Maengseok Noh

H-likelihood: problems and solutions

In recent issues of this journal it has been asserted in two papers that the use of h-likelihood is wrong, in the sense of giving unsatisfactory estimates of some parameters for binary data (Kuk and Cheng, 1999; Waddington and Thompson, 2004) or theoretically unsound (Kuk and Cheng, 1999). We wish to refute both these assertions.

Robust Modeling for Inference From Generalized Linear Model Classes

Generalized linear models (GLMs) are widely used for data analysis; however, their maximum likelihood estimators can be sensitive to outliers. We propose new statistical models that allow robust inferences from the GLM class of models, including Poisson and binomial GLMs, and their extension to generalized linear mixed models. The likelihood score equations from the new models give estimators with bounded influence, so that the resulting estimators are robust against outliers while maintaining high efficiency in the absence of outliers.

Does a geographical context of deprivation affect differences in injury mortality? A multilevel analysis in South Korean adults residing in metropolitan cities

Background This study aimed to examine whether the socioeconomic context of urban areas affects differences in adult mortality from injuries in the districts of all seven South Korean metropolitan cities, after adjusting for individual demographic and socioeconomic indicators. Methods Two different sets of data were used in this study: (1) the National Death Registration data from 2003 to 2008; and (2) the National Census in 2005. Variables for individual characteristics were gender, age, residential area and educational level. A geographic deprivation index was calculated based on the Carstairs Index. Multilevel Poisson regression models were used to analyse the relationship between area deprivation levels and injury mortality. Results Greater mortality risks of traffic accidents, falls, suicide and all injuries were found in the elderly, the less educated and men, compared with their counterparts. The most deprived districts were at greater risks of death due to traffic accidents (risk ratio (RR)=1.34; 95% CI 1.05 to 1.73), falls (RR=1.63; 95% CI 1.20 to 2.20), suicide (RR=1.09; 95% CI 1.01 to 1.17) and all injuries (RR=1.14; 95% CI 1.07 to 1.22) compared with the least deprived districts, even after individual level socioeconomic variables were controlled for. However, area level deprivation did not show cross level interactions with the individual level education in estimating fatal injury risks. Conclusions Both contextual and compositional effects of socioeconomic status on injury mortality among urban areas in South Korea should be considered in allocating resources for injury prevention.

Deprivation and suicide mortality across 424 neighborhoods in Seoul, South Korea: a Bayesian spatial analysis

ObjectivesA neighborhood-level analysis of mortality from suicide would be informative in developing targeted approaches to reducing suicide. This study aims to examine the association of community characteristics with suicide in the 424 neighborhoods of Seoul, South Korea.MethodsNeighborhood-level mortality and population data (2005–2011) were obtained to calculate age-standardized suicide rates. Eight community characteristics and their associated deprivation index were employed as determinants of suicide rates. The Bayesian hierarchical model with mixed effects for neighborhoods was used to fit age-standardized suicide rates and other covariates with consideration of spatial correlations.ResultsSuicide rates for 424 neighborhoods were between 7.32 and 71.09 per 100,000. Ninety-nine percent of 424 neighborhoods recorded greater suicide rates than the Organization for Economic Cooperation and Development member countries’ average. A stepwise relationship between area deprivation and suicide was found. Neighborhood-level indicators for lack of social support (residents living alone and the divorced or separated) and socioeconomic disadvantages (low educational attainment) were positively associated with suicide mortality after controlling for other covariates.ConclusionsFinding from this study could be used to identify priority areas and to develop community-based programs for preventing suicide in Seoul, South Korea.

Hierarchical-likelihood approach for nonlinear mixed-effects models

The restricted maximum likelihood (REML) procedure is useful for inferences about variance components in linear mixed models (LMMs). However, its extension to nonlinear mixed models (NLMMs) is often hampered by analytically intractable integrals. For NLMMs various estimation methods have been suggested, but they have suffered from unsatisfactory biases. In this paper we propose a statistically and computationally efficient REML procedure, based upon hierarchical likelihood. Numerical studies show that the proposed method reduces the biases in the existing methods that we studied. We also study how the current REML procedure for LMMs can be modified to compute the proposed estimators.

