A generalized linear mixed model for understanding determinant factors of student's interest in pursuing bachelor's degree at Universitas Syiah Kuala

Generalized Linear Mixed Model (GLMM) is a framework that has a response variable, fixed effects, and random effects. The response variable comes from an exponential family, whereas random effects have a normal distribution. Estimating parameters can be calculated using the maximum likelihood method using the Laplace approach or the Gauss-Hermite Quadrature (GHQ) approach. The purpose of this study was to identify factors that trigger student's interest to continue studying at Universitas Syiah Kuala (USK) using both techniques. The GLMM is suitable for the data because the variable response has a Bernoulli distribution, and the random effects are assumed to be having a normal distribution. Also, the model helps identify the relationship between the dependent variable and the predictors. This study utilizes data from six high schools in Banda Aceh city drawn using a two-stage sampling technique. Stage 1, we randomly chose six out of sixteen public senior high schools in Banda Aceh. Stage 2, we selected students from each school from four different major classes. The GLMM model includes one binary response variable, five numerical fixed-effects, and two random effects. The response variable is the interest of high school students to continue study at USK (yes or no). The five fixed effects in the model including scores of collaboration (C), Action (A), Emotion (E), Purposes (P), and Hope (H). Finally, the random effects are schools (S) and majors (M). In this study, both Laplace and GHQ techniques produce identical results. The predictors that can explain student interest are A, E, and H. These predictors have a positive effect. The random effects of schools and majors are not significantly different from zero. The model with three significant predictors is better than the complete predictor model.

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Multiple Group Comparisons of the Fixed and Random Effects From the Generalized Linear Mixed Model

Sociological Methods & Research ◽

10.1177/0049124120986182 ◽

2021 ◽

pp. 004912412098618

Author(s):

Daniel Kasper ◽

Katrin Schulz-Heidorf ◽

Knut Schwippert

Keyword(s):

Random Effects ◽

Fixed Effects ◽

Mixed Model ◽

Linear Mixed Model ◽

Asymptotic Properties ◽

Generalized Linear Mixed Model ◽

Test Statistic ◽

Multiple Group ◽

Fixed And Random Effects ◽

Group Comparisons

In this article, we extend Liao’s test for across-group comparisons of the fixed effects from the generalized linear model to the fixed and random effects of the generalized linear mixed model (GLMM). Using as our basis the Wald statistic, we developed an asymptotic test statistic for across-group comparisons of these effects. The test can be applied when the fixed and random effects are multivariate normally distributed, and it works well for any link function and conditional distribution of the dependent variable of the GLMM. We also derived the asymptotic properties of this test, and because power information does not exist for either our new test statistic or Liao’s test, we implemented a power study to demonstrate the superiority of these tests over the alternatively proposed F test. Using an example, we show the application of the test and then discuss its possible restrictions with respect to the distribution of the random effects.

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Analysis of aggregation, a worked example: numbers of ticks on red grouse chicks

Parasitology ◽

10.1017/s0031182001007740 ◽

2001 ◽

Vol 122 (5) ◽

pp. 563-569 ◽

Cited By ~ 267

Author(s):

D. A. ELSTON ◽

R. MOSS ◽

T. BOULINIER ◽

C. ARROWSMITH ◽

X. LAMBIN

Keyword(s):

Random Effects ◽

Mixed Model ◽

Linear Mixed Model ◽

Negative Binomial ◽

Generalized Linear Mixed Model ◽

Red Grouse ◽

Worked Example ◽

Fixed And Random Effects ◽

Individual Effects ◽

Lagopus Lagopus Scoticus

The statistical aggregation of parasites among hosts is often described empirically by the negative binomial (Poisson-gamma) distribution. Alternatively, the Poisson-lognormal model can be used. This has the advantage that it can be fitted as a generalized linear mixed model, thereby quantifying the sources of aggregation in terms of both fixed and random effects. We give a worked example, assigning aggregation in the distribution of sheep ticksIxodes ricinuson red grouseLagopus lagopus scoticuschicks to temporal (year), spatial (altitude and location), brood and individual effects. Apparent aggregation among random individuals in random broods fell 8-fold when spatial and temporal effects had been accounted for.

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Quasi-Monte Carlo Estimation in Generalized Linear Mixed Model with Correlated Random Effects

OALib ◽

10.4236/oalib.1102002 ◽

2015 ◽

Vol 02 (10) ◽

pp. 1-16

Author(s):

Yin Chen ◽

Yu Fei ◽

Jianxin Pan

Keyword(s):

Monte Carlo ◽

Random Effects ◽

Mixed Model ◽

Linear Mixed Model ◽

Generalized Linear Mixed Model ◽

Quasi Monte Carlo ◽

Correlated Random Effects ◽

Monte Carlo Estimation

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Generalized Linear Mixed Model Analysis of Acute Respiratory Infection Data on Children

International Journal of Scientific Research in Science Engineering and Technology ◽

10.32628/ijsrset207610 ◽

2020 ◽

pp. 110-115

Author(s):

Tiyas Yulita ◽

Tika Widayanti

Keyword(s):

