Sensitivity analysis

We exclude the Warning Alert episodes from the analysis.

Propensity score

mod<-gam(elipic ~ s(tempmax,k=7,bs="tp") + s(tempmoy,k=7, bs="tp") +s(lag_tempmax,k=7,bs="tp") + s(lag_tempmoy,k=7, bs="tp")+ s(lag2_tempmax,k=7,bs="tp") + s(lag2_tempmoy,k=7, bs="tp") + s(lag3_tempmax,k=7,bs="tp") + s(lag3_tempmoy,k=7, bs="tp") + Jours + mois  + jours_fériés + Vacances + annee + s(lag_O3,k=6) + s(lag2_O3,k=6) + s(lag3_O3,k=6) + s(lag_PM10,k=6) + s(lag2_PM10,k=6) + s(lag3_PM10,k=6), family="binomial", data=data)


data$SP<-NA
data$SP[4:nrow(data)]<-mod$fitted
data<-data[-c(1:3),]
data$nrow<-c(1:nrow(data))

 

Résultats du Modèle retenu

## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## elipic ~ s(tempmax, k = 7, bs = "tp") + s(tempmoy, k = 7, bs = "tp") + 
##     s(lag_tempmax, k = 7, bs = "tp") + s(lag_tempmoy, k = 7, 
##     bs = "tp") + s(lag2_tempmax, k = 7, bs = "tp") + s(lag2_tempmoy, 
##     k = 7, bs = "tp") + s(lag3_tempmax, k = 7, bs = "tp") + s(lag3_tempmoy, 
##     k = 7, bs = "tp") + Jours + mois + jours_fériés + Vacances + 
##     annee + s(lag_O3, k = 6) + s(lag2_O3, k = 6) + s(lag3_O3, 
##     k = 6) + s(lag_PM10, k = 6) + s(lag2_PM10, k = 6) + s(lag3_PM10, 
##     k = 6)
## 
## Parametric coefficients:
##                 Estimate Std. Error z value Pr(>|z|)    
## (Intercept)   -1.139e+01  2.084e+00  -5.468 4.56e-08 ***
## Joursjeudi     1.738e+00  5.921e-01   2.935 0.003330 ** 
## Jourslundi     1.761e+00  6.593e-01   2.670 0.007577 ** 
## Joursmardi     1.270e+00  6.372e-01   1.993 0.046283 *  
## Joursmercredi  2.233e+00  6.153e-01   3.629 0.000284 ***
## Jourssamedi    8.749e-01  5.942e-01   1.472 0.140923    
## Joursvendredi  1.420e+00  6.087e-01   2.333 0.019638 *  
## mois10        -1.098e+00  9.776e-01  -1.123 0.261599    
## mois11         9.982e-01  6.341e-01   1.574 0.115434    
## mois12        -1.364e-01  6.455e-01  -0.211 0.832678    
## mois2         -8.384e-01  5.544e-01  -1.512 0.130459    
## mois3         -6.603e-01  7.217e-01  -0.915 0.360213    
## mois4         -1.072e+00  9.312e-01  -1.151 0.249650    
## mois5         -1.664e+00  1.251e+00  -1.329 0.183729    
## mois6         -4.404e+01  3.105e+06   0.000 0.999989    
## mois7         -4.497e+01  3.056e+06   0.000 0.999988    
## mois8         -4.480e+01  3.056e+06   0.000 0.999988    
## mois9         -1.745e+00  1.242e+00  -1.405 0.159955    
## jours_fériés  -1.593e+00  1.253e+00  -1.271 0.203640    
## Vacances       1.051e+00  3.737e-01   2.813 0.004914 ** 
## annee2001     -4.318e+01  3.543e+06   0.000 0.999990    
## annee2002      1.561e+00  1.702e+00   0.917 0.359128    
## annee2003     -4.535e+01  3.543e+06   0.000 0.999990    
## annee2004     -4.354e+01  3.538e+06   0.000 0.999990    
## annee2005     -4.307e+01  3.543e+06   0.000 0.999990    
## annee2006      6.208e-02  1.718e+00   0.036 0.971180    
## annee2007      1.196e+00  1.631e+00   0.733 0.463529    
## annee2008     -4.457e+01  3.538e+06   0.000 0.999990    
## annee2009      9.162e-01  1.603e+00   0.572 0.567621    
## annee2010      4.836e-02  1.667e+00   0.029 0.976862    
## annee2011      2.079e+00  1.589e+00   1.308 0.190777    
## annee2012      4.484e+00  1.588e+00   2.824 0.004747 ** 
## annee2013      3.906e+00  1.601e+00   2.440 0.014699 *  
## annee2014      3.468e+00  1.620e+00   2.140 0.032333 *  
## annee2015      2.607e+00  1.597e+00   1.633 0.102420    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                   edf Ref.df Chi.sq  p-value    
## s(tempmax)      1.007  1.011 22.110 2.78e-06 ***
## s(tempmoy)      2.427  3.059 35.352 1.23e-07 ***
## s(lag_tempmax)  1.000  1.000  0.067   0.7961    
## s(lag_tempmoy)  1.000  1.000  3.141   0.0763 .  
## s(lag2_tempmax) 1.000  1.000  0.186   0.6661    
## s(lag2_tempmoy) 1.000  1.000  0.156   0.6925    
## s(lag3_tempmax) 1.000  1.000  0.582   0.4455    
## s(lag3_tempmoy) 1.000  1.000  0.163   0.6865    
## s(lag_O3)       3.812  4.256  8.803   0.0835 .  
## s(lag2_O3)      1.664  2.104  1.943   0.3976    
## s(lag3_O3)      1.000  1.000  0.382   0.5366    
## s(lag_PM10)     4.463  4.754 75.225 1.43e-14 ***
## s(lag2_PM10)    1.601  2.020  3.494   0.1903    
## s(lag3_PM10)    1.000  1.000  0.296   0.5864    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.476   Deviance explained =   65%
## UBRE = -0.91113  Scale est. = 1         n = 5821

