mesa.model: Example of a 'STmodel' structure
In SpatioTemporal: Spatio-Temporal Model Estimation
Description
Format
Details
Source
References
See Also
Examples
Description
Example of a model structure holding observations, geographic covariates,
observation locations, smooth temporal trends, spatio-temporal covariates,
and covariance specifications for the model.
Format
A list with elements, a detailed description of each elements is
given in details below
Details
A STmodel object consists of a list with, some or all of, the following
elements:
- obs
A data.frame with columns:
- obs
The value of each observation.
- date
The observations time, preferably of class
Date.
- ID
A character-class giving observation locations;
should match elements in locations$ID.
- idx
match between obs$ID and locations$ID for
faster computations.
The data.frame is sorted by date and idx.
- locations.list,locations
Specification of locations and data.frame
with locations for observations (and predictions), see
processLocation.
- D.nu,D.beta
Distance matrices for the locations in the, possibly
different coordinate systems for beta- and nu-fields. See
processLocation.
- cov.beta,cov.nu
Covariance structure for beta- and nu-fields, see
updateCovf.
- LUR.list,LUR
Specification of covariates for the beta-fields and
a list with covariates for each of the beta-fields, see
processLUR and createLUR.
- trend,trend.fnc
The temporal trends with one of the columns
being named date, preferably of class Date
providing the time alignment for the temporal trends.
- F
A matrix contaning smooth temporal trends for each observation;
elements taken from trend.
- ST.list,ST,ST.all
Spatio-termporal covariates, NULL if no
covariates. For the observations and all space-time locations respectively,
see processST and createST.
- old.trend,fit.trend
Additional components added if the observations
have been detrended, see
detrendSTdata.
Source
Contains monitoring data from the MESA Air project, see
Cohen et.al. (2009) and mesa.data.raw for details.
References
M. A. Cohen, S. D. Adar, R. W. Allen, E. Avol, C. L. Curl, T.
Gould, D. Hardie, A. Ho, P. Kinney, T. V. Larson, P. D. Sampson, L.
Sheppard, K. D. Stukovsky, S. S. Swan, L. S. Liu, J. D. Kaufman. (2009)
Approach to Estimating Participant Pollutant Exposures in the Multi-Ethnic
Study of Atherosclerosis and Air Pollution (MESA Air). Environmental Science
& Technology: 43(13), 4687-4693.
See Also
createSTmodel for creation of STmodel
objects.
createSTdata for creation of the originating
STdata object.
Other example data: MCMC.mesa.model,
est.cv.mesa, est.mesa.model,
mesa.data.raw,
pred.mesa.model
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
##load the data
data(mesa.model)
##examine components
names(mesa.model)
print(mesa.model)
summary(mesa.model)
##requested geographic and spatio-temporal covariates
mesa.model$LUR.list
mesa.model$ST.list
##covariates for the temporal intercept
head(mesa.model$LUR$const)
##...and the two smooth temporal trends
head(mesa.model$LUR$V1)
head(mesa.model$LUR$V2)
