Timo Alanko

**Background:** The present paper is concerned with modelling and estimating the 'true' intake distribution on the basis of survey recall scores from a short reference period. There is a long and highly sophisticated tradition for the problem (see e.g. Nusser et al., 1997, Dodd et al. 2006, Kipnis et al. 2009). We treat specifically the empirical case of estimating the true alcohol intake distribution from a series of Finnish alcohol consumption surveys. This work is a revised and updated version, based on Alanko (1997).

**Modeling:** Two unobservable/latent variates representing the 'true' rate of consumption and the 'true' mean amount consumed on a single occasion are introduced.

Observable variates representing, respectively, the number of occasions in the reference period and the average amount per occasion, are defined at the individual level to follow the condensed Poisson and the gamma sampling distributions.

The corresponding marginal distributions are derived as continuous mixtures of the individual level distributions by three (alternative) parametric prior distributions.

'True' volume consumed by a randomly chosen individual is defined as the product of the latent rate distribution and the latent mean amount consumed. The distribution of the true intake volume is derived and estimated by ML from the observed marginal distributions.

**Empirical:** The main empirical results of this study are the true distributions estimated from Finnish alcohol consumption surveys samples for several consequtive surveys starting from 1976, separately for males and females.

**Additional topics:** In addition to the main results, the modelling enables prediction and inference, i.e. scoring concerning the respondents in the sample. For that purpose regression techniques, based on the Bayesian approach, are developed.

The modelling approach employed gives also the opportunity to model (in a somewhat speculative sense) the mechanisms behind the survey measurement/response errors. Some suggestions for this are explored empirically.

**References:**

Alanko T. (1997), Statistical Models for Estimating the Distribution Function of Alcohol Consumption; A Parametric Approach, The Finnish Foundation for Alcohol Studies, Vol 44, Helsinki, 109 pages, ISBN 951-9192-61-1.

Dodd, K., et al. (2006), Statistical methods for estimating usual intake of nutrients and foods: A review of the theory. Journal of the American Dietetic Association 106, 1640–1650.

Kipnis, V., et al. (2009), Modeling Data with Excess Zeros and Measurement Error: Application to Evaluating Relationships between Episodically Consumed Foods and Health Outcomes. Biometrics, 65: 1003–1010.

Nusser, S.M., Fuller, W.A. and Guenther, P. (1997), Estimating Usual Dietary Intake Distributions: Adjusting for Measurement Error and Nonnormality in 24-Hour Food Intake Data, in: Lyberg, L. et al., Survey Measurement and Process Quality, John Wiley&Sons, New York, pp. 689-709

**Keywords:** usual/true intake distribution; alcohol consumption; consumption survey data; response error

**Biography:** Timo Alanko works currently as Head of Research (part time), at the Statistical Methodology R&D unit in Statistics Finland.

He is also adjunct professor (docent) at the Department of Statistics, University of Helsinki and President of the Finnish Statistical Society.

He has been associate editor of the International Statistical Review (2002-2009) and is currently associate editor of the Scandinavian Journal of Statistics. His interests include R&D management (official statistics), statistical consulting, statistical modelling and computational techniques, survey methodology, technical and engineering statistics, statistical computing and software.