Use of Survey Weights for the Analysis of Compositional Data: Some Simulation Results
Year: 2011
Type: conference-paper
Abstract: The compositional space can be seen as a vector space, where the vector addition corresponds to\nperturbation and the multiplication by a scalar corresponds to powering (Aitchison, 1986; PawlowskyGlahn\nand Egozcue, 2001). Whereas perturbation is a widely used operation in applications of compositional\nanalysis, powering is somewhat neglected. Survey data analysis on the other hand is a domain\nof applied statistics where the use of weights is predominant. The reason for introducing weights in\nsurvey data analysis is threefold: 1. the use of complex survey designs with unequal inclusion probabilities,\n2. the correction of non-response, and 3. calibration procedures. We shall introduce briefly\nthe rationale for weights in survey analysis and then discuss the connection between survey weights\nand the powering operation. Several examples will be given.\nSurveys are essentially built to optimize the estimation of totals in population subgroups for a\nnumber of variables. Practically, a key variable is chosen and the design is optimized for this variable,\nthe trade-off being between cost and precision. Totals are estimated by weighted sums of the sampled\nvalues. The weights are extrapolation factors that depend on the survey design. It is an important\naspect of the data quality to inform the user on the measurement error of the published figures. Survey\ndesign and estimation are described e.g. in S¨arndal, Swensson and Wretman (1992).\nIn a survey context, the interest is taken in totals or means across cases, but in a compositional\ncontext, totals have no meaning. So if we want to average cases, we have to go back to the original\nmeasurement scale and then make the closure operation. For the geometric mean composition on the\ncontrary, the result is the same, whether the amounts are averaged first and then a average composition\nis computed, or whether the geometric mean of the compositions is computed directly and then closed.\nThe design-based approach does not make any assumptions on the distribution of compositions.\nThis opens the way to parametrization by general partitions (Aitchison, 1986, section 2.7) without\nthe drawback of ad hoc assumptions on multivariate normality (Aitchison, 1986, definition 6.7). In\nhousehold expenditure surveys for instance, a hierarchy of commodities with broad categories are subdivided\ninto more detailed goods. A general partition can follow this organization and may be a more\nconvenient way to convey the information on the surveyed units. The joint probability distribution\nof transforms of this general partition is derived from the distribution of the sample inclusion indicator.\nAfter a brief review of survey methodology, we apply the design-based principles to the estimation\nof compositions, of compositional transforms and of their covariance matrix on a small population.\nThe properties of the estimators will be investigated by simulation. The talk will end with a discussion
Author: Monique Graf
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2603650085