FORUM STATISTIKA DAN KOMPUTASI : Indonesian Journal of Statistics Forum Statistika dan Komputasi (ISSN:0853-8115) was published scientific papers in the area of statistical science and the applications. It is issued twice a year. The papers should be research papers with, but not limited to, the following topics: experimental design and analysis, survey methods and analysis, operation research, data mining, statistical modeling, computational statistics, time series and econometrics, and statistics education. Started from October 2017 edition the name of Forum Statistika dan Komputasi was changed to Indonesian Journal of Statistics and Its Applications and the website was moved to the new website (http://journal.stats.id). Therefore, Authors who will submit new manuscripts should register on the new website. Meanwhile, the previous editions (up to 2017 edition) will still use Forum Statistika dan Komputasi as the title and could be accessed on the old website (http://journal.ipb.ac.id/index.php/statistika).
MODEL AVERAGING, AN ALTERNATIVE APPROACH TO MODEL SELECTION IN HIGH DIMENSIONAL DATA ESTIMATION
Model averaging is an alternative approach to classical model selection in model estimation. The model selection such as forward or stepwise regression, use certain criteria in choosing one best model fitted the data such as AIC and BIC. On the other hand, model averaging estimates one model whose parameters determined by weighted averaging the parameter of each approximation models. Instead of conducting inference and prediction only based one best chosen model, model averaging covering model uncertainty problem by including all possible model in determining prediction model. Some of its developments and applications also challenges will be described in this paper. Frequentist model averaging will be preferential described. Keywords : model selection, frequentist model averaging, high dimensional data
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SMALL AREA ESTIMATION FOR ESTIMATING THE NUMBER OF INFANT MORTALITY USING MIXED EFFECTS ZERO INFLATED POISSON MODEL
Demographic and Health Survey Indonesia (DHSI) is a national designed survey to provide information regarding birth rate, mortality rate, family planning and health. DHSI was conducted by BPS in cooperation with National Population and Family Planning Institution (BKKBN), Indonesia Ministry of Health (KEMENKES) and USAID. Based on the publication of DHSI 2012, the infant mortality rate for a period of five years before survey conducted is 32 for 1000 birth lives. In this paper, Small Area Estimation (SAE) is used to estimate the number of infant mortality in districts of West Java. SAE is a special model of Generalized Linear Mixed Models (GLMM). In this case, the incidence of infant mortality is a Poisson distribution which has equdispersion assumption. The methods to handle overdispersion are binomial negative and quasi-likelihood model. Based on the analysis results, quasi-likelihood model is the best model to overcome overdispersion problem. However, after checking the residual assumptions, still resulted that residuals of model formed two normal distributions. So as to resolve the issue used Mixed Effect Zero Inflated Poisson (ZIP) Model. The basic model of the small area estimation used basic area level model. Mean square error (MSE) which based on bootstrap method is used to measure the accuracy of small area estimates. Keywords : SAE, GLMM, Mixed Effect ZIP Model, Bootstrap
LAD-LASSO: SIMULATION STUDY OF ROBUST REGRESSION IN HIGH DIMENSIONAL DATA
The common issues in regression, there are a lot of cases in the condition number of predictor variables more than number of observations ( ) called high dimensional data. The classical problem always lies in this case, that is multicolinearity. It would be worse when the datasets subject to heavy-tailed errors or outliers that may appear in the responses and/or the predictors. As this reason, Wang et al in 2007 developed combined methods from Least Absolute Deviation (LAD) regression that is useful for robust regression, and also LASSO that is popular choice for shrinkage estimation and variable selection, becoming LAD-LASSO. Extensive simulation studies demonstrate satisfactory using LAD-LASSO in high dimensional datasets that lies outliers better than using LASSO. Keywords: high dimensional data, LAD-LASSO, robust regression
RIDGE AND LASSO PERFORMANCE IN SPATIAL DATA WITH HETEROGENEITY AND MULTICOLLINEARITY