AIC du modèle:

## [1] 517.3299

 

Statistiques Descriptives pour le Score de Propension:

Summary Statistics for the propensity score (PS):

##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## 0.0000000 0.0000000 0.0000001 0.0200996 0.0004032 0.9925082

Summary Statistics for the variable eligibility to intervention (polluted days):

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.0000  0.0000  0.0000  0.0201  0.0000  1.0000

 

Test moyenne Score de Propension Test de Student pour difference moyenne entre variable Score de Propension (x) et variable pic de pollution (y):

## 
##  Welch Two Sample t-test
## 
## data:  data$SP and data$elipic
## t = 1.9496e-13, df = 10394, p-value = 1
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.004395189  0.004395189
## sample estimates:
##  mean of x  mean of y 
## 0.02009964 0.02009964

La moyenne du score de propension predit par le modèle est statistiquement pas differente de la moyenne de la variable éligibilité.

Comparaison de la moyenne du score de propension entre jours éligibles et pas éligibles avec test de Student.

## 
##  Welch Two Sample t-test
## 
## data:  SP by elipic
## t = -17.368, df = 116.17, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.5383023 -0.4280944
## sample estimates:
## mean in group 0 mean in group 1 
##      0.01038753      0.49358586

Les jours éligibles ont une moyenne du SP statistiquement différente de la moyenne du SP des jours non éligibles.

 

Standard Deviation de la variable SP et Eligibilité:

## data$elipic: 0
## [1] 0.05681762
## ------------------------------------------------------------ 
## data$elipic: 1
## [1] 0.3008298

La Standard deviation de la variable SP est assez différente de celle de la variable éligibilité.

