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Longitudinal data consists of repeated observations made from time to time on each individual. The correlation between observations within the same unit in longitudinal data makes the Generalized Linear Mixed Model (GLMM) an appropriate method for the analysis of longitudinal data. GLMM will not have a good estimation if the data contains missing values. To solve this problem, the imputation method is used. This paper discusses two imputation methods, namely mean and median row. The missing value is filled with the average or median value of all the values in the subject. It is known that poverty cases in districts/cities in Eastern Indonesia contain the missing value. Thus, poverty cases in these areas can be used as case studies of the data used. The purpose of the study is to form a GLMM model longitudinal with the Poisson response variable on poverty data in Eastern Indonesia to obtain factors that positively and negatively affect poverty in eastern Indonesia and obtain the right method of median row and mean row in the imputation methods to handle missing values based on the AIC value of the resulting estimate using GLMM. A mean row method is recommended to impute the missing values in Longitudinal data of poverty cases in Eastern Indonesia's districts/cities. [ABSTRACT FROM AUTHOR]

Some of the collected data may have a non-normal distribution. One approach that can be used to model the phenomenon of data having non-normal response variables and random effects is the Generalized Linear Mixed Model (GLMM). In its development, the GLMM model can be combined with a decision tree-based method approach called the GLMM tree. Flooding is one of the problems faced by all local governments in Indonesia. Based on data from bnpb.go.id, in 2021 there were 724 flood disasters spread across almost all provinces in Indonesia. And the number of victims reached 4,682,923 people and 99,841 buildings were affected. This study aims to model the phenomenon of flooding that occurred in Indonesia with the GLMM tree approach. The focus of the research that will be discussed is related to flood victims and flood disasters that occurred in Indonesia. The data used in this study is secondary data obtained from several related institutions' websites. This research is expected to be input in terms of decision making and so on. [ABSTRACT FROM AUTHOR]

Variable selection is essential in linear regression analysis to improve predictability and select significant variables. Estimating the regression coefficient on high-dimensional data cannot be done using the least squares method, so it requires specific analytical techniques. Approaches that can take on high-dimensional data include SCAD, LASSO, and Elastic Net. This research will analyze the most crucial method between SCAD, LASSO, and Elastic Net on Low Birth Weight (LBW) data in East Nusa Tenggara (NTT). Two methods are used in this study, first, comparing the SCAD, LASSO, and Elastic Net methods using simulation data, and second, applying the logistic regression method to actual data. The data used in this study is the LBW data by fertile women in NTT from the 2017 IDHS (Indonesian Demographic and Health Survey) data. The analysis shows that the results obtained through simulation and data reveal, based on the value of the AIC model goodness test, the SCAD is better than the other methods with the smallest AIC value of 17. 58878, smaller than the AIC LASSO value of 17.90169 and Elnet of 17.88728. [ABSTRACT FROM AUTHOR]

One of the essential aspects of modeling is the model's simplicity. Several methods can simplify the model, including Ridge regression, LASSO, and Elastic Net. We developed an algorithm for selecting the variables in these models, namely Naïve and Covariance. Previous research revealed that the Covariance algorithm is superior in terms of time compared to the Naïve algorithm. It is evaluated by applying models and algorithms to male sex behavior data with the criteria of goodness, namely the simplicity of the model and the minimum AIC value. Based on the study's results, it found that the Covariance algorithm still outperformed the Naïve algorithm in all three models. [ABSTRACT FROM AUTHOR]

The infant Mortality rate (IMR) is an indicator normally used as an index of economic improvement, an indicator of the nice of existence, and the principle aspect figuring out the life expectancy of a society. IMR can be observed as longitudinal data, a combination of cross-section data and time-series data, where the same cross-section unit is observed at different times. When the data is repeatedly observed with a specific interval of time, then the time will correlate or not mutually exclusive. To overcome this, time is used as a random effect, so the appropriate method used is the Generalized Linear Mixed Model (GLMM). This study pursuits to version infant mortality data the use of the GLMM and have a look at the variables that affect the quantity of infant deaths in West Sumatra. Based on the results of the analysis, the quantity of low birth weight babies, the percentage of births assisted by non-medical personnel, the percentage of households that have access to proper sanitation services, the percentage of households that have adequate drinking water sources, the percentage of poor people, the quantity of health workers, and the quantity of health facilities has a very significant influence on infant mortality in the province of West Sumatra. [ABSTRACT FROM AUTHOR]

