Personal exposure to ultrafine particles: Two-level statistical
modeling of background exposure and time-activity patterns during
three seasons - Supplementary material
Veronika Deffnera, Helmut Küchenhoffa, Verena Maiera, Mike Pitzb, Josef Cyrysc,d, Susanne Breitnerc, Alexandra
Schneiderc, Jianwei Guc,d, Uta Geruschkatc, Annette Petersc
a
Statistical Consulting Unit, Department of Statistics, Ludwig-Maximilians-Universität, Akademiestr. 1, 80799
Munich, Germany
b
Bavarian Environment Agency (LfU), Augsburg, Germany
c
Helmholtz Zentrum München, Institute of Epidemiology II, Ingolstädter Landstr. 1, 85764 Neuherberg,
Germany
d
Environment Science Center, Universität Augsburg, Universitätsstr. 1a, 86159 Augsburg, Germany
1.
Analysis of comparison measurements
The usage of measurement devices over a longer period carries the danger of a gradually decreasing
performance of the mobile CPC devices resulting e.g. from degeneration or from soiling. This yields temporally
biased measurements. Since measurements from different devices involve a device-specific bias the joint
analysis of the data requires the correction of these biases. Comparison measurements were conducted before
and after each measurement campaign of our study. Data, analyses and correction procedures are described in
this chapter.
The following devices used in our study were included in the comparison measurements; they measure with
differing temporal resolutions:
•
Stationary:
 Condensation Particle Counter (CPC 3025, TSI Inc., USA); 1-min. average (PNC CPC UAS)
 Twin Differential mobility Particle Sizer (TDMPS)/Aerodynamic Particle Sizer (APS, model 3321, TSI Inc.,
USA); 10-min. average, updated every 20 minutes (PNC 10-800 UAS)
•
Mobile: three Condensation Particle Counters (CPC 3007, TSI Inc., USA); 1-min. average
The mobile devices operate with batteries limiting their operating time. The length of the comparison periods
varied between two and eight days.
For the purpose of comparison between the portable CPC 3007 devices and the devices at the measurement
station we used the PNC in the size range from 3 nm to 3 µm (measured by CPC 3025) and in the size range
from 10 nm until 800 nm (measured by TDMPS). The latter size range corresponds approximately to the size
range of particles measured by the portable CPC 3007, however the stationary PNC levels are recorded only
every 20 minutes. The different devices recorded the data in varying resolution. Therefore, the data were
aggregated appropriately to compare the measurements. Mobile as well as stationary CPC measurements were
aggregated to a 30-min. running mean for their comparison. For the comparison of the mobile measurements
with the measurements of the appropriate fractions of the particle size spectrometer, i.e. of particles between
10 and 800 nm, only the mobile measurements at the updating time points of the TDMPS/APS were used.
Linear models between the stationary and the mobile measurements yielded the correction formulas for the
mobile measurements. All comparison periods were analyzed simultaneously because temporally differences
were not consistent. The following correction formulas were obtained for the comparison with the stationary
TDMPS/APS, which were used for the exposure analysis:
Mobile device (X)
Stationary measurements (Y)
Correction formula
CPC 07061001
PNC 10-800 nm UAS
Y= EXP(0.397+0.955LOG(X))
CPC 07061002
PNC 10-800 nm UAS
Y= EXP(0.278+0.976LOG(X))
CPC 10070001
PNC 10-800 nm UAS
Y= EXP(0.553+0.946LOG(X))
Table S1: Correction formulas for 1-minute mobile measurements to reach comparability of the measurements
based on 30-minute averaged data.
The comparison measurements were conducted under controlled conditions with outdoor background data.
We have not adjusted for possible differences between the devices emerging in diverse other situations, e.g.
during indoor activities or in traffic.
2.
Detailed model formulas
2.1.
Stage 1: Background model (before variable selection)
Regression equations modeling PNC of individual i at time point t with the maximum set of predictors are
presented in the following. The random person intercept is denoted by .
represent smooth
functions which were modeled with P-splines.
Indoors:
Outdoors:
2.2. Stage 2: Activity model
The regression equations for modeling the residual (resulting from the background model) of realization j of
activity k at time point t are described in this paragraph.
Indoors:
Outdoors:
The outcomes in the activity models were the residuals from the background model and can be interpreted as
personal PNC levels which were adjusted for the background exposure to PNC. The association between the
outcome and the activities was modeled through their main effects. The background adjusted personal
exposure to PNC during each realization j of a particular activity k differs from the main effect of activity k; a
random intercept
was included in the model to represent realization-specific variations of the activities.
