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Background: Large-scale health surveys often consider sociodemographic characteristics and several health indicators influencing physical activity that often vary across units (regions or states). Data in a survey for some small units are often not representative of the larger population. This study developed a relatively simple multilevel regression and poststratification (MRP) model to estimate the proportion of leisure-time physical activity across Brazilian state capitals, based on the Brazilian cross-sectional national survey VIGITEL (2018). Methods: We used various approaches to evaluate whether the MRP approach outperforms single-level aggregated estimates, with various subsample proportions tested. Results: The mean absolute errors were consistently smaller for the MRP estimates than single-level regression estimates, particularly with smaller sample sizes. MRP consistently had predictions closer to the estimation target than single-level aggregated estimations. MRP presented substantially smaller uncertainty estimates compared to aggregated estimates. Conclusions: Our results confirm that MRP is a promising strategy to derive disaggregated data for health-related outcomes and, in particular, physical activity indicators from aggregated-level surveys. Overall, the MRP is superior to single-level aggregated estimates and disaggregation, yielding smaller errors and more accurate estimates. MRP significantly expands the scope of issues for which researchers can better address participation bias and interpret interactions to estimate descriptive population quantities. The observations present in this study highlight the need for further research, potentially incorporating more information in the models to better interpret interactions and types of activities across target populations.

Made available in DSpace on 2019-10-06T16:27:42Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-07-01 Quantifying animal aggressive behavior by behavioral units, either displays or attacks, is a common practice in animal behavior studies. However, this practice can generate a bias in data analysis, especially when the variables have different temporal patterns. This study aims to use Bayesian Hierarchical Linear Models (B-HLMs) to analyze the feasibility of pooling the aggressive behavior variables of four cichlids species. Additionally, this paper discusses the feasibility of combining variables by examining the usage of different sample sizes and family distributions to aggressive behaviour variables. The subject species were: the angelfish (Pterophyllum scalare), the tiger oscar (Astronotus ocellatus), the Cichlasoma paranaense and the Nile tilapia (Oreochromis niloticus). For each species, 15 groups of 3 individuals were assigned to daily observations (10-min recordings) for 5 days. Aggressive behavior data was labeled according to its aggressive intensity. The variables chase (C), tail beating (TB), push (P), lateral attack (LA) and bite (B) were classified as high intensity. The variables undulation (U), lateral threat (LT) and frontal displays (FD) were classified as low intensity. These behaviors, however, were not present in all species. Model parameters were estimated by Monte Carlo Markov chains using non-informative priors. B-HLMs were performed to assess the impact probability of each variable in the analysis. Results revealed that when combining variables, the resulting distribution is strongly influenced by only one variable in each category. Moreover, in some cases the aggregate values altered the results, which changed the probabilities of the main variables. Species with low aggressive behavior frequencies, such as A. ocellatus, are more sensitive to this bias. LT was the main low intensity variable for all species, while B was the main high intensity variable for the P. scalare and the O. niloticus. LA was the high intensity category variable that was the most relevant for the C. paranaense and A. ocellatus. Moreover, combining the variables did not impact the feasibility of reducing the sample size when compared to using the most quantitative variable. For all species a sample size of 12 did not change the study conclusions. With respect to family distribution, based on DIC values the Gaussian model is more suitable for most of the studied species. However, caution should be taken, because the Gaussian posterior probability distribution overlapped 0 in some cases, which is biologically impossible in aggressive behaviors. The only exception is the A. ocellatus, which, based on DIC values, was the only species better modeled by a Poisson distribution. Bayesian analysis can be therefore considered a strong tool for analyzing aggressive behavior Universidade Estadual Paulista “Júlio de Mesquita Filho” (UNESP/IBILCE) Departamento de Zoologia e Botânica Aquaculture Center UNESP (CAUNESP), R. Cristóvão Colombo, 2265 Instituto Español de Oceanografía Centro Oceanográfico de Vigo, Subida a Radio Faro, 50-52 Fishing Ecology Management and Economics (FEME) - Universidade Federal do Rio Grande do Norte – UFRN Depto. de Ecologia Statistical Modeling Ecology Group (SMEG) Departament d'Estadística i Investigació Operativa Universitat de València, C/Dr. Moliner 50, Burjassot Universidade Estadual Paulista “Júlio de Mesquita Filho” (UNESP/IBILCE) Departamento de Zoologia e Botânica Aquaculture Center UNESP (CAUNESP), R. Cristóvão Colombo, 2265