The number of DBD patients in DKI Jakarta in 2017-2020 is counted data so Poisson regression can be used to modellling the relationship between climatic factors and the number of DBD patients. However, in its application, this model has violated the overdispersion assumption so that handling is carried out using the Generalized Linear Mixed Model (GLMM) with Poisson regression and Negative Binom regression. The GLMM model was used to accommodate the random effects of measurement time and measurement location. For both models, the Autoregressive 1 (AR1) variance matrix is used because there is a strong correlation between observations and previous observations. The GLMM model with Negative Binom regression is considered the best model because it has a lower AIC value than the GLMM model AIC with Poisson regression. In this model, only the variables of average temperature per month and average humidity per month have a significant effect on the number of DBD patients in DKI Jakarta in 2017-2020 at the 5% significance level. [ABSTRACT FROM AUTHOR]

The generalized Mixed Linear Model is applicable in Indonesia's Low Birth Weight (LBW) case. During 2003-2028, this case happened 2.6% to 8.9% of total birth. The lowest low birth weight case was in Jambi province, and the highest was in Central Sulawesi. The forms of LBW models include census blocks as random influences, and the fixed effects used are parents' background, household socio-economic conditions, maternal conditions. The link function used was logit because the response is binary. Therefore, this research aims to estimate the GLMM of each province and then do the selection using the glmmLasso model by L1-norm. The results indicate that the results of the selection method using the glmmLasso method are simpler than the GLMM for both Jambi and Central Sulawesi provinces. This result is supported by the goodness of fit (BIC and AIC), where the BIC for glmmLasso for Jambi and Central Sulawesi provinces are 135.488 and 214.783, respectively. Equivalent to the goodness of the model, estimation of the random effect influences for the glmmLasso model is also smaller than GLMM. The variable with a significant effect on LBW in Jambi province is the mother's age, and two variables are shrunk toward zero. However, the glmmLasso LWB's model of Central Sulawesi has four variables that have a significant effect. Those variables are the father's occupation, mother's education level, level of the wealth index, and multiple births, and just one variable is reduced. [ABSTRACT FROM AUTHOR]

Indonesia is currently facing the Covid-19 pandemic, which all countries in the world have also faced in the past year. The contribution of daily cases from each province is the key to the high and low number of positive cases of Covid- 19 in.Indonesia. Based on data from the Covid-19 handling task force for Indonesia, it was noted that Jakarta is the province with the highest spread of Covid-19 cases in Indonesia. Daily positive cases in Jakarta contributed 25% to national cases. For this reason, this study aims to analyze the incidence of positive cases of Covid-19 in.Jakarta through a prediction model for time series data. The multi-input transfer function model used is one of the multivariate time series models to predict Covid-19 cases in Jakarta based on several external variables. The external variables or input series used are the Covid-19 cases in Bodetabek, close contact data, and death case data. All variables used are time-series data from April 2020 to April 2021. The analysis results show that the three input variables significantly correlate in predicting Covid-19 cases in Jakarta. The multi-input transfer function model that has been formed has a pretty good performance in predicting Covid-19 cases in Jakarta with a MAPE of 10%. [ABSTRACT FROM AUTHOR]

Growth curves are widely used in modeling the growth process. These curves can capture the pattern of the growth process to explain the characteristic of the growth process. In this research, growth curves are modelled to time series form models in the growth rate form by allowing lagged in the model. These growth time series models are applied in weekly new cases of positive COVID-19 in.Jakarta to forecast the number of new cases in the five weeks ahead in the testing data. Three schemes are made to be modelled. The growth curves that employed in this research are Logistic and Richard growth curves. Evaluations value of the Richard and Logistic models are evaluated by RMSEP of the forecasting result in testing data and RMSE of the prediction in training data to determine which model is better to fit in the weekly new cases of positive COVID-19 in.Jakarta. Time series model based on Richard growth curve seems to have better performance than Logistic growth curve in forecasting weekly new cases of COVID-19 in.Jakarta, because Richard time series models have smaller RMSE and RMSEP in almost all scheme than Logistic models. Other than that more testing data fall into the 95% confidence interval of weekly new cases in Richard time series model than Logistic time series model in all scheme. [ABSTRACT FROM AUTHOR]

Mixed model is a model that combines fixed factors and random factors while fixed model is a model that only contains fixed factors. Observations made over time with the same object being observed are called repeated measurement. This research was conducted to determine the determinant factors of internet data quota sales which are influenced by SA (Sales Area), MC (Mutual Check), PC (Product Category), and time factors using a nested linear mixed model with repeated measurement and fixed model with repeated measurement. SA, PC, and time factors as fixed factors while the MC factor nested in SA as a random factor. The results showed that in nested linear mixed model with repeated measurement, the interaction effect between three fixed factors, namely between SA, PC, and time have a significant effect on the sales volume of internet data quota. In fixed model the analysis used the average value of internet data quota sales for each MC, so there is no interaction effect between three fixed factors in the fixed model. This shows that the fixed model is simpler than the mixed model. The nested mixed model with repeated measurement can better explain the effect of MC in SA because it includes random factors, namely the MC factor nested in SA. The fixed model with repeated measurement can better explain the effect of SA because SA is a fixed factor which is the average of MC. [ABSTRACT FROM AUTHOR]