Propensity score Matching

Several types of matching were compared. Differents matches were determined by following parameters:

The matching minimazing the standardized mean difference for numerical variables included in the SP predictions was retained. The selected matching include M=3, no caliper requirement and it handles ties deterministically, that means that ties are randomly broken.

var.match<-cbind(data$SP,data$period)
App<-Match(Tr = data$elipic,X=var.match, M=3, ties=FALSE)

summary(App)
## 
## Estimate...  0 
## SE.........  0 
## T-stat.....  NaN 
## p.val......  NA 
## 
## Original number of observations..............  5821 
## Original number of treated obs...............  117 
## Matched number of observations...............  117 
## Matched number of observations  (unweighted).  351
control=data.frame(App$index.control)
treated=data.frame(App$index.treated)


colnames(control) <- c("nrow")
colnames(treated) <- c("nrow")

cas<-unique(treated)

cas$PAIR<-c(1:nrow(cas))

treated<-merge(treated,cas,by="nrow")

control$PAIR <- treated$PAIR

casm<-merge(cas,data,by="nrow")
controlm<- merge(control,data, by ="nrow")

datam<-rbind(casm,controlm)

datam<-datam[order(datam[,"PAIR"]),]

 

Comparing SP for eligible days and not eligible days before and after matching:

 

Comparing PS average for eligible days and not eligible days after matching through Student test:

## 
##  Welch Two Sample t-test
## 
## data:  SP by elipic
## t = -0.06671, df = 199.62, p-value = 0.9469
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.06553790  0.06124869
## sample estimates:
## mean in group 0 mean in group 1 
##       0.4914413       0.4935859

 

Mean PS values for eligible days and not eligible days after matching are not statistically different.

Balance statistics for matching

 

Standardized mean differences for continuos variables after matching:
temp max LAG temp max LAG2 temp max LAG3 temp max temp moy LAG temp moy LAG2 temp moy LAG3 temp moy lag_O3 lag2_O3 lag3_O3 lag_PM10 lag2_PM10 lag3_PM10 tot_SMD
Before Matching 0.15550 0.15698 0.16795 0.17938 0.24011 0.23926 0.24659 0.25465 0.17406 0.14968 0.14453 0.45596 0.36767 0.29251 3.22482
After Matching 0.03318 0.03330 0.03976 0.02557 0.04073 0.02885 0.03340 0.03497 0.04221 0.02486 0.03760 0.03245 0.02457 0.03632 0.46776

 

Love Plot for standardized mean difference

 

Stars indicates variables with mean differences that have been standardized

 

Comparing average number of non accidental, cardiovascular and respiratory deaths per month for eligible days and not eligible days before intervention in the after-matching data:

Descriptive Statistics before and after the measures implementation
Before PM10 Regulation
After PM10 Regulation
Non-Polluted days Polluted days Non-Polluted days Polluted days
Non acc Deaths 120.2778 117.0000 113.2540 114.3786
Cardio Deaths 33.11111 31.42857 26.67302 26.37864
Respi Deaths 8.166667 7.928571 8.679365 7.912621
Minimum Temperature 2.486111 2.007143 3.493968 3.038835
Maximum Temperature 10.49167 9.80000 10.81048 10.42816
Mean Temperature 6.372685 5.546429 7.143836 6.734102

 

Differences in Differences

### Model to study effect on PM10 concentration
fixPM10<-plm(moyPM10 ~ Period + elipic + Period*elipic, data=datam, model="within")


### Model to study effect on mortality

## Linear Version
# Non accidental mortality
nocc<-plm(nocc_tot ~ Period + elipic + Period*elipic, data=datam, model="within")

# Cardiovascual causes mortality
cardio<-plm(cv_tot ~ Period + elipic + Period*elipic, data=datam, model="within")

# Respiratory causes mortality
respi<-plm(respi_tot ~ Period + elipic + Period*elipic, data=datam, model="within")


## Poisson Version
# Non accidental mortality
noccP<-pglm(nocc_tot ~ Period + elipic + Period*elipic, data=datam, family=poisson(link = "log"), model="within")

# Cardiovascual causes mortality
cardioP<-pglm(cv_tot ~ Period + elipic + Period*elipic, data=datam, family=poisson(link = "log"), model="within")