##Some important dimensions of the model
loglikeSTdim(mesa.model)
Example output
Loading required package: Matrix
[1] "obs" "trend" "trend.fnc" "locations.list"
[5] "locations" "cov.beta" "cov.nu" "LUR.list"
[9] "ST.list" "LUR.all" "LUR" "ST.all"
[13] "ST" "F" "D.nu" "D.beta"
[17] "nt"
STmodel-object with:
No. locations: 25 (observed: 25)
No. time points: 280 (observed: 280)
No. obs: 4577
Trend with 2 basis function(s):
[1] "V1" "V2"
with dates:
1999-01-13 to 2009-09-23
Models for the beta-fields are:
$const
~log10.m.to.a1 + s2000.pop.div.10000 + km.to.coast
$V1
~km.to.coast
$V2
~km.to.coast
1 spatio-temporal covariate(s):
[1] "lax.conc.1500"
Covariance model for the beta-field(s):
Covariance type(s): exp, exp, exp
Nugget: No, No, No
Covariance model for the nu-field(s):
Covariance type: exp
Nugget: ~type
Random effect: No
All sites:
AQS FIXED
20 5
Observed:
AQS FIXED
20 5
For AQS:
Number of obs: 4178
Dates: 1999-01-13 to 2009-09-23
For FIXED:
Number of obs: 399
Dates: 2005-12-07 to 2009-07-01
Summary of observations:
obs date
Min. :0.678 Min. :1999-01-13
1st Qu.:3.330 1st Qu.:2001-11-28
Median :3.786 Median :2004-09-15
Mean :3.774 Mean :2004-08-11
3rd Qu.:4.269 3rd Qu.:2007-05-23
Max. :5.752 Max. :2009-09-23
Summary of locations:
ID x y x.beta
Length:25 Min. :-10918 Min. :3742 Min. :-10918
Class :character 1st Qu.:-10898 1st Qu.:3770 1st Qu.:-10898
Mode :character Median :-10888 Median :3780 Median :-10888
Mean :-10884 Mean :3778 Mean :-10884
3rd Qu.:-10864 3rd Qu.:3786 3rd Qu.:-10864
Max. :-10846 Max. :3801 Max. :-10846
y.beta x.nu y.nu long
Min. :3742 Min. :-10918 Min. :3742 Min. :-118.5
1st Qu.:3770 1st Qu.:-10898 1st Qu.:3770 1st Qu.:-118.3
Median :3780 Median :-10888 Median :3780 Median :-118.2
Mean :3778 Mean :-10884 Mean :3778 Mean :-118.2
3rd Qu.:3786 3rd Qu.:-10864 3rd Qu.:3786 3rd Qu.:-118.0
Max. :3801 Max. :-10846 Max. :3801 Max. :-117.8
lat type
Min. :33.67 AQS :20
1st Qu.:33.93 FIXED: 5
Median :34.01
Mean :33.99
3rd Qu.:34.07
Max. :34.20
Summary of geographic covariates:
$const
(Intercept) log10.m.to.a1 s2000.pop.div.10000 km.to.coast
Min. :1 Min. :1.825 Min. :1.555 Min. : 1.023
1st Qu.:1 1st Qu.:2.614 1st Qu.:2.785 1st Qu.: 5.948
Median :1 Median :2.862 Median :4.106 Median :15.000
Mean :1 Mean :2.864 Mean :4.245 Mean :11.432
3rd Qu.:1 3rd Qu.:3.224 3rd Qu.:5.219 3rd Qu.:15.000
Max. :1 Max. :3.812 Max. :8.206 Max. :15.000
$V1
(Intercept) km.to.coast
Min. :1 Min. : 1.023
1st Qu.:1 1st Qu.: 5.948
Median :1 Median :15.000
Mean :1 Mean :11.432
3rd Qu.:1 3rd Qu.:15.000
Max. :1 Max. :15.000
$V2
(Intercept) km.to.coast
Min. :1 Min. : 1.023
1st Qu.:1 1st Qu.: 5.948
Median :1 Median :15.000
Mean :1 Mean :11.432
3rd Qu.:1 3rd Qu.:15.000
Max. :1 Max. :15.000
Summary of smooth trends:
V1 V2 date
Min. :-2.0807 Min. :-2.27852 Min. :1999-01-13
1st Qu.:-0.8828 1st Qu.:-0.72370 1st Qu.:2001-09-15
Median : 0.1345 Median :-0.01471 Median :2004-05-19
Mean : 0.0000 Mean : 0.00000 Mean :2004-05-19
3rd Qu.: 0.8756 3rd Qu.: 0.73483 3rd Qu.:2007-01-20
Max. : 1.8503 Max. : 2.08859 Max. :2009-09-23
Summary of spatio-temporal covariates.