Moreover, the variance of the outcome differed between the activities resulting in heteroscedastic variances.
Therefore, activity-specific residual variances were allowed in the model. Autocorrelation of the residuals of the
activity model within a realization of an activity were considered through a rational quadratic correlation
structure (see Supplementary Materials 6).
3.
Variable selection via model based boosting
Variable selection in the background models was conducted using model-based boosting (Bühlmann and
Hothorn, 2007), which is implemented in the R (R Core Team, 2013) package “mboost” (Hothorn et al., 2013).
Boosting algorithms estimate coefficients by iteratively approximating the solution with small steps. Adding up
the coefficients of a specific covariate of all iteration steps results in the common regression coefficients. As
usual, these can be interpreted as conditional effects adjusted for the other covariates included in the model.
This approach offers three advantages: (I) the association between exposure and only the relevant covariates is
modeled, (II) the multicollinearity problem of the measurement values from the stationary monitor in a usual
regression model is avoided and (III) the combination of base–learners for linear, smooth and random effects
flexibly models the underlying structure in the data.
Categorical covariates were modeled with componentwise ordinary least squares base–learners. The
continuous covariates in our study were smoothly estimated using componentwise smoothing splines with
three degrees of freedom. Componentwise estimation means that only the predictor with the best
improvement is updated in each iteration. The cross–validation criterion to stop the iterative boosting
procedure ensured the inclusion of only significantly contributing covariates.
4.
Reduced data for the background models
Stationary measurements above the 95% quantile and personal measurements above the 90% quantile were
excluded for the background model in the first modeling stage. This choice is visualized in the following two
figures:
Figure S1: Scatterplots between personal indoor measurements of 1-minute PNC (x-axes) and stationary 1minute PM measurements (y-axes); the 90 % quantile of the personal measurements and the 95 % quantile of
the stationary measurements are marked with lines.
Figure S2: Scatterplots between personal outdoor measurements of 1-minute PNC (x-axes) and stationary 1minute PM measurements (y-axes); the 90 % quantile of the personal measurements and the 95 % quantile of
the stationary measurements are marked with lines.
Through the exclusion of observations with extreme stationary measurements the smooth effects in the
background model at the upper border of the domain could be regarded as reliable because enough
information was available. This was of major relevance because the uncertainty of the predictions in the first
stage was not included in the second stage models.
Using the boosting algorithm as well as other regression methods, the model is calculated through minimizing
the size of the residuals. Thus, observations with high residuals potentially have a higher impact on the model
calculation than other observations.
Extreme personal exposure might have possibly emerged from particle generating activities which were not
documented or did not fit in any of the categories of the activity diary (e.g. very high individual exposure of a
volunteer while staying in the cafeteria of the university). These observations did not describe individual
background exposure and were therefore excluded for the calculation of the background exposure model.
Extreme stationary measurements might have emerged from particle generating events which have no bearing
on the actual background exposure.
Figures S1 and S2 showed that, extreme values were in the majority of observations only measured with the
stationary or with the mobile device and not with both devices. The Figures also indicated the appropriateness
of the choice of the 90 % quantile for the individual measurements and of the 95 % quantile for the stationary
measurements for the exclusion of extreme measurements.
5.
Relevance of predictor groups
Let
denote the predictors in a linear regression model for the outcome variable
. Further, it is assumed that the set of predictors
into
uncorrelated
subgroups
with
explained
by
a
specific
can be divided
,
,…,
as the group index. The fraction of variance
predictor
group
with
is
determined
through
. This relation was used
to evaluate the relevance of the predictor groups
(individual; time including, week, day of the week and
time of day; meteorology including temperature, relative humidity and dew point temperature; categorical
surrounding variables including at home/not at home and status of windows (indoor models); stationary
measurements including PNC and particle mass levels of various size ranges and black carbon concentrations) in
the background models.
6.
Categorical effects in highly correlated time series
Different modeling strategies for categorical effects in longitudinal data are evaluated in this chapter with an
example data set for exposure and activity data. Since the data generating process is very complex, the
modeling approaches were compared using real data instead of simulated data. A small data set was used in
order to explain the characteristics of models in combination with a visual imagination of the data. Three
exemplary time series from the validation study, depicted in Figure S3, were chosen, one without any activity
and two further time series with cooking and candle lighting.
Figure S3: Three exemplary time series of personal exposure to 1-min. PNC (in 1/cm³), adjusted for background
exposure.
