Modelos para dados toxicol\'ogicos agrupados com superdispers\~ao em bioensaio com fungo entomapatog\^enico
Conteúdo do artigo principal
Resumo
Consideram-se dados discretos de mortalidade para grupos de indiv\'iduos observados ao longo do tempo. O ajuste de curvas de mortalidade acumulada como uma fun\c{c}\~ao do tempo envolve a modelagem longitudinal de uma resposta multinomial. Tipicamente, tais dados exibem superdispers\~ao, isto \'e, varia\c{c}\~ao maior do que aquela predita pela distribui\c{c}\~ao multinomial. Para modelar a varia\c{c}\~ao extra-multinomial (superdispers\~ao) s\~ao considerados um modelo multinomial-Dirichlet, um modelo com intercepto aleat\'orio e um modelo com intercepto e coeficiente angular aleat\'orios. Estimadores assint\'oticos e robustos s\~ao obtidos para erros-padr\ão dos estimadores dos par\^ametros de regress\~ao. Na aplica\c{c}\~ao dessa metodologia para a an\'alise de um conjunto de dados proveniente de um ensaio de controle biol\'ogico de \textit{Heterothermes tenuis} pelo fungo \textit{Beauveria bassiana}, notam-se algumas rela\c{c}\~oes simples nos resultados e mostra-se que s\~ao simplesmente consequ\^encia da estrutura dos dados. Os modelos ajustados s\~ao usados para fazer infer\^encias sobre a efic\'acia e a consist\^encia dos diferentes isolados dos fungos para fazer recomenda\c{c}\~oes sobre o uso desse fungo no campo como controle biol\'ogico.
Detalhes do artigo
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Referências
Almeida, J. E. M., Alves, S. B. & Pereira, R. M. Selection of Beauveria spp. isolates for control of the termite Heterotermes tenuis (Hagen, 1958).Journal of Applied Entomology 121, 539–543(1997).
Corsini, N. & Viroli, C. Dealing with overdispersion in multivariate count data. Computational Statistics & Data Analysis 170, 107447 (2022).
Crowder, M. Beta-binomial anova for proportions. Applied Statistics 27, 34–37 (1978).
Einbeck, J., Darnell, R. & Hinde, J.npmlreg: Nonparametric Maximum Likelihood Estimationfor Random Effect Models R package version 0.46-5 (2018). https://CRAN.R-project.org/package=npmlreg.
Fallah, L., Freitas, S. M. d., Demétrio, C. B. & Hinde, J. P.Longitudinal modelling of grouped mortality data In preparation. 2023.
Finney, D. Probit Analysis. 3thed.(Cambridge University Press, London, 1971).
Freitas, S. M. d. Modelos para Proporções com Superdispersão proveniente de Ensaios Toxicológicos no Tempo.(Ph.D. thesis, ESALQ, Universidade de São Paulo, 2001).
Glonek, G. F. V. & McCullagh, P. Multivariate logistic models. Journal of the Royal Statistical Society, Series B,57,149–192 (1995).
Hinde, J. P & Demétrio, C. G. B. Overdispersion: models and estimation. Computational Statistics and Data Analysis 27, 151–170 (1998).
Lange, N. & Laird, N. M. The Effect of Covariance Structure on Variance Estimation in Bal-anced Growth-Curve Models with Random Parameters. Journal of the American Statistical Association 84, 241–247 (1989).
Liang, K.-Y. & Zeger, S. L. Longitudinal data analysis using generalized linear models. Biometrika 73, 13–22 (1986).
Martinez, M.-J. & Hinde, J. Random effects ordinal time models for grouped toxicological data from a biological control assay. in Statistical Modelling: Papers in Biostatistics and Bioinformatics (edsMacKenzie, G. & Peng, D.) (Springer, 2014), 45–58.
McCullagh, P. Regression models for ordinal data (with Discussion). Journal of the Royal Statistical Society, Series B, 42, 109–151 (1980).
McCullagh, P. & Nelder, J. A.Generalized Linear Models. 2nd ed(Chapman-Hall, London,1989).
McElroy, F. W. Optimality of Least Squares in Linear Models with Unknown Error Covariance Matrix. Journal of the American Statistical Association 71, 374–377 (1976).
Moore, D. F. Modelling the extraneous variance in the presence of extra-binomial variation. Applied Statistics 36, 8–14 (1987).
Moral, R. A., Hinde, J. & Demétrio, C. G. Half-normal plots and overdispersed models in R:The hnp package. Journal of Statistical Software 81,1–23 (2017).
Mosimann, J. E. On the compound multinomial distribution, the multivariate β–distribution, and correlations among proportions. Biometrika 49,65–82 (1962).
O’Hara Hines, R. J. & Lawless, J. F. Modelling overdispersion in toxicological mortality data grouped over time. Biometrics 49,107–121 (1993).
O'Hara Hines, R. J., Lawless, J. F. & Carter, E. M. Diagnostics for a Cumulative Multino-mial Generalized Linear Model, with Applications to Grouped Toxicological Mortality Data. Journal of the American Statistical Association 87, 1059–1069 (1992).
Petkau, A. J. & Sitter, R. R. Models for quantal response experiments over time. Biometrics 45,1299–1308 (1989).
R Development Core Team.R: A Language and Environment for Statistical Computing Vienna, Austria, 2010. http://www.r-project.org/.
Rao, C. R. Least squares theory using an estimated dispersion matrix and its application to measurement of signals in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics 5(1967), 355–373.
Rao, C. R.Linear Statistical Inference and its Applications (John Wiley & Sons, Inc., 1973).
Salvador, M. L., Junior, E. E. R., Taconeli, C. A. & Lara, I. A. R. Analysis of multinomial data with overdispersion diagnostics and application. Brazilian Journal of Biometrics 40 (2022).
Tamai, M. A. Avaliacão de fungos entomopatogenicos para o controle de Tetranychus urticae Koch (Master thesis, ESALQ, Universidade de São Paulo, 1997).
Williams, D. A. Extra-binomial variation in logistic-linear models. Applied Statistics31,144–148 (1982).