final_program_abstracts[1]

11 IMSC Session Program
Generalised linear mixed models, for the modeling of monthly
average temperature in a tropical weather
Tuesday - Parallel Session 8
Mercedes Andrade-Bejarano, Edinson Andrés Zuluaga, John Jairo Millán
Hernández and Gabriel Conde Arango
School of Industrial Engineering and Statistics, Universidad del Valle, Cali,
Colombia
Andrade (2009) modelled monthly average temperature by using lineal mixed models,
with spatial and temporal correlated errors. However, the errors did not show normal
behaviour, the tails show departures from the fitted line and from the bands at α= 0:05
of the normality plots and also the Anderson Darling Test (A2) show small p-values
(< 0.005). These heavy tails of residuals are determined because of the extreme
values of monthly average temperature in years when the "El Niño" and "La Niña"
phenomena occur (Pabón et al. 2002).
In this research, we modelled monthly average temperature by using generalised
linear mixed models (McCullagh and Nelder 1989; Lin 1997), as an alternative to
solve the lack of normality in models fitted for monthly average temperature by
Andrade (2009). Data for this research come from time series of monthly average
temperature from 28 sites, collected over the period 1971 to 2002. Due to the
geographical location of the study zone (Valle del Cauca, Colombia, South America);
monthly average temperature is affected by the altitude and the "El Niño" and "La
Niña" phenomena. Time series for some of the sites show a tendency to increase. Also
due to the two dry and wet periods in the study zone, a seasonal behaviour in monthly
average temperature is seen. A random effect for year is included in the models and
the trends of the time series are modelled through random coefficients. The altitude
variable is included in the fixed part of the models and the "El Niño" and "La Niña"
phenomena are modelled by including the Southern Oscillation Index. The seasonal
patterns are eliminated by fitting models by month. Geographical position (in the
valley and mountains) is also included in the modelling. Variograms are used to
explore the spatial and the temporal correlation in the errors. Spatial and temporal
covariance structures are modelled individually using isotropic models. Maps of
predicted temperatures throughout the study area for the "El Niño", "La Niña" and
normal conditions are drawn.
Andrade, M. (2009). Monthly average temperature modelling for Valle del Cauca
(Colombia). (Unpublished PhD. Thesis. The University of Reading, United
Kingdom).
Lin, X. (1997), 'Variance component testing in generalised linear models with random
effects', Biometrika 84(2), 309-326.
McCullagh, P. and Nelder, J. F. (1989), Generalized Linear Models, second edn,
Chapman and Hall. Great Britain.
Pabón, J., Zea, J., León, G., Hurtado, G., González, O. and Montealegre, J. (2002), La
Atmósfera, el Tiempo y el Clima, Instituto de Hidrología, Meteorología y Estudios
Ambientales IDEAM. Colombia.
Abstracts 157