# Respiratory causes mortality
respiP<-pglm(respi_tot ~ Period + elipic + Period*elipic, data=datam, family=poisson(link = "log"), model="within")

Effet sur le niveau de concentration de PM10 de la période post-mésures par rapport à la période avant l’entrée de la réglementation des PM10:

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = moyPM10 ~ Period + elipic + Period * elipic, data = datam, 
##     model = "within")
## 
## Balanced Panel: n = 117, T = 4, N = 468
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -27.25452  -6.01524  -0.17353   5.21009  33.46841 
## 
## Coefficients:
##                Estimate Std. Error t-value  Pr(>|t|)    
## Period2         -5.9702     3.8230 -1.5617  0.119276    
## elipic          31.6553     3.1207 10.1436 < 2.2e-16 ***
## Period2:elipic -10.3647     3.3207 -3.1212  0.001952 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    80065
## Residual Sum of Squares: 33648
## R-Squared:      0.57974
## Adj. R-Squared: 0.43602
## F-statistic: 160.017 on 3 and 348 DF, p-value: < 2.22e-16

Effet sur la mortalité de la période post-mésures par rapport à la période avant l’entrée de la réglementation des PM10:

Modèle Linéaire:

Non accidental mortality

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = nocc_tot ~ Period + elipic + Period * elipic, data = datam, 
##     model = "within")
## 
## Balanced Panel: n = 117, T = 4, N = 468
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -33.71211  -8.17036   0.80393   7.56250  33.55393 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)
## Period2         -6.3292     5.5684 -1.1366   0.2565
## elipic          -3.8484     4.5455 -0.8466   0.3978
## Period2:elipic   5.0642     4.8368  1.0470   0.2958
## 
## Total Sum of Squares:    71832
## Residual Sum of Squares: 71387
## R-Squared:      0.0061946
## Adj. R-Squared: -0.33364
## F-statistic: 0.723058 on 3 and 348 DF, p-value: 0.53877

Cardiovascular causes mortality

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = cv_tot ~ Period + elipic + Period * elipic, data = datam, 
##     model = "within")
## 
## Balanced Panel: n = 117, T = 4, N = 468
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -12.564535  -3.314535   0.095894   2.935465  18.693606 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)   
## Period2         -6.6172     2.1693 -3.0504 0.002461 **
## elipic          -1.9747     1.7708 -1.1151 0.265559   
## Period2:elipic   1.7166     1.8843  0.9110 0.362935   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    11136
## Residual Sum of Squares: 10834
## R-Squared:      0.027122
## Adj. R-Squared: -0.30556
## F-statistic: 3.23392 on 3 and 348 DF, p-value: 0.022468

Respiratory causes mortality

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = respi_tot ~ Period + elipic + Period * elipic, 
##     data = datam, model = "within")
## 
## Balanced Panel: n = 117, T = 4, N = 468
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -7.79300 -2.56001 -0.49599  2.30102 15.20700 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)
## Period2        -0.52800    1.53896 -0.3431   0.7317
## elipic         -0.17200    1.25626 -0.1369   0.8912
## Period2:elipic -0.62393    1.33677 -0.4667   0.6410
## 
## Total Sum of Squares:    5504
## Residual Sum of Squares: 5452.7
## R-Squared:      0.0093129
## Adj. R-Squared: -0.32946
## F-statistic: 1.09045 on 3 and 348 DF, p-value: 0.35315

Modèle de Poisson:

Non accidental mortality

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -1388.075 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)
## Period2        -0.05171    0.03511  -1.473   0.141
## elipic         -0.03239    0.02924  -1.108   0.268
## Period2:elipic  0.04310    0.03118   1.382   0.167
## --------------------------------------------

Cardiovascular causes mortality

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -1013.191 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)   
## Period2        -0.20351    0.06881  -2.958  0.0031 **
## elipic         -0.06073    0.05626  -1.080  0.2803   
## Period2:elipic  0.05107    0.06058   0.843  0.3992   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------