Spatial heterogeneity becomes a separate issue on the analysis of spatial data. GWR (Geographically Weighted Regression) is a statistical technique to explore spatial nonstationarity by form the differrent regression models at different point in observation space. Multicollinearity is a condition that the independent variables in model have linear relationship. It would be a problem for estimation parameters process, because that condition produces unstable model. This problem may be found in GWR models, which allow the linear relationship between independent variables at each location called local multicollinearity. GWRR (Geographically Weighted Ridge Regression) and GWL (Geographically Weighted Lasso) which use the concept of ridge and lasso is shrink the regression coefficient in GWR model. GWRR and GWL techniques are consider to be capable of overcoming local multicollinearity to produce more stable models with lower variance. In this study, GWRR and GWL is used to model Gross Regional Domestic Product (GRDP) in Java using kernel exponential weighted function. The results showed that GWL has better performance to predict GRDP with lower RMSE and higher value than GWRR. Keyword : Spatial Heterogeneity, GWR, Local Multicollinearity, Ridge, Lasso
SURVIVAL ANALYSIS WITH EXTENDED COX MODEL ABOUT DURABILITY DEBTOR EFFORTS ON CREDIT RISK
The application of survival analysis on the data of credit motorcycle financing experiencing bad loans after the credit starts early, with sixteen covariates were considered. The model used in survival analysis is the Cox proportional hazard models. Cox models have the assumption that the proportional hazard assumption. Extended Cox models selected to improve cox proportional hazard models when one or more covariates did not meet the assumption of proportional hazards. Extended cox models is an extension of cox models that involve time-dependent variables. Covariates that do not meet the proportional hazards assumption in the Cox models diinteraksikan extended with functions appropriate time, in order to obtain time-dependent covariates. So on the model covariates that are not dependent on time and time dependent covariates. The parameters of these covariates estimated using partial maximum likelihood method. To determine whether the extended Cox model is a suitable model for the data in a particular case, likelihood ratio test was used. The results indicate that extended Cox models with functions time appropriate, provide the best model. Keywords : Credit Risk, Survival Analysis, Cox Proportional Hazard , Extended Cox Model
A SIMULATION STUDY OF LOGARITHMIC TRANSFORMATION MODEL IN SPATIAL E MPIRICAL BEST LINEAR UNBIASED PREDICTION (SEBLUP) METHOD OF SMALL AREA ESTIMATION
There have been many studies developed to improve the quality of estimates in small area estimation (SAE). The standard method known as EBLUP (Empirical Unbiased Best Linear Predictor) has been developed by incorporating spatial effects into the model. This modification of the method was known SEBLUP (Spatial EBLUP) since it incorporates the spatial correlations which exist among the small areas. The data obtained (variables of concern) usually have a large variance and tend to have a a nonsymmetric distribution and therefore tend to have nonlinear relationship pattern between concomitant variables and variables of concern. the results showed that the method SEBLUP using logarithmic transformation produces estimator more than the other methods. Keywords : EBLUP, SAE, SEBLUP
NONLINEAR PRINCIPAL COMPONENT ANALYSIS AND PRINCIPAL COMPONENT ANALYSIS WITH SUCCESSIVE INTERVAL IN K-MEANS CLUSTER ANALYSIS
K-Means Cluster is a cluster analysis for continuous variables with the concept of distance used is a euclidean distance where that distance is used as observation variables which are uncorrelated with each other. The case with the type data that is correlated categorical can be solved either by Nonlinear Principal Component Analysis or by making categorical data into numerical data by the method called successive interval and then used Principal Component Analysis. By comparing the ratio of the variance within cluster and between cluster in poverty data of East Nusa Tenggara Province in K-Means cluster obtained that Principal Component Analysis with Successive interval has a smaller variance ratio than Nonlinear Principal Component Analysis. Variables that take effect to the clusterformation are toilet, fuel,and job. Keywords: K-Means Cluster Analysis, Nonlinear Principal Component Analysis, Principal Component Analysis, Successive interval.
