[Forum SIS] seminario 21 settembre "EM algorithms for maximum likelihood estimation of correlated probit models for longitudinal ordinal data"

[Paola Rebora]

Nell'ambito del Dottorato di Sanità Pubblica abbiamo il piacere di ospitare la Dott.ssa Denitsa Grigorova (Faculty of Mathematics and Informatics, Sofia University, Bulgaria) 
che ci parlerà di modelli multivariati per dati ordinali longitudinali con un’applicazione nell’ambito dell’Health and Retirement Study (http://hrsonline.isr.umich.edu/,).

Title: EM algorithms for maximum likelihood estimation of correlated probit models for longitudinal ordinal data

Abstract: Binary and ordinal data are common outcomes in medical surveys (presence of an illness (yes, no), different concentrations of a substance in the blood (low, medium, high), stage
of cancer (stage I, II, III, IV), pain level (mild, moderate, severe) and many others). Bliss [1, 2] and Gaduum [3] were the first to introduce the probit models for binary data. The
main characteristic of the probit models is the assumption of a latent normally distributed variable behind the observed ordinal outcome. Correlated probit models (CPMs) are widely
used for modeling of longitudinal ordinal data or joint analyses of ordinal and continuous data. When we have clustered or longitudinal data CPMs with random effects are used to
take into account the dependence between clustered measurements. When the dimension of the random effects is large, finding of the maximum likelihood estimates (MLEs) of the model
parameters via standard numerical approximations is computationally cumbersome or in some cases impossible. EM algorithms for ML estimation of CMP for one ordinal longitudinal
variable [4] and of a joint CPM for one ordinal and one continuous longitudinal variable [5] were recently developed. ECM algorithm for ML estimation of CPM for two longitudinal
ordinal variables will be presented. The algorithm is applied to estimation of CPM for a joint analysis of the longitudinal ordinal outcomes self-rated health and categorized body mass index
from the Health and Retirement Study (http://hrsonline.isr.umich.edu/, HRS). Results from fitting the model to the data and also results from some simulation studies will be reported.
References
[1] Bliss, C. I. The method of probits. Science 79, 2037 (1934), 38-39.
[2] Bliss, C. I. The method of probits - a correction. Science 79, 2053 (1934), 409-410.
[3] Gaddum, J. H. Methods of biological assay depending on a quantal response. Reports on biological standards. III. (1933).
[4] Grigorova, D., and Gueorguieva, R. Implementation of the EM algorithm for maximum likelihood estimation of a random e ects model for one longitudinal ordinal outcome. Pliska
Stud. Math. Bulgar. 22 (2013), 41-56.
[5] Grigorova, D., and Gueorguieva, R. Correlated probit analysis of repeatedly measured ordinal and continuous outcomes with application to the Health and Retirement Study. Statistics in Medicine 35, 23 (2016), 4202-4225. sim.6982.

Giovedì 21 Settembre alle ore 14:30 presso l’edificio U8-Aula 2 

Dipartimento di Medicina e Chirurgia dell’Università di Milano-Bicocca, via Cadore 48 20900 Monza

http://www.medicina.unimib.it/21-settembre-em-algorithms-for-maximum-likelihood-estimation-of-correlated-probit-models-for-longitudinal-ordinal-data/

L’invito è aperto a tutti gli interessati,

Paola Rebora 
School of Medicine and Surgery
University of Milano-Bicocca
Via Cadore, 48
20900 Monza (MB)
Italy
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