Each temporal coherent period with the same activity (or non-activity) of an individual was called the
realization of an activity. Because the model contained only categorical covariates, Figure S3 lead to suspect
heteroscedastic residuals, i.e. the variance of the residuals within a realization of an activity varied between the
different realizations. Also realization-specific correlation structures were considerable. Furthermore,
categorical effects in highly autocorrelated continuous time series could be biased if an AR(1) process for the
residuals was assumed because mainly the marginal observations of the activities were used to calculate the
effect. Therefore, also other correlation structures were examined. These approaches were evaluated with the
following models concerning their coefficient estimates, model fit and compliance of the assumptions using the
example data:
M1: Linear mixed model (M1a) and additional realization-specific variance of the error term (M1b)
M2: Linear mixed model with AR(1) structure for the error term (M2a) and additional realization-specific
variance of the error term (M2b)
M3: Linear mixed model with AR(1) structure for the error term and realization-specific correlation
coefficients (M3a) and additional realization-specific variance of the error term (M3b)
M4: Linear mixed model with rational quadratic correlation structure (Pinheiro and Bates, 2000) for the
error term (M4a) and additional realization-specific variance of the error term (M4b)
M5: Linear mixed model with rational quadratic correlation structure for the error term and realizationspecific correlation coefficients (M5a) and additional realization-specific variance of the error term
(M5b)
M6: Additive mixed models with few (every tenth observation) (M6a) and many (every third observation)
(M6b) knots
The rational correlation structure is defined as
with
denoting the nugget,
the distance of the time points and the range (Pinheiro and Bates, 2000).
The exposure to PNC during single realizations of activities was assumed to be independent resulting in a blockdiagonal correlation structure; the blocks were determined through the realizations of the activities. A
realization-specific random intercept was included in all models. Also realization-specific correlation structures
were considered, because the level of autocorrelation may vary depending on the way of conducting a certain
activity.
If the model was correctly specified, the linear mixed model M1 provided consistent estimates of the effect
coefficients. Therefore, models accounting for heteroscedastic and autocorrelated residuals should yield similar
estimates for the coefficients. Further reference criteria for the evaluation of the different approaches referred
to the homoscedasticity (Breusch-Pagan test (BP test, Breusch and Pagan, 1979)) and independence of the
residuals (AC-coef.). In addition, the models were compared concerning their fit via the Akaike information
criterion (AIC). The results of the model comparison are depicted in Figure S4.
The linear mixed model (M1a) with random person intercept showed a bad model fit and strong violations of
the model assumptions regarding highly autocorrelated and heteroscedastic residuals, which was only partially
eliminated through the realization-specific residual variances (M1b). Including an overall as well as a
realization-specific correlation structure (M2 and M3) fractionally alleviated the problem of autocorrelation
and improved the model fit but did not identify the visually apparent effects of the activities. The models with
an autoregressive process of order one for the residuals exhibited a strong bias in one or even both activity
effect estimates of about 40 000 particles. Instead, using the rational quadratic correlation structure (M4)
provided adequate estimates for the coefficients, a comparably good model fit and met the model
assumptions. Individual-specific rational quadratic correlation coefficients (M5) degraded the model fit due to
the convergence of the algorithm to a local maximum. Smoothing splines (M6) for modeling the temporal
dependencies were not able to remove the autocorrelation of the residuals; furthermore, the AIC of these
models was high. Model M4b showed the best properties and was used for the analyses.
Figure S4: Model comparison regarding coefficients, residual autocorrelation (AC-coef.), heteroscedasticity (BP test, asterisks mark significance) and model fit (AIC).
7.