lax.conc.1500
Min. : 0.00000
1st Qu.: 0.09528
Median : 1.81705
Mean : 3.47925
3rd Qu.: 5.12175
Max. :34.00420
Summary for observations of type AQS
obs date
Min. :0.8102 Min. :1999-01-13
1st Qu.:3.3406 1st Qu.:2001-09-19
Median :3.7916 Median :2004-03-17
Mean :3.7836 Mean :2004-04-22
3rd Qu.:4.2751 3rd Qu.:2006-12-30
Max. :5.7516 Max. :2009-09-23
Summary for observations of type FIXED
obs date
Min. :0.678 Min. :2005-12-07
1st Qu.:3.217 1st Qu.:2006-12-06
Median :3.755 Median :2007-10-10
Mean :3.669 Mean :2007-10-28
3rd Qu.:4.196 3rd Qu.:2008-08-27
Max. :5.285 Max. :2009-07-01
$const
~log10.m.to.a1 + s2000.pop.div.10000 + km.to.coast
$V1
~km.to.coast
$V2
~km.to.coast
[1] "lax.conc.1500"
(Intercept) log10.m.to.a1 s2000.pop.div.10000 km.to.coast
60370002 1 2.861509 1.733283 15.000000
60370016 1 3.461672 1.645386 15.000000
60370030 1 2.561133 6.192630 15.000000
60370031 1 3.111413 2.088930 1.023311
60370113 1 2.762193 7.143731 6.011075
60371002 1 2.760931 4.766780 15.000000
(Intercept) km.to.coast
60370002 1 15.000000
60370016 1 15.000000
60370030 1 15.000000
60370031 1 1.023311
60370113 1 6.011075
60371002 1 15.000000
(Intercept) km.to.coast
60370002 1 15.000000
60370016 1 15.000000
60370030 1 15.000000
60370031 1 1.023311
60370113 1 6.011075
60371002 1 15.000000
$T
[1] 280
$m
[1] 3
$n
[1] 25
$n.obs
[1] 25
$p
const V1 V2
4 2 2
$L
[1] 1
$npars.beta.covf
exp exp exp
2 2 2
$npars.beta.tot
exp exp exp
2 2 2
$npars.nu.covf
[1] 2
$npars.nu.tot
[1] 4
$nparam.cov
[1] 10
$nparam
[1] 19
SpatioTemporal documentation built on May 2, 2019, 8:49 a.m.
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Description Format Details Source References See Also Examples
Description
Example of a model structure holding observations, geographic covariates, observation locations, smooth temporal trends, spatio-temporal covariates, and covariance specifications for the model.
Format
A list with elements, a detailed description of each elements is given in details below
Details
A STmodel object consists of a list with, some or all of, the following
elements:
- obs
A data.frame with columns:
- obs
The value of each observation.
- date
The observations time, preferably of class
Date.- ID
A
character-class giving observation locations; should match elements inlocations$ID.- idx
match between
obs$IDandlocations$IDfor faster computations.
The data.frame is sorted by
dateandidx.- locations.list,locations
Specification of locations and data.frame with locations for observations (and predictions), see
processLocation.- D.nu,D.beta
Distance matrices for the locations in the, possibly different coordinate systems for beta- and nu-fields. See
processLocation.- cov.beta,cov.nu
Covariance structure for beta- and nu-fields, see
updateCovf.- LUR.list,LUR
Specification of covariates for the beta-fields and a list with covariates for each of the beta-fields, see
processLURandcreateLUR.- trend,trend.fnc
The temporal trends with one of the columns being named
date, preferably of classDateproviding the time alignment for the temporal trends.- F
A matrix contaning smooth temporal trends for each observation; elements taken from
trend.- ST.list,ST,ST.all
Spatio-termporal covariates,
NULLif no covariates. For the observations and all space-time locations respectively, seeprocessSTandcreateST.- old.trend,fit.trend
Additional components added if the observations have been detrended, see
detrendSTdata.
Source
Contains monitoring data from the MESA Air project, see
Cohen et.al. (2009) and mesa.data.raw for details.
