• The Korean Journal of Applied Statistics
• /
• v.25 no.6
• /
• pp.1037-1047
• /
• 2012

The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.

• The Korean Journal of Applied Statistics
• /
• v.13 no.2
• /
• pp.541-562
• /
• 2000

The generalized linear mixed model framework is for handling count-type categorical data as well as for clustered or overdispersed non-Gaussian data, or for non-linear model data. In this study, we review its general formulation and estimation methods, based on quasi-likelihood and Monte-Carlo techniques. The current research areas and topics for further development are also mentioned.

• Communications for Statistical Applications and Methods
• /
• v.21 no.5
• /
• pp.423-433
• /
• 2014

Test statistics using cumulative sums of residuals have been widely used in various regression models including generalized linear models(GLM). Recently, Pan and Lin (2005) extended this testing procedure to the generalized linear mixed models(GLMM) having random effects, in which we encounter difficulties in computing the marginal likelihood that is expressed as an integral of random effects distribution. The Gaussian quadrature algorithm is commonly used to approximate the marginal likelihood. Many commercial statistical packages provide an option to apply this type of goodness-of-fit test in GLMs but available programs are very rare for GLMMs. We suggest a computational algorithm to implement the testing procedure in GLMMs by a freely accessible R package, and also illustrate through practical examples.

• Asian-Australasian Journal of Animal Sciences
• /
• v.11 no.6
• /
• pp.642-647
• /
• 1998

A Poisson error model as a generalized linear mixed model (GLMM) has been suggested for genetic analysis of counted observations. One of the assumptions in this model is the normality for random effects. Since this assumption is not always appropriate, a more flexible model is needed. For count traits, a Poisson hierarchical generalized linear model (HGLM) that does not require the normality for random effects was proposed. In this paper, a Poisson-Gamma HGLM was examined along with corresponding analytical methods. While a difficulty arises with Poisson GLMM in making inferences to the expected values of observations, it can be avoided with the Poisson-Gamma HGLM. A numerical example with simulated embryo yield data is presented.

• Communications for Statistical Applications and Methods
• /
• v.26 no.3
• /
• pp.315-323
• /
• 2019

Panel data sets have recently been developed in various areas, and many recent studies have analyzed panel, or longitudinal data sets. Often a dichotomous dependent variable occur in survival analysis, biomedical and epidemiological studies that is analyzed by a generalized linear mixed effects model (GLMM). The most common estimation method for the binary panel data may be the maximum likelihood (ML). Many statistical packages provide ML estimates; however, the estimates are computed from numerically approximated likelihood function. For instance, R packages, pglm (Croissant, 2017) approximate the likelihood function by the Gauss-Hermite quadratures, while Rchoice (Sarrias, Journal of Statistical Software, 74, 1-31, 2016) use a Monte Carlo integration method for the approximation. As a result, it can be observed that different packages give different results because of different numerical computation methods. In this note, we discuss the pros and cons of numerical methods compared with the exact computation method.

• The Korean Journal of Applied Statistics
• /
• v.34 no.5
• /
• pp.697-710
• /
• 2021

Relative error prediction is preferred over ordinary prediction methods when relative/percentile errors are regarded as important, especially in econometrics, software engineering and government official statistics. The relative error prediction techniques have been developed in linear/nonlinear regression, nonparametric regression using kernel regression smoother, and stationary time series models. However, random effect models have not been used in relative error prediction. The purpose of this article is to extend relative error prediction to some of generalized linear mixed model (GLMM) with panel data, which is the random effect models based on gamma, lognormal, or inverse gaussian distribution. For better understanding, the real auto insurance data is used to predict the claim size, and the best predictor and the best relative error predictor are comparatively illustrated.

• The Korean Journal of Applied Statistics
• /
• v.17 no.2
• /
• pp.185-196
• /
• 2004

It is an important research area in Integrated Pest Management System to estimate the pest density within plants, because the artificial controls such as spraying pesticides or biological enemies depend on the information of pest density. This paper studies the population density distribution of two-spotted spider mite in glasshouse roses. As the data were collected repeatedly on the same subject, Subject-Specific and Population Averaged approaches are used and compared.

• Research in Community and Public Health Nursing
• /
• v.29 no.4
• /
• pp.414-428
• /
• 2018

Purpose: The purpose of this study is to identify the spatial distribution of hypertension prevalence and to investigate individual and regional-level factors contributing to the prevalence of hypertension in the region. Methods: This study is a cross-sectional research using the 2015 Community Health Survey. Total 64,473 people from 7 metropolitan cities were used for the final analysis. Geoda program was adopted to identify the regional distribution of hypertension prevalence and analyzed by descriptive statistics, one-way ANOVA and correlation analysis using SPSS statistics 23.0 program. Multi-level analysis was performed using SPSS (GLMM). Results: The prevalence of hypertension was related to individual level factors such as age, monthly household income, normal salt intake, walking practice days, and regional level factors including number of doctors per 10,000 population, number of parks, and fast food score. Besides, regional level factors were associated with hypertension prevalencies independently without the effects of individual level factors even though the influences of individual level factors ware larger than those of regional factors. Conclusion: Respectively, both individual and regional level factors should be considered in hypertension intervention programs. Also, a national level research is further required by exploring various environmental factors and those influences relating to the hypertension prevalence.

• The Korean Journal of Applied Statistics
• /
• v.21 no.6
• /
• pp.923-932
• /
• 2008

We are likely to face complex multivariate data which can be characterized by having a non-trivial correlation structure. For instance, omitted covariates may simultaneously affect more than one count in clustered data; hence, the modeling of the correlation structure is important for the efficiency of the estimator and the computation of correct standard errors, i.e., valid inference. A standard way to insert dependence among counts is to assume that they share some common unobservable variables. For this assumption, we fitted correlated random effect models considering multilevel model. Estimation was carried out by adopting the semiparametric approach through a finite mixture EM algorithm without parametric assumptions upon the random coefficients distribution.

• Journal of the Korean housing association
• /
• v.25 no.4
• /
• pp.93-100
• /
• 2014

The purpose of this study, analyzing the primary factors for residential mobility and housing preference of Daegu citizens, is to provide a basic data for future housing policies. The results are as follows: First, 32.1% of Daegu citizens have intention of residential mobility. Especially the residents in central (50.0%), southern (59.0%) and western Daegu showed more intention than those in other districts. Second, we used the GLMM (Generalized Linear Mixed Models) to analyze the main factors for residential mobility. The results are as follows; 1) the residents who have lower housing satisfaction with the type of housing, parking, and educational environment, 2) those who are male and younger, 3) those who live in rented house have more intention of housing mobility. Third, based on the analysis on the preference change of the type of housing, the preference of the apartments is getting higher, while that of the detached houses is getting lower (past: 40.1%${\rightarrow}$present: 54.8%${\rightarrow}$future: 66.7%). 28.8% of the respondents (444) expressed intention to live in the public rental houses, in case they are provided in the areas they are moving to. Fourth, when we analyzed the size of the houses they actually lived in and that of the houses they prefer to live in case of moving, we found that in general they tend to move in smaller housing than in the past. The results of the analysis showed that in order to minimize the possible moving away from the current residential areas due to the dissatisfaction with the housing environment, in the first place the improvement in the quality of the houses, parking and education environment is needed.