Relative durations of activities
Winter
Spring
Public
City
Sum m er
Public
City
Public
City
Scenario
Car
transport
center
Car
transport
center
Car
transport
center
indoors, at hom e
57.0
53.3
0.1
56.9
54.1
0.0
60.4
56.1
0.0
indoors, not at hom e
20.4
18.6
30.5
18.1
17.7
25.6
18.2
18.3
30.6
opened
4.3
3.1
0.9
14.1
12.1
7.7
8.4
11.3
3.8
closed
65.8
64.6
25.4
48.8
39.8
13.0
57.5
36.2
25.1
tilted
5.8
2.8
0.7
10.8
20.3
2.2
13.0
27.1
1.3
air conditioning/ventilation
0.4
0.0
0.6
0.0
0.0
0.0
0.0
0.0
0.0
passive sm oking
0.6
1.4
2.4
0.3
0.1
1.5
0.0
0.3
1.3
sm oke of w ood
0.6
0.8
0.0
2.0
0.0
0.0
0.0
0.0
0.0
sm oke of candles
6.1
4.4
1.3
0.5
1.6
0.1
3.0
0.6
0.0
cooking
6.0
4.2
0.7
6.3
6.2
0.0
5.4
4.7
0.0
cleaning
2.9
2.2
0.0
4.5
2.7
0.0
3.8
2.0
0.0
ironing
1.0
5.4
0.0
0.0
3.3
0.0
3.0
1.6
0.0
spray
0.6
0.4
0.0
1.2
0.3
0.0
1.1
0.8
0.0
dust
5.4
3.3
0.0
8.2
7.2
0.0
5.4
7.2
0.0
smell of food
1.7
0.0
0.6
1.2
2.0
0.1
1.9
2.5
0.1
smell of smoke
0.6
0.3
0.2
0.4
0.4
0.5
0.1
0.1
0.3
smell of vehicle exhaust
0.0
0.0
0.4
0.0
0.0
0.1
0.0
0.0
0.0
building site
0.0
0.0
0.0
0.0
0.0
0.1
0.0
0.0
1.1
steam
0.4
0.2
0.0
0.4
0.4
0.0
0.5
0.1
0.0
laser printer
0.7
0.0
0.0
0.0
0.0
0.0
0.1
1.0
0.0
1.6
0.9
5.4
1.9
1.4
6.4
1.7
2.0
5.8
12.8
20.2
52.3
13.6
19.0
58.4
11.8
16.8
55.8
11.9
0.0
0.0
11.7
1.3
0.0
10.8
0.0
0.0
pedestrian
0.8
2.6
52.3
1.9
1.3
58.4
1.0
2.0
55.8
public transport (bus/tram/train)
0.0
17.6
0.0
0.0
16.5
0.0
0.0
14.8
0.0
w indow
sm ell
abnorm alities
outdoors, not in traffic
outdoors, in traffic
m eans of transport
car
Table S2: Percentage frequency of activities (recorded every minute) during the three scenarios for each
measurement period.
8.
Daily variations of 5–min. averaged PNC
Figure S5: Mean diurnal variation of 5-minute averaged PNC; solid: personal PNC levels, dashed: PNC levels at
the stationary monitor.
Mean personal exposure to PNC was higher than the concentration measured at the station. Increased indoor
exposure to PNC was mainly measured at about noon during scenarios “car” and “public transport”, when the
volunteers prepared their food. Mean personal exposure to PNC was similar to stationary measured PNC levels
during scenario “city center”.
9.
Correlations between personal and stationary measured PNC levels
Indoors
Outdoors
Winter
Spring
Summer
Winter
Spring
Summer
Air temperature
-0.037 *
-0.122 *
-0.164 *
-0.138 *
-0.048 *
0.010
Rel. humidity
-0.164 *
0.059 *
-0.055 *
-0.126 *
-0.039 *
-0.018
Dew point temperature
-0.214 *
-0.095 *
-0.155 *
-0.323 *
-0.073 *
-0.017
PM2.5
0.069 *
0.173 *
0.003
-0.047 *
0.078 *
0.208 *
PM10
0.120 *
0.199 *
0.067 *
0.010
0.126 *
0.211 *
NC CPC
0.164 *
0.150 *
0.228 *
0.347 *
0.413 *
0.294 *
BC
0.093 *
0.122 *
0.103 *
0.169 *
0.273 *
0.154 *
NC 10-800
0.210 *
0.190 *
0.229 *
0.365 *
0.414 *
0.334 *
Table S3: Spearman rank correlations between 1-minute personal PNC levels and stationary concentration levels
and personally measured meteorology; coefficients which significantly differ from zero are marked with *.
The correlations (Spearman rank correlation) of personal exposure to PNC with mobile meteorology
measurements and particulate matter concentrations from the stationary monitor are presented in Table S3.
Indoor personal exposure to PNC was not correlated with any of the examined variables (|r| < 0.23).
Correlations of outdoor personal PNC levels with the number concentration of the corresponding particle size
range and the stationary PNC levels were slightly stronger with highest values in spring. Stationary PNC
measurements weakly correlated with PM2.5 (r = 0.374) and PM10 (r = 0.431) recorded at the stationary monitor.
10. Exposure ratio: logarithmically scaled abscissa
Figure S5: Ratio between the median 1-minute exposure to PNC of each volunteer during a particular activity
and the median 1-minute exposure to PNC of all individuals stratified on the season, separately for indoor and
outdoor activities (dots; blue: winter, green: spring, red: summer). Exposure ratios for more than four persons
are summarized by a boxplot.
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