Abstract. Maximum likelihood estimates in GLMM are often difficult to be obtained since the calculation involves high dimensional integrals. It is not easy to find analytical solutions for the integral so that the approximation approach is needed. In this paper, we discuss several approximation methods to solve high dimension integrals including the Laplace, Penalized Quasi likelihood (PQL) and Adaptive Gaussian Quadrature (AGQ) approximations. The performance of these methods was evaluated through simulation studies. The 'true' parameter in the simulation was set to be similar with parameter estimates obtained by analyzing a real data, particularly salamander data (McCullagh & Nelder, 1989). The simulation results showed that the Laplace approximation produced better estimates when compared to PQL and AGQ approximations in terms of their relative biases and mean square errors.
The purpose of research is to evaluate the GLM, GLMM and HGLM models to poverty data in Aceh Province and then identify the best model. The response variable is the percentage of district or city poverty while the fixed effect is population density, sex ratio, the number of populations, the number of industries, area types, percentage of PLN user, poverty line and percentage of productive age group. The random effect for the GLMM and HGLM models is the average monthly expenditure. The data in 2019 were taken from website of the Aceh Central Statistics Agency (BPS) on April 13, 2020. For aggregate, the response variable and the random effect met the normal and gamma distribution. the results showed that the population density has an influence on the percentage of poverty in the GLM and HGLM, while in the GLMM, there are no factors that affect it. The scores of determination coefficient (R2) for GLM, GLMM and HGLM were 75.795%, 68.441% and 75.881%, respectively whereas scores of RMSE of them were 0.121, 1.917 and 0.120, respectively. Because the HGLM model has the largest R2 and the smallest RMSE, the HGLM was said to be the best model for the case.
The proportional odds model (POM) and the non-proportional odds model (NPOM) are very useful in ordinal modeling. However, the proportional odds assumption is often violated in practice. In this paper, the non-proportional odds model is chosen as an alternative model when the proportional odds assumption is not violated. This paper aims to compare Proportional Odds Model (POM) and Non-Proportional Odds Model (NPOM) in cases of birth size in Indonesia based on the 2017 Indonesian Demographic and Health Survey (IDHS) data. The results showed that in the POM there was a violation of the proportional odds assumption, so the alternative NPOM model was used. NPOM had better use than POM. The goodness of fit shows that the deviance test failed to reject H0, and the value of Mac Fadden R2 is higher than POM. The risk factors that have a significant influence on all categories of birth size are the residence and gender of the child.
Survival analysis has three approaches, parametric, non-parametric, and semi-parametric. The parametric model requires the distribution of survival time to be known. Weibull regression is one of the most popular forms of parametric approaches with advantages in flexibility and simplicity of hazard functions and survival functions. Stratified Cox regression is a semi-parametric approach method that is rightly used when the proportional hazard assumption is violated. The comparison between Weibull regression and stratified Cox regression was applied in the case of the duration of exclusive breastfeeding in infants aged 0-6 months in Indonesia. Before the model was formed, the data were tested for the Weibull distribution and the results were met properly. Whereas for testing proportional hazard assumptions the results are not fulfilled so that semi-parametric models can be used. Based on the results of the study, the Weibull regression is better than the stratified Cox regression.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.