Abstract
High levels of airborne olive pollen represent a problem for a large proportion of the population because of the many allergies it causes. Many attempts have been made to forecast the concentration of airborne olive pollen, using methods such as time series, linear regression, neural networks, a combination of fuzzy systems and neural networks, and functional models. This paper presents a functional logistic regression model used to study the relationship between olive pollen concentration and different climatic factors, and on this basis to predict the probability of high (and possibly extreme) levels of airborne pollen, selecting the best subset of functional climatic variables by means of a stepwise method based on the conditional likelihood ratio test.
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References
Agresti A (2002) Categorical data analysis. Wiley, New York
Aguilera AM, Escabias M, Valderrama MJ (2008a) Discussion of different logistic models with functional data. Application to Systemic Lupus Erythematosus. Comput Stat Data Anal 53:151–163
Aguilera AM, Escabias M, Valderrama MJ (2008b) Forecasting binary longitudinal data by a functional PC-ARIMA model. Comput Stat Data Anal 52:3187–3197
Alba F, Díaz de la Guardia C, Comtois P (2000) The effect of meteorological parameters on diurnal patterns of airborne olive pollen concentration. Grana 39:200–208
Aznarte JL, Benítez JM, Nieto D, Linares C, Díaz de la Guardia C, Alba F (2007) Forecasting airborne pollen concentration time series with neural and neuro-fuzzy models. Expert Syst Appl 32:1218–1225
Belmonte J, Canela M (2002) Modelling aerobiological time series. Application to Urticaceae. Aerobiologia 18:287–295
Cardot H, Sarda P (2005) Estimation in generalized linear models for functional data via penalized likelihood. J Multivar Anal 92:24–41
Castellano-Méndez M, Aira MJ, Iglesias I, Jato V, González-Manteiga W (2005) Artificial neural network as a useful tool to predict the risk level of Betula pendula in the air. Int J Biometeorol 49:310–316
D’Amato G, Lobefalo G (1989) Allergenic pollen in the southern Mediterranean area. J Allergy Clin Immunol 83:116–122
De Boor C (2001) A practical guide to Splines. Springer, New York
Díaz de la Guardia C, Alba F, Sánchez F, Trigo MM, Galán C, Ruíz L, Sabariego, S (2003) Aerobiological analysis of Olea europaea L. pollen in different localities of southern Spain. Grana 42:234–243
Escabias M, Aguilera AM, Valderrama MJ (2004) Principal component estimation of functional logistic regression. J Nonparametric Stat 16(3–4):365–384
Escabias M, Aguilera AM, Valderrama MJ (2005) Modeling environmental data by functional principal component logistic regression. Environmetrics 16:95–107
Escabias M, Aguilera AM, Valderrama MJ (2007) Functional PLS logit regression model. Comput Stat Data Anal 51:4891–4902
Ferraty F, Vieu P (2006) Nonparametric functional data analysis. Springer, New York
Galán C, García-Mozo H, Vázquez L, Ruíz L, Díaz de la Guardia C, Trigo MM (2005) Heat requirement for the onset of the Olea europaea L. pollen season in several sites in Andalusia and the effect of the expected future climate change. Int J Biometeorol 49:184–188
Hosmer DW, Hosmer T, Le Cessie S, Lemeshow S (1997) A comparison of goodness-of-fit tests for the logistic regression model. Stat Med 16:965–980
Hosmer DW, Lemeshow S (1989) Applied logistic regression. Wiley, New York
James JM (2002) Generalized linear models with functional predictors. J R Stat Soc Ser B 64(3):411–432
Macchia L, Caiffa MF, D’Amato G, Tursi A (1991) Allergenic significance of Oleaceae pollen. In: D’Amato G, Spieksma FThM, Bonini S (eds) Allergenic Olea pollen in southern Spain pollen and pollinosis in Europe. Blackwell Scientific Publication, Oxford. pp 87–93
Müller HG (2008) Functional modeling of longitudinal data. In: Fitzmaurice G, Davidian M, Verbeke G, Molenberghs G (eds) Longitudinal data analysis (Handbooks of modern statistical methods). CRC, New York. pp 223–252
Ocaña-Peinado FM, Valderrama MJ, Aguilera AM (2008) A dynamic regression model for air pollen concentration. Stoch Environ Res Risk Assess 22(1):59–63
Ramsay JO, Silverman BW (1997) Functional data analysis. Springer-Verlag, New York
Ramsay JO, Silverman BW (2005) Functional data analysis, 2nd edn. Springer-Verlag, New York
Ratcliffe SJ, Heller GZ, Leader LR (2002) Functional data analysis with application to periodically stimulated foetal heart rate data. II: functional logistic regression. Stat Med 21:1115–1127
Rossi N, Wang X, Ramsay JO (2002) Nonparametric item response function estimates with the EM algorithm. J Behav Educ Sci 27:291–317
Sánchez-Mesa JA, Galán C, Martínez-Heras JA, Hervas-Martínez C (2002) The use of a neural network to forecast daily grass pollen concentration in a Mediterranean region: the southern part of the Iberian Peninsula. Clin Exp Allergy 32:1606–1612
Valderrama MJ, Ocaña FA, Aguilera AM, Ocaña-Peinado FM (2010) Forecasting pollen concentration by a two-step functional model. Biometrics 66(2):578–585
Vázquez LM, Galán C, Domínguez-Vilches E (2003) Influence of meteorological parameters on olea pollen concentrations in Córdoba (South-western Spain). Int J Biometeorol 48(2):83–90
Acknowledgments
This research was supported by Projects MTM2010-20502 from Dirección General de Investigación del MEC, Spain, and FQM-307 from Consejería de Innovación, Ciencia y Empresa de la Junta de Andalucía Spain. The authors are grateful to the Aerobiology Research Group at the University of Granada for providing data for our study. The authors also want to thank the referees their suggestions that have allowed to prepare this improved version of the paper.
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Escabias, M., Valderrama, M.J., Aguilera, A.M. et al. Stepwise selection of functional covariates in forecasting peak levels of olive pollen. Stoch Environ Res Risk Assess 27, 367–376 (2013). https://doi.org/10.1007/s00477-012-0655-0
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DOI: https://doi.org/10.1007/s00477-012-0655-0