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When relative and absolute information matter: compositional predictor with a total in generalized linear models. (English) Zbl 07289494
Summary: The analysis of compositional data (CoDa) consists in the study of the relative importance of parts of a whole rather than the size of the whole because absolute information is either unavailable or not of interest. On the other hand, when absolute and relative information are both relevant, research hypotheses concern both. This article introduces a model including both the logratios used in CoDa and a total variable carrying absolute information as predictors in an otherwise standard statistical model. It shows how logratios can be tailored to the researchers’ hypotheses and alternative ways of computing the total. The interpretational advantages with respect to traditional approaches are presented and the equivalence and invariance properties are proven. A sequence of nested models is presented to test the relevance of relative and absolute information. The approach can be applied to dependent metric, binary, ordinal or count variables. Two illustrations are provided, the first on tourist expenditure and satisfaction and the second on solid waste management and floating population.
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[1] Aitchison, J (1986) The Statistical Analysis of Co- mpositional Data: Monographs on Statistics and Applied Probability (Reprinted 2003 with additional material by the Blackburn Press). London, UK: Chapman and Hall Ltd.
[2] Barcelo-Vidal, C, Martín-Fernández, JA (2016) The mathematics of compositional analysis. Austrian Journal of Statistics, 45, 57-71.
[3] Brida, JG, Scuderi, R (2013) Determinants of tourist expenditure: A review of microeconometric models. Tourism Management Perspectives, 6, 28-40.
[4] Di Marzio, M, Panzera, A, Venieri, C (2015) Non-parametric regression for compositional data. Statistical Modelling, 15, 113-33. · Zbl 07258981
[5] Egozcue, JJ, Pawlowsky-Glahn, V (2005) Groups of parts and their balances in compositional data analysis. Mathematical Geology, 37, 795-828. · Zbl 1177.86018
[6] Egozcue, JJ, Pawlowsky-Glahn, V, Mateu-Figueras, G, Barcelo-Vidal, C (2003) Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35, 279-300. · Zbl 1302.86024
[7] Ferrer-Rosell, B, Coenders, G, Marine-Roig, E (2017) Is planning through the Internet (un)related to trip satisfaction? Information Technology & Tourism, 17. doi: 10.1007/s40558-017-0082-7.
[8] Ferrer-Rosell, B, Coenders, G, Martinez-Garcia, E (2015) Determinants in tourist expenditure composition: The role of airline types. Tourism Economics, 21, 9-32.
[9] Ferrer-Rosell, B, Coenders, G, Martinez-Garcia, E (2016b) Segmentation by tourist expen- diture composition: An approach with compositional data analysis and latent classes. Tourism Analysis, 21, 589-602.
[10] Ferrer-Rosell, B, Coenders, G, Mateu-Figueras, G, Pawlowsky-Glahn, V (2016a) Under- standing low cost airline users’ expenditure pattern and volume. Tourism Economics, 22, 269-91.
[11] ITE (2014) Tourist expenditure survey: Meth- odology. Madrid (ES): Instituto de Turismo de Espana. URL http://estadisticas.tourspain.es/es-ES/estadisticas/egatur/metodologia/Referencia%20Metodolgica/Nota%20Metodol%C3%B3gica%20Encuesta%20de%20Gasto%20Tur%C3
[12] Kalivodová, A, Hron, K, Filzmoser, P, Najdekr, L, Janečkova, H, Adam, T (2015) PLS-DA for compositional data with application to metabolomics. Journal of Chemometrics, 29, 21-8.
[13] Kogovsek, T, Coenders, G, Hlebec, V (2013) Predictors and outcomes of social network compositions: A compositional structural equation modeling approach. Social Networks, 35, 1-10.
[14] Lee, S, Jee, W, Funk, D, Jordan, J (2015) Analysis of attendees’ expenditure patterns to recurring annual events: Examining the joint effects of repeat attendance and travel distance. Tourism Management, 46, 177-86.
[15] Martín-Fernández, JA, Barcelo-Vidal, C, Pawlowsky-Glahn, V (2003) Dealing with zeros and missing values in compositional data sets using nonparametric imputation. Mathematical Geology, 35, 253-78. · Zbl 1302.86027
[16] Martín-Fernández, JA, Hron, K, Templ, M, Filzmoser, P, Palarea-Albaladejo, J (2015) Bayesian-multiplicative treatment of count zeros in compositional data sets. Statistical Modelling, 15, 134-58. · Zbl 07258982
[17] Martín-Fernández, JA, Palarea-Albaladejo, J, Olea, RA (2011) Dealing with zeros. In Pawlowsky-Glahn, V, Buccianti, A, Compositional Data Analysis: Theory and Applications, 47-62. Chichester, UK: John Wiley & Sons.
[18] Mateu-Figueras, G, Pawlowsky-Glahn, V, Egozcue, JJ (2011) The principle of working on coordinates. In Pawlowsky-Glahn, V, Buccianti, A, Compositional Data Analysis: Theory and Applications, 31-42. Chichester, UK: John Wiley & Sons.
[19] Mateu-Sbert, J, Ricci-Cabello, I, Villalonga-Olives, E, Cabeza-Irigoyen, E (2013) The impact of tourism on municipal solid waste generation: The case of Menorca Island (Spain). Waste Management, 33, 2589-93.
[20] Mendes, P, Santos, AC, Nunes, LM, Teixeira, MR (2013) Evaluating municipal solid waste management performance in regions with strong seasonal variability. Ecological Indicators, 30, 170-77.
[21] Palarea-Albaladejo, J, Martín-Fernández, JA, Gomez-Garcia, J (2007) A parametric approach for dealing with compositional rounded zeros. Mathematical Geology, 39, 625-45. · Zbl 1130.86001
[22] Pawlowsky-Glahn, V, Buccianti, A (2011) Compositional Data Analysis: Theory and Applications. Chichester, UK: John Wiley & Sons. · Zbl 1103.62111
[23] Pawlowsky-Glahn, V, Egozcue, JJ (2011) Exploring compositional data with the CoDa-dendrogram. Austrian Journal of Statistics, 40, 103-13.
[24] Pawlowsky-Glahn, V, Egozcue, JJ, Tolosana-Delgado, R (2011) Principal balances. In Egozcue, JJ, Tolosana-Delgado, R, Ortego, MI, Proceedings of the 4th International Workshop on Compositional Data Analysis. Girona, ES: University of Girona.
[25] Pawlowsky-Glahn, V, Egozcue, JJ, Tolosana-Delgado, R (2015a) Modeling and Analysis of Compositional Data (Statistics in Practice). Chichester, UK: John Wiley & Sons.
[26] Pawlowsky-Glahn, V, Egozcue, JJ, Lovell, D (2015b) Tools for compositional data with a total. Statistical Modelling, 15, 175-90. · Zbl 07258984
[27] Pivnenko, K, Eriksena, MK, Martn-Fernandez, JA, Eriksson, E, Astrup, TF (2016) Recycling of plastic waste: Presence of phthalates in plastics from households and industry. Waste Management, 54, 44-52.
[28] Russell, MA (2014) Mining the Social Web: Data Mining Facebook, Twitter, LinkedIn, Google+, GitHub, and More. Sebastopol, CA: OReilly.
[29] Thrane, C (2014) Modelling micro-level tourism expenditure: Recommendations on the choice of independent variables, functional form and estimation technique. Tourism Economics, 20, 51-60.
[30] van den Boogaart, KG, Tolosana-Delgado, R (2013) Analyzing Compositional Data with R. Heidelberg, DE: Springer. · Zbl 1276.62011
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