Surveys, ipsative and compositional data analysis (CODA)
|Convenor||Dr Berta Ferrer-rosell (University of Girona - Department of Economics )|
|Coordinator 1||Dr Josep Daunis-i-estadella (University of Girona - Department of Computer Science, Applied Mathematics and Statistics)|
|Coordinator 2||Professor Vera Pawlowsky-glahn (University of Girona - Department of Computer Science, Applied Mathematics and Statistics)|
Multidimensional forced choice instruments ask respondents to rank traits along a set of items and convey information on the relative importance of traits. Data are ipsative and have a fixed sum. This is why they violate the assumptions of standard statistical techniques while they are fit for COmpositional Data Analysis (CODA). The paper discusses how CODA gets the most out of the relative information in the data and solves all concerns about ipsativity and assumptions. The simplest CODA approaches are presented: how alternative log-ratio transformations of the data are computed and how zeros are dealt with.
We propose a method combining canonical correlation analysis and compositional data analysis in order to relate two sets of ipsative variables obtained from multidimensional forced choice questionnaires. In these questionnaires respondents are asked to rank a set of dimensions over a number of items. We derive some key desirable statistical properties of the proposed method, which solves all concerns about ipsativity while revealing the information on the relative importance of the dimensions carried by ipsative data. Once the data have been appropriately transformed, the method is no more complex than standard canonical correlation analysis.
Kolb’s experiential learning theory suggests four learning modes, which are dialectically related by pairs. The dimension of grasping knowledge opposes the Concrete Experience mode to the Abstract Conceptualization mode; the dimension of transforming knowledge opposes Reflective Observation to Active Experimentation. Grasping and transforming as a whole have never been compared.
Being a 4-term composition, learning modes require three log ratios. In this paper we show how CODA allows the third dimension comparing grasping and transformation to emerge as a log-ratio. The paper gathers evidence of the third dimension by relating it to student nationality and social and
We experimentally compared a number of response formats in reporting either frequency or monetary spend for two different topics (DVDs by type of move; quick service restaurants by brand). Our formats included constant sum, open numeric, and grid response formats. Using two measures of validity, we found that constant sum tasks had generally lower validity than independent measures.
Tourists are heterogeneous in the way they adapt their trip budget to economic crises by reducing expenditure in some budget parts. We derive tourist market segments from the trip budget allocation (share of transportation, accommodation and food, and activities) and study the evolution of the found segments during the current crisis by using year (2006-2012) as an illustrative variable.
Budget share is a particular case of compositional data, which makes clustering difficult. The centred log-ratio transformation makes the Euclidean distance equivalent to the Aitchison distance and standard clustering techniques, such as k-means, can be used.