Respiratory causes mortality

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 3 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -900.6758 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)
## Period2        -0.06650    0.13834  -0.481   0.631
## elipic         -0.02123    0.11232  -0.189   0.850
## Period2:elipic -0.07457    0.11942  -0.624   0.532
## --------------------------------------------

 

Alternative analysis with three periods: 1) before PM10 concentration regulation 2) first PM10 regulation 3) more recent PM10 regulation

Après création de 2 dataframes par type d’appariement et par période 1 ou 2, analyse diff in diff via regression linéaire pour évaluer l’effet des mesures sur le niveau de PM10 et via regression de Poisson pour évaluer effet sur mortalité non accidentelle:

# Periode 1:

## Create panel data dataframe 
#datam_p1<-pdata.frame(datam_p1,index="PAIR")
#datam_p2<-pdata.frame(datam_p2,index="PAIR")


### Model to study effect on PM10 concentration
fixPM10_P1<-plm(moyPM10 ~ period + elipic + period*elipic, data=datam_p1, model="within")

fixPM10_P2<-plm(moyPM10 ~ period + elipic + period*elipic, data=datam_p2, model="within")


### Model to study effect on mortality

## Non accidental causes 
# Gaussian Version
nocc_P1<-plm(nocc_tot ~ period + elipic + period*elipic, data=datam_p1, model="within")

nocc_P2<-plm(nocc_tot ~ period + elipic + period*elipic, data=datam_p2, model="within")

# Poisson Version
noccP_P1<-pglm(nocc_tot ~ period + elipic + period*elipic, data=datam_p1, family=poisson(link = "log"), model="within")

noccP_P2<-pglm(nocc_tot ~ period + elipic + period*elipic, data=datam_p2, family=poisson(link = "log"), model="within")


## Cardiovascular causes 
# Gaussian Version
cv_P1<-plm(cv_tot ~ period + elipic + period*elipic, data=datam_p1, model="within")

cv_P2<-plm(cv_tot ~ period + elipic + period*elipic, data=datam_p2, model="within")

# Poisson Version
cvP_P1<-pglm(cv_tot ~ period + elipic + period*elipic, data=datam_p1, family=poisson(link = "log"), model="within")

cvP_P2<-pglm(cv_tot ~ period + elipic + period*elipic, data=datam_p2, family=poisson(link = "log"), model="within")


## Respiratory causes 
# Gaussian Version
respi_P1<-plm(respi_tot ~ period + elipic + period*elipic, data=datam_p1, model="within")

respi_P2<-plm(respi_tot ~ period + elipic + period*elipic, data=datam_p2, model="within")

# Poisson Version
respiP_P1<-pglm(respi_tot ~ period + elipic + period*elipic, data=datam_p1, family=poisson(link = "log"), model="within")

respiP_P2<-pglm(respi_tot ~ period + elipic + period*elipic, data=datam_p2, family=poisson(link = "log"), model="within")

Première Période:

PM10 Concentration

Effet sur niveau de concentration de PM10 période 1 vs. Période 2 :

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = moyPM10 ~ period + elipic + period * elipic, data = datam_p1, 
##     model = "within")
## 
## Unbalanced Panel: n = 38, T = 1-4, N = 128
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -26.6665  -7.1961  -1.6413   6.8866  27.6099 
## 
## Coefficients:
##                Estimate Std. Error t-value  Pr(>|t|)    
## period2         -3.5384     5.6630 -0.6248    0.5337    
## elipic          31.6818     4.4623  7.0999 3.208e-10 ***
## period2:elipic  -4.8993     5.9049 -0.8297    0.4090    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    37830
## Residual Sum of Squares: 17145
## R-Squared:      0.54678
## Adj. R-Squared: 0.3384
## F-statistic: 34.9867 on 3 and 87 DF, p-value: 6.2764e-15