References
M. A. Cohen, S. D. Adar, R. W. Allen, E. Avol, C. L. Curl, T. Gould, D. Hardie, A. Ho, P. Kinney, T. V. Larson, P. D. Sampson, L. Sheppard, K. D. Stukovsky, S. S. Swan, L. S. Liu, J. D. Kaufman. (2009) Approach to Estimating Participant Pollutant Exposures in the Multi-Ethnic Study of Atherosclerosis and Air Pollution (MESA Air). Environmental Science & Technology: 43(13), 4687-4693.
See Also
createSTmodel for creation of STmodel
objects.
createSTdata for creation of the originating
STdata object.
Other example data: MCMC.mesa.model,
est.cv.mesa, est.mesa.model,
mesa.data.raw,
pred.mesa.model
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ##load the data
data(mesa.model)
##examine components
names(mesa.model)
print(mesa.model)
summary(mesa.model)
##requested geographic and spatio-temporal covariates
mesa.model$LUR.list
mesa.model$ST.list
##covariates for the temporal intercept
head(mesa.model$LUR$const)
##...and the two smooth temporal trends
head(mesa.model$LUR$V1)
head(mesa.model$LUR$V2)
##Some important dimensions of the model
loglikeSTdim(mesa.model)
|
Example output
Loading required package: Matrix
[1] "obs" "trend" "trend.fnc" "locations.list"
[5] "locations" "cov.beta" "cov.nu" "LUR.list"
[9] "ST.list" "LUR.all" "LUR" "ST.all"
[13] "ST" "F" "D.nu" "D.beta"
[17] "nt"
STmodel-object with:
No. locations: 25 (observed: 25)
No. time points: 280 (observed: 280)
No. obs: 4577
Trend with 2 basis function(s):
[1] "V1" "V2"
with dates:
1999-01-13 to 2009-09-23
Models for the beta-fields are:
$const
~log10.m.to.a1 + s2000.pop.div.10000 + km.to.coast
$V1
~km.to.coast
$V2
~km.to.coast
1 spatio-temporal covariate(s):
[1] "lax.conc.1500"
Covariance model for the beta-field(s):
Covariance type(s): exp, exp, exp
Nugget: No, No, No
Covariance model for the nu-field(s):
Covariance type: exp
Nugget: ~type
Random effect: No
All sites:
AQS FIXED
20 5
Observed:
AQS FIXED
20 5
For AQS:
Number of obs: 4178
Dates: 1999-01-13 to 2009-09-23
For FIXED:
Number of obs: 399
Dates: 2005-12-07 to 2009-07-01
Summary of observations:
obs date
Min. :0.678 Min. :1999-01-13
1st Qu.:3.330 1st Qu.:2001-11-28
Median :3.786 Median :2004-09-15
Mean :3.774 Mean :2004-08-11
3rd Qu.:4.269 3rd Qu.:2007-05-23
Max. :5.752 Max. :2009-09-23
Summary of locations:
ID x y x.beta
Length:25 Min. :-10918 Min. :3742 Min. :-10918
Class :character 1st Qu.:-10898 1st Qu.:3770 1st Qu.:-10898
Mode :character Median :-10888 Median :3780 Median :-10888
Mean :-10884 Mean :3778 Mean :-10884
3rd Qu.:-10864 3rd Qu.:3786 3rd Qu.:-10864
Max. :-10846 Max. :3801 Max. :-10846
y.beta x.nu y.nu long
Min. :3742 Min. :-10918 Min. :3742 Min. :-118.5
1st Qu.:3770 1st Qu.:-10898 1st Qu.:3770 1st Qu.:-118.3
Median :3780 Median :-10888 Median :3780 Median :-118.2
Mean :3778 Mean :-10884 Mean :3778 Mean :-118.2