ALTERNATIVE SEMIPARAMETRIC ESTIMATION FOR NON-NORMALITY IN CENSORED REGRESSION MODEL WITH LARGE NUMBER OF ZERO OBSERVATION
A large number of zero observation on the response variable in the socio-economic field are often found in household demand models. This will imply on the method to estimate parameters in the model used. Ordinary least square estimators of linear models to be biased and inconsistent. One model to overcome is using censored regression model is also know as tobit model. However, non-normality in the Tobit Estimators being inconsistent. Another alternative estimators is censor least absolute deviations (CLAD). CLAD estimator is consistent and asymptotically normal for a wide class of distribution. This study was to focus on the application of Tobit and Censored Least Absolute Deviations (CLAD) estimators for LPG demand. The data used is the LPG expenditure in rural areas in the provinces of West Java that the number zero observations is 39 percent of the sample. The result shows that CLAD and Tobit estimators are consistent estimators. But along with increasing the number of samples, the CLAD estimators performance is getting better than Tobit estimators. Keywords : Zero observation, CLAD, Tobit, Consistent estimator, LPG demand
MODELLING OF FORECASTING MONTHLY INFLATION BY USING VARIMA AND GSTARIMA MODELS
The model parameters could be different form the well to the factors of time and location. A general model of GSTAR can be used to establish model the inflation in some locations by using GSTARIMA model if time series data is self-contained autoregressive, differentiation, and moving averages. This study examines whether the effect of such locations on the GSTARIMA model is better than the VARIMA model that regardless of the location influences. The aim of this study is to establish two models of inflation six provincial capitals in Java using VARIMA model and GSTARIMA model with inverse distance weighting. Dummy variables have been used to overcome normality and white noise problems. The best forecasting of monthly inflation in provincial captitals in Java Island is GSTAR(1;1) with inverse distance weighting. It has smallest RMSE value of 0.9199. Key words : GSTARIMA, Inverse Distance, RMSE, VARIMA
CLUSTERING PROVINCE IN INDONESIA BY COMMUNICATION TECHNOLOGY RELATED VARIABLES
Technological developments in Indonesia growth rapidly. Almost all systems used in daily life have been using the technology. One of its technology is communication technology. It because communication technology is a important tool for send information. All was done in order to communicate easier and faster. It is therefore important to research the condition of the existing communication technology in Indonesia. Communications technology also one of the focus of the government in national development. But not easy to know the state of communication technology in Indonesia because Indonesia has a large region and different geographically. The purpose of this research was to determine the grouping of provinces in Indonesia to increase the communication sector in order to support national development. The method used in this research is cluster hierarchical analysis method and criterion of determining the best method and many cluster optimal use Cubic Clustering Criterion (CCC). The data used is secondary data from the Statisctics Indonesia (BPS) and the Ministry of Communication and Information. The results showed that the number of cluster based on related communication technology variables are 3 cluster which 1st cluster members consist of 21 provinces, 2nd cluster members consist of 7 provinces and 3rd cluster members consist of 3 provinces. Key words : Communications Technology, Cluster Analysis, Hierarchical Method, Cubic Clustering Criterion (CCC)
SMALL AREA ESTIMATION OF LITERACY RATES ON SUB-DISTRICT LEVEL IN DISTRICT OF DONGGALA WITH HIERARCHICAL BAYES METHOD
Literacy Rate (LR) is defined as percentage of population aged over 15 with ability to read and write. LR, as one of people welfare indicators, is a measurement of educational development. The indicator, as a measurement of government performance on education, can be measured if all variables related is available. Statistics Indonesia (BPS) each year calculated LR based on National Socio-Economic Survey (SUSENAS) with estimation available only on provincial level and district level. Along with establishment of autonomous regional policy, where regional government had greater power to manage its own region, availability of LR on lower levels to monitor educational development is necessary. Due to sampling design of SUSENAS, accommodated only estimation on district level, will give high variance if used to estimate on lower sub-district level, although still unbiased. Modelling LR was done with Logit-Normal approach, because LR data followed Binomial Distribution. Good estimators from inadequate sample size can be obtained with method of Small Area Estimation (SAE). Hierarchical Bayes (HB) method is one of SAE methods which are proven to give good estimate on binomial distributed data as LR. Estimation on sub-district level in District of Donggala with HB method gave better result compared to the direct estimation with lower Mean Square Error (MSE). Key words : Small Area Estimation, Literacy Rate, Hierarchical Bayes, Logit-Normal Model
COMPARISON OF LOW BIRTH WEIGHT RATE ESTIMATES BASED ON DIFFERENT AGGREGATE LEVELS DATA USING LOGISTIC REGRESSION MODEL
