GENERALIZED ADDITIVE MODEL FOR COUNT TIME SERIES: AN APPLICATION TO QUANTIFY THE IMPACT OF AIR POLLUTANTS ON HUMAN HEALTH

Camara, Ana Julia A.; Franco, Glaura C.; Reisen, Valderio A.; Bondon, Pascal

doi:10.1590/0101-7438.2021.041.00241120

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ARTICLES • Pesqui. Oper. 41 • 2021 • https://doi.org/10.1590/0101-7438.2021.041.00241120 copy

GENERALIZED ADDITIVE MODEL FOR COUNT TIME SERIES: AN APPLICATION TO QUANTIFY THE IMPACT OF AIR POLLUTANTS ON HUMAN HEALTH

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The generalized additive model (GAM) has been used in many epidemiological studies where frequently the response variable is a nonnegative integer-valued time series. However, GAM assume that the observations are independent, which is generally not the case in time series. In this paper, an autoregressive moving average (ARMA) component is incorporated to the GAM. The resulting GAM-ARMA model is based on the generalized linear autoregressive moving average (GLARMA) model where some linear components are replaced by natural splines. Numerical simulations are presented and show that the ARMA component influences the estimation. In a real data analysis of the effects of air pollution on respiratory disease in the metropolitan area of Belo Horizonte, Brazil, it is shown that the proposed model presents a better fit when compared to the classical GAM approach, that does not take into account the autocorrelation of the data.

Keywords:
GAM; ARMA model; semiparametric model; Poisson-valued time series

	${\hat{μ}}_{\hat{ϕ}}$	${\hat{μ}}_{{\hat{β}}_{0}}$	${\hat{μ}}_{{\hat{β}}_{1}}$	${\hat{μ}}_{{\hat{β}}_{2}}$	${\hat{μ}}_{{\hat{α}}_{1}}$	${\hat{μ}}_{{\hat{α}}_{2}}$	${\hat{μ}}_{{\hat{α}}_{3}}$
$ϕ = 0.1$	0.0845	0.7637	0.0986	-0.1953	0.5455	-0.9812	0.8134
$ϕ = 0.1$	(0.0074)	(0.1795)	(0.0078)	(0.0036)	(0.1264)	(0.9071)	(0.0917)
$ϕ = 0.4$	0.3927	0.6907	0.0945	-0.1956	0.5332	-0.8401	0.9035
$ϕ = 0.4$	(0.0055)	(0.1852)	(0.0067)	(0.0028)	(0.1236)	(0.7623)	(0.0985)
$ϕ = 0.6$	0.5311	0.7078	0.0362	-0.2443	0.2491	-0.6168	0.9289
$ϕ = 0.6$	(0.0128)	(0.2084)	(0.0145)	(0.0049)	(0.2183)	(0.9690)	(0.1587)

	Min	Max	Q1	Q3	Mean	Median	s.d.
Cases	10	196	27	66	54.93	41	42.3
NO (µg/m3)	0.57	33.11	9.05	15.52	12.97	12.01	5.80
Tmin(ºC)	13.87	21.15	16.43	19.62	17.89	18.27	1.90
RH (%)	45.83	77.63	56.17	67.55	61.60	61.60	7.48

Parameter	β1	β2	β3	β4	β5	β6
Estimate	0.0545	0.2470	-0.5562	-0.3137	-0.2522	0.0096
Standard error	0.0032	0.0415	0.0611	0.0306	0.0326	0.0007

Parameter	β1	β2	β3	β4	β5	β6	ϕ
Estimate	0.0515	0.3271	-0.5221	-0.3068	-0.2324	0.0127	0.0700
Standard error	0.0029	0.0499	0.0615	0.0349	0.0362	0.0010	0.0053

NO	GAM	GAM-AR(1)
$\hat{R R}$	1.0627	1.0591
$\hat{CI}$	[1.0553;1.0702]	[1.0524;1.0658]

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