Environ Sci Pollut Res (2014) 21:13420–13433 DOI 10.1007/s11356-014-3125-z RESEARCH ARTICLE Spatial modeling of factor analysis scores The case of heavy metal biomonitoring in mainland Portugal Helena Piairo · Raquel Menezes · Inˆ es Sousa · Rui Figueira · Cec´ ılia S´ ergio Received: 21 March 2014 / Accepted: 28 May 2014 / Published online: 11 July 2014 © Springer-Verlag Berlin Heidelberg 2014 Abstract The use of mosses as biomonitors operates as an indicator of their concentration in the environment, becom- ing a methodology which provides a significant interpreta- tion in terms of environmental quality. The different types of pollution are variables that can not be measured directly in the environment - latent variables. Therefore, we pro- pose the use of factor analysis to estimate these variables in order to use them for spatial modelling. On the contrary, the main aim of the commonly used principal components analysis method is to explain the variability of observed variables and it does not permit to explicitly identify the dif- ferent types of environmental contamination. We propose to model the concentration of each heavy metal as a linear combination of its main sources of pollution, similar to the case of multiple regression where these latent variables are identified as covariates, though these not being observed. Moreover, through the use of geostatistical methodologies, we suggest to obtain maps of predicted values for the dif- ferent sources of pollution. With this, we summarize the information acquired from the concentration measurements of the various heavy metals, and make possible to easily determine the locations that suffer from a particular source of pollution. Responsible editor: Michael Matthies H. Piairo () · R. Menezes · I. Sousa Department of Mathematics and Applications, University of Minho, Campus de Azur´ em, 4800-058, Guimar˜ aes, Potugal e-mail: helena.piairo@gmail.com R. Figueira Institute of Tropical Scientific Research, Guimar˜ aes, Potugal C. S´ ergio National Museum of Natural History and Science, University of Lisbon, Lisbon, Portugal Keywords Biomonitors · Heavy metals · Sources of pollution · Latent variables · Factor analysis · Geostatistical methodologies 1 Introduction In the last centuries in Europe, pollution has been increasing dramatically since the industrial revolution. Many pollu- tants were, and still are today, released into the atmosphere through various means (for example, with the burning of coal, road traffic, industrial activities, etc.). Humans health is the most affected one by this type of pollution, especially with the presence of some heavy metals, for example lead, manganese, cadmium and mercury, found regularly in the atmosphere McGranahan and Murray (2003). The awareness about the problems associated with pol- lution (such as water and soil contamination) and the con- cern about the toxic effects of pollutants on living beings, led, in the last half of the twentieth century, to the need of quantifying the pollutants in the environmental system Hill (2010), which has been analysed both at a scientific and administration levels. Therefore, it became essential to establish nationwide sampling networks. In the particular case of Portugal, there still exists a very small number of base stations equipped for the direct measurement of atmo- spheric deposition of metals and this same situation also occurs in many other European countries. Due to the high costs associated to these monitoring stations, it was neces- sary to use living organisms for environmental monitoring. This method began to be recognized and recommended by national and international agencies from countries such as Norway, Poland, Spain, Italy, among others (Berg and Steinnes 1997; Grodzinska et al. 1999; Fern´ andez et al. 2000; Gerdol et al. 2000). Although the concentrations of