3rd Qu.:3786 3rd Qu.:-10864 3rd Qu.:3786 3rd Qu.:-118.0
Max. :3801 Max. :-10846 Max. :3801 Max. :-117.8
lat type
Min. :33.67 AQS :20
1st Qu.:33.93 FIXED: 5
Median :34.01
Mean :33.99
3rd Qu.:34.07
Max. :34.20
Summary of geographic covariates:
$const
(Intercept) log10.m.to.a1 s2000.pop.div.10000 km.to.coast
Min. :1 Min. :1.825 Min. :1.555 Min. : 1.023
1st Qu.:1 1st Qu.:2.614 1st Qu.:2.785 1st Qu.: 5.948
Median :1 Median :2.862 Median :4.106 Median :15.000
Mean :1 Mean :2.864 Mean :4.245 Mean :11.432
3rd Qu.:1 3rd Qu.:3.224 3rd Qu.:5.219 3rd Qu.:15.000
Max. :1 Max. :3.812 Max. :8.206 Max. :15.000
$V1
(Intercept) km.to.coast
Min. :1 Min. : 1.023
1st Qu.:1 1st Qu.: 5.948
Median :1 Median :15.000
Mean :1 Mean :11.432
3rd Qu.:1 3rd Qu.:15.000
Max. :1 Max. :15.000
$V2
(Intercept) km.to.coast
Min. :1 Min. : 1.023
1st Qu.:1 1st Qu.: 5.948
Median :1 Median :15.000
Mean :1 Mean :11.432
3rd Qu.:1 3rd Qu.:15.000
Max. :1 Max. :15.000
Summary of smooth trends:
V1 V2 date
Min. :-2.0807 Min. :-2.27852 Min. :1999-01-13
1st Qu.:-0.8828 1st Qu.:-0.72370 1st Qu.:2001-09-15
Median : 0.1345 Median :-0.01471 Median :2004-05-19
Mean : 0.0000 Mean : 0.00000 Mean :2004-05-19
3rd Qu.: 0.8756 3rd Qu.: 0.73483 3rd Qu.:2007-01-20
Max. : 1.8503 Max. : 2.08859 Max. :2009-09-23
Summary of spatio-temporal covariates.
lax.conc.1500
Min. : 0.00000
1st Qu.: 0.09528
Median : 1.81705
Mean : 3.47925
3rd Qu.: 5.12175
Max. :34.00420
Summary for observations of type AQS
obs date
Min. :0.8102 Min. :1999-01-13
1st Qu.:3.3406 1st Qu.:2001-09-19
Median :3.7916 Median :2004-03-17
Mean :3.7836 Mean :2004-04-22
3rd Qu.:4.2751 3rd Qu.:2006-12-30
Max. :5.7516 Max. :2009-09-23
Summary for observations of type FIXED
obs date
Min. :0.678 Min. :2005-12-07
1st Qu.:3.217 1st Qu.:2006-12-06
Median :3.755 Median :2007-10-10
Mean :3.669 Mean :2007-10-28
3rd Qu.:4.196 3rd Qu.:2008-08-27
Max. :5.285 Max. :2009-07-01
$const
~log10.m.to.a1 + s2000.pop.div.10000 + km.to.coast
$V1
~km.to.coast
$V2
~km.to.coast
[1] "lax.conc.1500"
(Intercept) log10.m.to.a1 s2000.pop.div.10000 km.to.coast
60370002 1 2.861509 1.733283 15.000000
60370016 1 3.461672 1.645386 15.000000
60370030 1 2.561133 6.192630 15.000000
60370031 1 3.111413 2.088930 1.023311
60370113 1 2.762193 7.143731 6.011075
60371002 1 2.760931 4.766780 15.000000
(Intercept) km.to.coast
60370002 1 15.000000
60370016 1 15.000000
60370030 1 15.000000
60370031 1 1.023311
60370113 1 6.011075
60371002 1 15.000000
(Intercept) km.to.coast
60370002 1 15.000000
60370016 1 15.000000
60370030 1 15.000000
60370031 1 1.023311
60370113 1 6.011075
60371002 1 15.000000
$T
[1] 280
$m
[1] 3
$n
[1] 25
$n.obs
[1] 25
$p
const V1 V2
4 2 2
$L
[1] 1
$npars.beta.covf
exp exp exp
2 2 2
$npars.beta.tot
exp exp exp
2 2 2
$npars.nu.covf
[1] 2
$npars.nu.tot
[1] 4
$nparam.cov
[1] 10
$nparam
[1] 19
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