PM 2.5 mass concentration measurements made using a 50 C TEOM monitor. Here we extend the model further to also include samplers located at multiple monitoring sites.…”

“…In our previous study (Bilonick et al, 2015), the classic measurement error model was thoroughly described and was applied to calibrate collocated measurements made by multiple PM 2.5 samplers at a single site. Fig.…”

“…For samplers that do not depend on temperature (samplers of type 1, 9 and 12), the b labels are the same across all temperature strata, i.e., the second subscript is always a #. The method used to define the eight temperature strata was described in Bilonick et al (2015).…”

“…In this study, a comprehensive measurement error model was constructed making it possible to determine the calibration equation linking any two monitor types. The basic methodology was described for a single monitoring site in our previous article (Bilonick et al, 2015). This methodology is extended here to simultaneously calibrate measurements made from all 97 samplers at the 47 monitoring sites used in PARIES.…”