Non accidental mortality

Effet sur mortalité non accidentelle période 1 vs. Période 3 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = nocc_tot ~ period + elipic + period * elipic, data = datam_p1, 
##     model = "within")
## 
## Unbalanced Panel: n = 38, T = 1-4, N = 128
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -33.7026  -9.5902  -1.1279   9.2567  33.9467 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)
## period2         -6.6041     6.8198 -0.9684   0.3355
## elipic          -3.8103     5.3738 -0.7091   0.4802
## period2:elipic   6.5972     7.1110  0.9277   0.3561
## 
## Total Sum of Squares:    25290
## Residual Sum of Squares: 24865
## R-Squared:      0.016794
## Adj. R-Squared: -0.43525
## F-statistic: 0.495343 on 3 and 87 DF, p-value: 0.68645

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -381.4521 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)
## period2        -0.05432    0.03655  -1.486   0.137
## elipic         -0.03211    0.02929  -1.096   0.273
## period2:elipic  0.05687    0.03908   1.455   0.146
## --------------------------------------------

Cardiovascular causes mortality

Effet sur mortalité par causes cardiovasculaires période 1 vs. Période 3 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = cv_tot ~ period + elipic + period * elipic, data = datam_p1, 
##     model = "within")
## 
## Unbalanced Panel: n = 38, T = 1-4, N = 128
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -13.80914  -3.67853  -0.32667   2.42623  17.59543 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)  
## period2         -6.8729     2.8513 -2.4105  0.01804 *
## elipic          -2.0016     2.2467 -0.8909  0.37544  
## period2:elipic   5.3834     2.9731  1.8107  0.07364 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    4771
## Residual Sum of Squares: 4346.4
## R-Squared:      0.088994
## Adj. R-Squared: -0.32986
## F-statistic: 2.83294 on 3 and 87 DF, p-value: 0.042916

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -282.6061 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)   
## period2        -0.21478    0.07202  -2.982 0.00286 **
## elipic         -0.06201    0.05635  -1.100 0.27118   
## period2:elipic  0.18275    0.07629   2.396 0.01659 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------

Respiratory causes mortality

Effet sur mortalité par causes respiratoires période 1 vs. Période 3 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = respi_tot ~ period + elipic + period * elipic, 
##     data = datam_p1, model = "within")
## 
## Unbalanced Panel: n = 38, T = 1-4, N = 128
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -7.77065 -1.77207 -0.23398  0.93022 15.22935 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)
## period2        -1.19653    1.51606 -0.7892   0.4321
## elipic         -0.08259    1.19461 -0.0691   0.9450
## period2:elipic  0.14666    1.58080  0.0928   0.9263
## 
## Total Sum of Squares:    1237.8
## Residual Sum of Squares: 1228.8
## R-Squared:      0.0072462
## Adj. R-Squared: -0.44919
## F-statistic: 0.211672 on 3 and 87 DF, p-value: 0.88807

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 3 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -217.6639 
## 3  free parameters
## Estimates:
##                 Estimate Std. error t value Pr(> t)
## period2        -0.159146   0.148575  -1.071   0.284
## elipic         -0.008954   0.112500  -0.080   0.937
## period2:elipic  0.019088   0.151636   0.126   0.900
## --------------------------------------------

Deuxième Période:

PM10 Concentration

Effet sur niveau de concentration de PM10 période 2 vs. Période 3 :

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = moyPM10 ~ period + elipic + period * elipic, data = datam_p2, 
##     model = "within")
## 
## Unbalanced Panel: n = 110, T = 1-4, N = 418
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -21.766631  -4.867384  -0.043927   4.732145  25.967375 
## 
## Coefficients:
##                Estimate Std. Error t-value  Pr(>|t|)    
## period3        -10.3530     3.0424 -3.4029 0.0007557 ***
## elipic          25.7560     2.3299 11.0545 < 2.2e-16 ***
## period3:elipic  -6.3046     2.5977 -2.4270 0.0158030 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    60673
## Residual Sum of Squares: 23671
## R-Squared:      0.60985
## Adj. R-Squared: 0.46659
## F-statistic: 158.919 on 3 and 305 DF, p-value: < 2.22e-16