In this paper, we analyze the effect on posterior parameter distributions of four possible alternative prior distributions, namely Normal-Inverse Gamma, Normal-Scaled Beta two, Student’s $t$-Inverse Gamma and Student’s $t$-Scaled Beta two. We show the effects of these prior distributions when there is apparently conflict between the sample information and the elicited hyperparameters. In particular, we show that there is not systematic differences of posterior parameter distributions associated with these four priors using data of piped water demand in a linear model with autoregressive errors. To test the hypothesis that this result is due to using a moderate sample size and a relatively high level of expert’s uncertainty, we perform some simulation exercises assuming smaller sample sizes and lower expert’s uncertainty. We obtain the general same pattern, although Student’s $t$ models are slightly less affected by prior information when there is a high level of expert’s certainty, and Scaled Beta two models exhibit a higher level of posterior dispersion of the variance parameter.

Made available in DSpace on 2018-12-11T17:15:13Z (GMT). No. of bitstreams: 0 Previous issue date: 2017-12-01 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) This study aims to describe a Bayesian Hierarchical Linear Model (HLM) approach for longitudinal designs in fish's experimental aggressive behavior studies as an alternative to classical methods In particular, we discuss the advantages of Bayesian analysis in dealing with combined variables, non-statistically significant results and required sample size using an experiment of angelfish (Pterophyllum scalare) species as case study. Groups of 3 individuals were subjected to daily observations recorded for 10 min during 5 days. The frequencies of attacks, displays and the total attacks (attacks + displays) of each record were modeled using Monte Carlo Markov chains. In addition, a Bayesian HLM was performed for measuring the rate of increase/decrease of the aggressive behavior during the time and to assess the probability of difference among days. Results highlighted that using the combined variable of total attacks could lead to biased conclusions as displays and attacks showed an opposite pattern in the experiment. Moreover, depending of the study, this difference in pattern can happen more clearly or more subtly. Subtle changes cannot be detected when p-values are implemented. On the contrary, Bayesian methods provide a clear description of the changes even when patterns are subtle. Additionally, results showed that the number of replicates (15 or 11) invariant the study conclusions as well that using a small sample size could be more evident within the overlapping days, that includes the social rank stability. Therefore, Bayesian analysis seems to be a richer and an adequate statistical approach for fish's aggressive behavior longitudinal designs. Universidade Estadual Paulista Júlio Mesquita Filho (UNESP/IBILCE) Zoology and Botany Department, R. Cristóvão Colombo, 2265 Aquaculture Center of Sao Paulo State University (CAUNESP) Fishing Ecology Management and Economics (FEME) Universidade Federal do Rio Grande do Norte – UFRN Depto. de Ecologia Statistical Modeling Ecology Group (SMEG) Departament d'Estadística i Investigació Operativa Universitat de València, C/Dr. Moliner 50, Burjassot Instituto Español de Oceanografía Centro Oceanográfico de Murcia, C/Varadero 1, San Pedro del Pinatar Universidade Estadual Paulista Júlio Mesquita Filho (UNESP/IBILCE) Zoology and Botany Department, R. Cristóvão Colombo, 2265 Aquaculture Center of Sao Paulo State University (CAUNESP) CNPq: #2016-26160-2

In longitudinal studies with small samples and incomplete data, multivariate normal-based models continue to be a powerful tool for analysis. This has included a broad scope of biomedical studies. Testing the assumption of multivariate normality (MVN) is critical. Although many methods are available for testing normality in complete data with large samples, a few deal with the testing in small samples. For example, Liang et al. (J. Statist. Planning and Inference 86 (2000) 129) propose a projection procedure for testing MVN for complete-data with small samples where the sample sizes may be close to the dimension. To our knowledge, no statistical methods for testing MVN in incomplete data with small samples are yet available. This article develops a test procedure in such a setting using multiple imputations and the projection test. To utilize the incomplete data structure in multiple imputation, we adopt a noniterative inverse Bayes formulae (IBF) sampling procedure instead of the iterative Gibbs sampling to generate iid samples. Simulations are performed for both complete and incomplete data when the sample size is less than the dimension. The method is illustrated with a real study on an anticancer drug.

In this work, we propose a heteroscedastic Von Bertalanffy growth model considering a multiplicative heteroscedastic dispersion matrix. All estimates were obtained using a sampling based approach, which allows information to be input beforehand with lower computational effort. Simulations were carried out in order to verify some frequentist properties of the estimation procedure in the presence of small and moderate sample sizes. ¶ The methodology is illustrated on a real Kubbard female chicken corporeal weight dataset.