Are There Spatial and Temporal Correlations in the Incidence Distribution of Scrub Typhus in Korea

Objectives: A hierarchical generalized linear model (HGLM) was applied to estimate the transmission pattern of scrub typhus from 2001 to 2011 in the Republic of Korea, based on spatial and temporal correlation. Methods: Based on the descriptive statistics of scrub typhus incidence from 2001 to 2011 reported to the Korean Centers for Disease Control and Prevention, the spatial and temporal correlations were estimated by HGLM. Incidences according to age, sex, and year were also estimated by the best-fit model out of nine HGLMs. A disease map was drawn to view the annual regional spread of the disease. Results: The total number of scrub typhus cases reported from 2001 to 2011 was 51,136: male, 18,628 (36.4%); female, 32,508 (63.6%). The best-fit model selected was a combination of the spatial model (Markov random-field model) and temporal model (first order autoregressive model) of scrub typhus transmission. The peak incidence was 28.80 per 100,000 persons in early October and the peak incidence was 40.17 per 100,000 persons in those aged 63.3 years old by the best-fit HGLM. The disease map showed the spread of disease from the southern central area to a nationwide area, excepting Gangwon-do (province), Gyeongsangbuk-do (province), and Seoul. Conclusion: In the transmission of scrub typhus in Korea, there was a correlation to the incidence of adjacent areas, as well as that of the previous year. According to the disease map, we are unlikely to see any decrease in the incidence in the near future, unless ongoing aggressive measures to prevent the exposure to the vector, chigger mites, in rural areas, are put into place.

Spatial and Temporal Distribution of Plasmodium vivax Malaria in Korea Estimated with a Hierarchical Generalized Linear Model

Objectives The spatial and temporal correlations were estimated to determine Plasmodium vivax malarial transmission pattern in Korea from 2001–2011 with the hierarchical generalized linear model. Methods Malaria cases reported to the Korea Centers for Disease Control and Prevention from 2001 to 2011 were analyzed with descriptive statistics and the incidence was estimated according to age, sex, and year by the hierarchical generalized linear model. Spatial and temporal correlation was estimated and the best model was selected from nine models. Results were presented as diseases map according to age and sex. Results The incidence according to age was highest in the 20–25-year-old group (244.52 infections/100,000). Mean ages of infected males and females were 31.0 years and 45.3 years with incidences 7.8 infections/100,000 and 7.1 infections/100,000 after estimation. The mean month for infection was mid-July with incidence 10.4 infections/100,000. The best-fit model showed that there was a spatial and temporal correlation in the malarial transmission. Incidence was very low or negligible in areas distant from the demilitarized zone between Republic of Korea and Democratic People’s Republic of Korea (North Korea) if the 20–29-year-old male group was omitted in the diseases map. Conclusion Malarial transmission in a region in Korea was influenced by the incidence in adjacent regions in recent years. Since malaria in Korea mainly originates from mosquitoes from North Korea, there will be continuous decrease if there is no further outbreak in North Korea.

Modelling random effect variance with double hierarchical generalized linear models

Random-effect models are becoming increasingly popular in the analysis of data. Lee and Nelder (2006) introduced double hierarchical generalized linear models (DHGLMs) in which not only the mean but also the residual variance (overdispersion) can be further modelled as random-effect models. In this article, we introduce DHGLMs that allow random-effect models for both the variances of random effects and the residual variance. We show how to use this general model class for the analysis of data and discuss how to select the best fitting model using the likelihood and various model-checking plots.

Hierarchical likelihood methods for nonlinear and generalized linear mixed models with missing data and measurement errors in covariates

Nonlinear mixed-effects (NLME) models and generalized linear mixed models (GLMM) are popular in the analyses of longitudinal data and clustered data. Covariates are often introduced to partially explain the large between individual (cluster) variation. Many of these covariates, however, contain missing data and/or are measured with errors. In these cases, likelihood inference can be computationally very challenging since the observed data likelihood involves a high-dimensional and intractable integral. Computationally intensive methods such as Monte-Carlo EM algorithms may offer computational difficulties such as very slow convergence or even non-convergence. In this article, we consider hierarchical likelihood methods which approximate the observed-data likelihood using Laplace approximation so completely avoid the intractable integral. We evaluate the methods via simulation and illustrate the methods by two examples.

Spatial modeling of data with excessive zeros applied to reindeer pellet‐group counts

Abstract We analyze a real data set pertaining to reindeer fecal pellet‐group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi‐Poisson hierarchical generalized linear model (HGLM), zero‐inflated Poisson (ZIP), and hurdle models. The quasi‐Poisson HGLM allows for both under‐ and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi‐Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi‐Poisson HGLM with spatial random effects.