One of the problems faced by the Province of West Java is poverty. The response data used in this study is the percentage of the poor who have a non-normal distribution. Fixed effects variables consist of life expectancy, school year expectancy, and school enrollment rates aged 16-18 years. Years and clusters variables will be included as independent variables but are random effects. Therefore, for this data case, the appropriate model to be developed is Binomial GLMM and Beta-Binomial HGLM. The modeling performed on the percentage of poor population data gives relatively the same results between the model approaches using Binomial GLMM and Beta-Binomial HGLM with a random effect of years. The random effect in both models shows that there is a variation in the percentage of poor people in years, but the variabilitybetween years cannot be shown by the data. Likewise, the modeling carried out on the percentage of poor population data gives relatively the same results between the model approaches using Binomial GLMM and Beta-Binomial HGLM with clusters random effect. Fixed effects variables and random effects have a significant effect on the percentage of poor people for all models. The model obtained by involving all fixed effects and random effects (clusters) is the best model because itprovides the smallest CAIC value compared to models using random effects (Years). [ABSTRACT FROM AUTHOR]

The Generalized Linear Model method and the Generalized Linear Mixed Model method are methods that delete the assumption of data normality for the response variables. The two methods are compared and applied to the Human Development Index (HDI) panel data to see the best model and determine what factors affect HDI. The predictor variables used include: GRDP, ratio of elementary school teachers to elementary students, ratio of junior high school teachers to junior high school students, ratio of high school teachers to high school students, number of health workers, population and poverty ratio. The data source comes from BPS by taking three provinces classified into provinces with very high HDI represented by DKI Jakarta province, Province with high HDI represented by West Java province, and provinces with moderate HDI represented by NTB province. The results showed that neither the GLM method nor the GLMM method could be used to model HDI data. The factors that influence the HDI for the data for the provinces of Jakarta and NTB are the GRDP factor, the ratio of elementary school teachers to elementary students, the ratio of junior high school teachers to junior high school students, the number of health workers, and the total population. In the data for the province of Jakarta, an anomaly in economic theory is found which states that an increase in GRDP causes a decrease in the HDI value. This indicates that the GRDP factor for the DKI Jakarta province isnot sufficient to represent the economic dimension as one of the indicators in forming the HDI value. The factors that influence the HDI value in the province of West Java are the GRDP factor and the poverty ratio, while other factors have no significant effect on the HDI value. [ABSTRACT FROM AUTHOR]

The objective of this study is to model the Generalized Linear Mixed Model (GLMM) on the Consumer Price Index (CPI) data for 34 provinces as panel data in Indonesia. This modeling aims to predict and to see the causes of the CPI movement. This paper contains the formulation, interpretation and inference of the formed GLMM model. The modeling results show that the CPI response variable is assumed to follow the Gamma distribution with a regional random effect better than other models in this paper, this is indicated by the smaller AIC value of 70.2. This study provides a theoretical contribution to dealing with nonnormal distributed data in the CPI as panel data in Indonesia (in this case, we assume that the CPI have Gamma and Lognormal Distributed). In addition, this research is also practically useful for determining the most suitable modeling for CPI data as panel data in Indonesia. [ABSTRACT FROM AUTHOR]

The development model of the GLM for longitudinal data that has not normally distributed (but still in the exponential family) and correlates with response variables is the Generalized Estimating Equations (GEE) and Generalized Linear Mixed-effects Model (GLMM) models. This study compares the GEE model with the GLMM on longitudinal data in modeling poor people in Indonesia in 2015-2019. The data source used is from the publication of the Central Statistics Agency. Based on the smaller RMSE and AIC criteria, the GLMM model is better than the GEE model in modeling the percentage of poor people in Indonesia. The Gini ratio, the rate of Households in Slums, and the percentage of Informal Workers have a significant positive effect on the percentage of poor people. Meanwhile, the percentage of households having access to HDI, economic growth, domestic and foreign investment value have a significant negative impact on poor people. [ABSTRACT FROM AUTHOR]