Respiratory Infection ◽

Acute Respiratory Infection ◽

Mixed Model ◽

Linear Mixed Model ◽

Generalized Linear Mixed Model ◽

Combination Method ◽

Predictor Variables ◽

Minimum Bias ◽

Response Variable ◽

Shrinkage Coefficient

Statistical modeling often involves data which has a distribution of the exponential family. Generalized Linear Model (GLM) was developed to model these data by using a link function between the mean of the response variable and the linear form of the predictor variable. If the data of the response variable comes from several census blocks that are taken randomly, then the diversity between census blocks should not be ignored because it can increase bias. The Generalized Linear Mixed Model (GLMM) is a method that can capture a variety of random effects. However, it does not rule out if there are many predictor variables involved in the model and we use GLMMLasso as a combination method of GLMM and Lasso to shrink the parameter coefficients to zero, it is used to reduce the variance. In this study, a simulation was conducted to GLMMLasso use different numbers of predictor variables and different values of shrinkage coefficients to determine which shrinkage coefficient values have a minimum bias on parameter prediction. Acute Respiratory Infection (API) data on children in Jakarta is used to know the factors that could cause increased cases. The simulation result is the shrinkage coefficient which produces a minimum bias is 30, and the R2 value of data analysis on the model is 99.24%

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Survey of Models for Random Effects Covariance Matrix in Generalized Linear Mixed Model

Korean Journal of Applied Statistics ◽

10.5351/kjas.2015.28.2.211 ◽

2015 ◽

Vol 28 (2) ◽

pp. 211-219 ◽

Cited By ~ 1

Author(s):

Jiyeong Kim ◽

Keunbaik Lee

Keyword(s):

Covariance Matrix ◽

Random Effects ◽

Mixed Model ◽

Linear Mixed Model ◽

Generalized Linear Mixed Model

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Privacy-preserving construction of generalized linear mixed model for biomedical computation

Bioinformatics ◽

10.1093/bioinformatics/btaa478 ◽

2020 ◽

Vol 36 (Supplement_1) ◽

pp. i128-i135

Author(s):

Rui Zhu ◽

Chao Jiang ◽

Xiaofeng Wang ◽

Shuang Wang ◽

Hao Zheng ◽

...

Keyword(s):

Em Algorithm ◽

Random Effects ◽

Mixed Model ◽

Linear Mixed Model ◽

Generalized Linear Mixed Model ◽

Privacy Preserving ◽

Supplementary Information ◽

Genome Wide Association Studies ◽

Linear Predictor ◽

Biomedical Computation

Abstract Motivation The generalized linear mixed model (GLMM) is an extension of the generalized linear model (GLM) in which the linear predictor takes random effects into account. Given its power of precisely modeling the mixed effects from multiple sources of random variations, the method has been widely used in biomedical computation, for instance in the genome-wide association studies (GWASs) that aim to detect genetic variance significantly associated with phenotypes such as human diseases. Collaborative GWAS on large cohorts of patients across multiple institutions is often impeded by the privacy concerns of sharing personal genomic and other health data. To address such concerns, we present in this paper a privacy-preserving Expectation–Maximization (EM) algorithm to build GLMM collaboratively when input data are distributed to multiple participating parties and cannot be transferred to a central server. We assume that the data are horizontally partitioned among participating parties: i.e. each party holds a subset of records (including observational values of fixed effect variables and their corresponding outcome), and for all records, the outcome is regulated by the same set of known fixed effects and random effects. Results Our collaborative EM algorithm is mathematically equivalent to the original EM algorithm commonly used in GLMM construction. The algorithm also runs efficiently when tested on simulated and real human genomic data, and thus can be practically used for privacy-preserving GLMM construction. We implemented the algorithm for collaborative GLMM (cGLMM) construction in R. The data communication was implemented using the rsocket package. Availability and implementation The software is released in open source at https://github.com/huthvincent/cGLMM. Supplementary information Supplementary data are available at Bioinformatics online.

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A Generalized Linear Mixed Model Approach to Assess Emerald Ash Borer Diffusion

ISPRS International Journal of Geo-Information ◽

10.3390/ijgi9070414 ◽

2020 ◽

Vol 9 (7) ◽

pp. 414

Author(s):

Yuan Zhong ◽

Baoxin Hu ◽

G. Brent Hall ◽

Farah Hoque ◽

Wei Xu ◽

...

Keyword(s):

Random Effects ◽

Mixed Model ◽

Linear Mixed Model ◽

Climatic Factors ◽

Anthropogenic Activities ◽

Emerald Ash Borer ◽

Predictive Performance ◽

Generalized Linear Mixed Model ◽

Agrilus Planipennis ◽

Mixed Model Approach

The Asian Emerald Ash Borer beetle (EAB, Agrilus planipennis Fairmaire) can cause damage to all species of Ash trees (Fraxinus), and rampant, unchecked infestations of this insect can cause significant damage to forests. It is thus critical to assess and model the spread of the EAB in a manner that allows authorities to anticipate likely areas of future tree infestation. In this study, a generalized linear mixed model (GLMM), combining the features of the commonly used generalized linear model (GLM) and a random effects model, was developed to predict future EAB spread patterns in Southern Ontario, Canada. The GLMM was designed to deal with autocorrelation in the data. Two random effects were established based on the geographic information provided with the EAB data, and a method based on statistical inference was proposed to identify the most significant factors associated with the distribution of the EAB. The results of the model showed that 95% of the testing data were correctly classified. The predictive performance of the GLMM was substantially enhanced in comparison with that obtained by the GLM. The influence of climatic factors, such as wind speed and anthropogenic activities, had the most significant influence on the spread of the EAB.

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