Non accidental mortality

Effet sur mortalité non accidentelle période 2 vs. Période 3 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = nocc_tot ~ period + elipic + period * elipic, data = datam_p2, 
##     model = "within")
## 
## Unbalanced Panel: n = 110, T = 1-4, N = 418
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -30.68063  -7.68063   0.30563   7.23626  33.50462 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)
## period3         0.78535    4.86263  0.1615   0.8718
## elipic          1.01849    3.72391  0.2735   0.7847
## period3:elipic  0.25900    4.15186  0.0624   0.9503
## 
## Total Sum of Squares:    60586
## Residual Sum of Squares: 60470
## R-Squared:      0.0019135
## Adj. R-Squared: -0.3646
## F-statistic: 0.194916 on 3 and 305 DF, p-value: 0.89982

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -1209.748 
## 3  free parameters
## Estimates:
##                Estimate Std. error t value Pr(> t)
## period3        0.006922   0.032136   0.215   0.829
## elipic         0.009030   0.024871   0.363   0.717
## period3:elipic 0.002193   0.027703   0.079   0.937
## --------------------------------------------

Cardiovascular causes mortality

Effet sur mortalité par causes cardiovasculaires période 2 vs. Période 3 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = cv_tot ~ period + elipic + period * elipic, data = datam_p2, 
##     model = "within")
## 
## Unbalanced Panel: n = 110, T = 1-4, N = 418
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -11.80331  -3.29901   0.11419   2.70099  17.53747 
## 
## Coefficients:
##                Estimate Std. Error t-value Pr(>|t|)   
## period3        -0.18157    1.88700 -0.0962 0.923410   
## elipic          3.14988    1.44510  2.1797 0.030045 * 
## period3:elipic -4.34592    1.61117 -2.6974 0.007378 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    9360.8
## Residual Sum of Squares: 9106.3
## R-Squared:      0.027192
## Adj. R-Squared: -0.33004
## F-statistic: 2.84184 on 3 and 305 DF, p-value: 0.038045

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 2 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -882.0198 
## 3  free parameters
## Estimates:
##                 Estimate Std. error t value Pr(> t)   
## period3        -0.003836   0.064832  -0.059 0.95282   
## elipic          0.111815   0.049387   2.264 0.02357 * 
## period3:elipic -0.157860   0.055681  -2.835 0.00458 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------

Respiratory causes mortality

Effet sur mortalité par causes respiratoires période 2 vs. Période 3 :

Linear Normal Regression

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = respi_tot ~ period + elipic + period * elipic, 
##     data = datam_p2, model = "within")
## 
## Unbalanced Panel: n = 110, T = 1-4, N = 418
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -6.95383 -2.63852 -0.45383  2.27990  9.23109 
## 
## Coefficients:
##                 Estimate Std. Error t-value Pr(>|t|)  
## period3         3.059845   1.361054  2.2481  0.02528 *
## elipic         -0.075654   1.042324 -0.0726  0.94219  
## period3:elipic -0.739653   1.162108 -0.6365  0.52494  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    4867.2
## Residual Sum of Squares: 4737.5
## R-Squared:      0.026658
## Adj. R-Squared: -0.33077
## F-statistic: 2.78446 on 3 and 305 DF, p-value: 0.041035

Poisson Regression

## --------------------------------------------
## Maximum Likelihood estimation
## Newton-Raphson maximisation, 3 iterations
## Return code 1: gradient close to zero
## Log-Likelihood: -789.4229 
## 3  free parameters
## Estimates:
##                 Estimate Std. error t value Pr(> t)   
## period3         0.390786   0.125761   3.107 0.00189 **
## elipic         -0.008585   0.097696  -0.088 0.92998   
## period3:elipic -0.086745   0.107598  -0.806 0.42013   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## --------------------------------------------