This paper discusses fixed-b asymptotic distribution models which have been developed for panel data suffered by the problems of autocorrelation and heteroscedasticity. The fixed-b asymptotic distribution models can be used to infer the parameter of interest. For the purpose of inference the Bartlett Kernel Fixed-b Critical Values have been utilized. This technique is applied to analyze drop-out rates for the elementary and junior high school students in Central Java. The results showed that the drop-out rates in Central Java Province are significantly affected by morbidity rates, GRDP, and gross enrolment rates. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A small area is an area with small sample size to estimate parameters in survey sampling. The direct estimation will produce inaccurate estimation since the sample size is not enough to produce estimation with acceptable precision. Small Area Estimation (SAE) is a solution to obtain more precise estimation in a small area. A well-known method in SAE is an empirical best linear unbiased prediction (EBLUP). EBLUP is the estimator of small area means. It will provide an accurate estimation under normality assumptions but it can be sensitive when the data are contaminated by outliers. In this article, we discussed a resistant method in SAE, i.e. robust empirical best linear unbiased prediction (REBLUP). We apply REBLUP from unit-level models to the data obtained from the National Socio-economic Survey (SUSENAS). The means of per capita expenditures are calculated for all small areas. We compare the estimates of per capita expenditure in the small area using direct estimation, EBLUP and REBLUP methods using data that contain outliers. The result shows that REBLUP estimation has produced more accurate estimates when compared to the other methods. [ABSTRACT FROM AUTHOR]

Empirical Best Linear Unbiased Prediction (EBLUP) is one of indirect estimating methods which used to estimate parameters of small areas. EBLUP methods works in using auxiliary variables of area while adding the area random effects. In estimating non-sampled area, the standard EBLUP can no longer be used due to no information of area random effects. To obtain more proper estimation methods for non sampled area, the standard EBLUP model has to be modified by adding cluster information. The aim of this research was to study clustering methods using factor analysis by means of simulation, provide better cluster information. The criteria used to evaluate the goodness of fit of the methods in the simulation study were the mean percentage of clustering accuracy. The results of the simulation study showed the use of factor analysis in clustering has increased the average percentage of accuracy particularly when using Ward method. The method was taken into account to estimate the per capita expenditures based on Small Area Estimation (SAE) techniques. The method was eventually used to estimate the per capita expenditures from SUSENAS and the quality of the estimates was measured by RMSE. This research has shown that the standard-modified EBLUP model provided with factor analysis better estimates when compared with standard EBLUP model and the standard-modified EBLUP without the factor analysis. Moreover, it was also shown that the clustering information is important in estimating non sampled area. [ABSTRACT FROM AUTHOR]

Labor force surveys conducted over time by the rotating panel design have been carried out in many countries, including Indonesia. Labor force survey in Indonesia is regularly conducted by Statistics Indonesia (Badan Pusat Statistik- BPS) and has been known as the National Labor Force Survey (Sakernas). The main purpose of Sakernas is to obtain information about unemployment rates and its changes over time. Sakernas is a quarterly survey. The quarterly survey is designed only for estimating the parameters at the provincial level. The quarterly unemployment rate published by BPS (official statistics) is calculated based on only cross-sectional methods, despite the fact that the data is collected under rotating panel design. The study purpose to estimate a quarterly unemployment rate at the district level used small area estimation (SAE) model by combining time series and cross-sectional data. The study focused on the application and comparison between the Rao-Yu model and dynamic model in context estimating the unemployment rate based on a rotating panel survey. The goodness of fit of both models was almost similar. Both models produced an almost similar estimation and better than direct estimation, but the dynamic model was more capable than the Rao-Yu model to capture a heterogeneity across area, although it was reduced over time. [ABSTRACT FROM AUTHOR]

The objective of this research is to build a nested generalized linear mixed model using an ordinal response variable with some covariates. There are three main jobs in this paper, i.e. parameters estimation procedure, simulation, and implementation of the model for the real data. At the part of parameters estimation procedure, concepts of threshold, nested random effect, and computational algorithm are described. The simulations data are built for 3 conditions to know the effect of different parameter values of random effect distributions. The last job is the implementation of the model for the data about poverty in 9 districts of Java Island. The districts are Kuningan, Karawang, and Majalengka chose randomly in West Java; Temanggung, Boyolali, and Cilacap from Central Java; and Blitar, Ngawi, and Jember from East Java. The covariates in this model are province, number of bad nutrition cases, number of farmer families, and number of health personnel. In this modeling, all covariates are grouped as ordinal scale. Unit observation in this research is sub-district (kecamatan) nested in district, and districts (kabupaten) are nested in province. For the result of simulation, ARB (Absolute Relative Bias) and RRMSE (Relative Root of mean square errors) scale is used. They show that prov parameters have the highest bias, but more stable RRMSE in all conditions. The simulation design needs to be improved by adding other condition, such as higher correlation between covariates. Furthermore, as the result of the model implementation for the data, only number of farmer family and number of medical personnel have significant contributions to the level of poverty in Central Java and East Java province, and only district 2 (Karawang) of province 1 (West Java) has different random effect from the others. The source of the data is PODES (Potensi Desa) 2008 from BPS (Badan Pusat Statistik). [ABSTRACT FROM AUTHOR]