Low Birth-Weight (LBW) is defined as a birth weight of a live-born infant of less than 2.500 grams regardless of gestational age. Case of LBW is associated with infant mortality, infant morbidity, inhibited growth and slow cognitive development, also chronic diseases in later life. It is vital because with high LBW rate the generation hardly grow into its full potential. There are many risk factors, whether direct or indirect, can cause a birth as a high risk of Low Birth Weight case. These factors are genetics, obstetrics, nutrition intakes, diseases, toxic exposures, pregnancy care and social factors. With these factors measured, statistical modelling can be used to estimate rate on group level or probability on individual level of the Low Birth Weight event. As the case is a binary response, Logistic Regression Model is commonly used. Data of LBW case and the risk factors came from Indonesian Demographic and Health Survey (IDHS) 2012. Published national rate of LBW was 7.3% with provincial rates fell between 4.7-15.7 %. Although the national rate was considered low, the wide variation of provincial rates showed that the problem was not handled so well. However, these rates cannot be measured yearly due to 5 year period of the survey. With the availability of risk factors data a model can be built to estimate the LBW rates. But, another problem for the model is the case when aggregate level data is available instead of individual level data. So, the purpose of this study was to compare models based on different aggregate levels and theirs estimated provincial rates. Comparison was done among individual birth level, mother level, household level and census block (cluster) level. Models from three former levels were quite similar with adequate significant parameters, while cluster level model was resulted only a few significant parameters. But instead, LBW rate estimates from cluster level model were the closest to the direct estimates. But the variance of these estimates was still higher than the other models. Key words : Low Birth-Weight, IDHS, Logistic Regression, GLM, Aggregate Data
ADVECTION-DIFFUSION MODEL WITH TIME DEPENDENT FOR AIR POLLUTANTS DISTRIBUTION IN UNSTABLE ATMOSPHERIC CONDITION
Air pollution levels are quite high in urban areas. They are emitted from various sources and have an impact on humans and the environment. There are some physical processes that occur when pollutants disperse in the atmosphere. The main processes are advection and diffusion. Therefore, a two-dimensional mathematical model is presented to study the dispersion of air pollution under the effect of mesoscale wind as an effect of urban heat islands. This model is solved by using the implicit Crank-Nicolson finite difference scheme under stability-dependent meteorological parameters involved in large scale wind, mesoscale wind and eddy diffusivity. The main goal of this research is to analyze air pollution distribution using the advection-diffusion model. The results of this model have been analyzed for the dispersion of air pollutants in an urban area in the downwind and vertical direction for unstable atmospheric conditions. Key words : Advection, Diffusion, Mesoscale Wind, Pollutant Dispersion
EBLUP METHOD OF TIME SERIES AND CROSS-SECTION DATA FOR ESTIMATING EDUCATION INDEX IN DISTRICT PURWAKARTA
Since decentralisation was implemented in Indonesia, more detailed information about the condition of an area becomes very necessary to know as an evaluation of development that the government has done. the success development of a region can be seen through the Human Development Index (HDI). HDI consists of three basic dimensions, knowledge as one of that three basic measured by the index of education. This index is measured by the Adult Literacy Rate and Mean Years of Schooling. Education is one of the important factors in improving human development. The enhancement of education index results in increasing the HDI of an area. Purwakarta has a vision that is made as a district that excels in education in West Java, but until now Purwakarta’s education index is still below the West Java province. One step that can be done is to seek information on the education index each district in Purwakarta, with the aim to provide the right policy in each region. Direct estimation of the components forming the HDI for districts is not feasible because these estimates will generate a great value of variance, This is due to the size of the sample used is too small. This study proposes a statistical method by performing the estimation using small area estimation. These estimates using information from surrounding areas that can improve the effectiveness of the sample size and the lower the standard error. Some surveys are conducted regularly every year, in conducting indirect estimation in the survey such as this, efficiency of estimating education index for district level can be improved by including the random effect of the area as well as the random effect of time (Sadik and Notodipuro, 2006). So in this study will be used Empirical Best Linear Unbiased Prediction (EBLUP) by combining the time series and cross-section data for estimating the education index at the level of districts in Purwakarta. The direct estimation of education index produce a larger variance than our methode, it shown by comparing mean square error (MSE) of direct method and indirect method, direct method have the largest MSE. Key words : Indirect Estimation, Small Area Estimator, EBLUP, Time Series and Cross-Section, HDI, Education Index.
GEOGRAPHICALLY WEIGHTED REGRESSION (GWR) INCLUDED THE DATA CONTAINING MULTICOLLINEARITY
One of the reasons of spatial effect of each location is spatial variety. Beside of spatial variety, number of independent variable (X) causes local multicolinearity, that is one or more independent variable, which collaborated with other variable in each location of observation. The methods can be used to solve spatial diversity problem and local multicollinearity in Geographically Weighted Regression (GWR) model that is GWPCA. This research aim to examine GWPCAR feasibility model for PDRB data in 2010 at 113 districts/cities in Java. analysis indicate that GWPCA method can overcome local multicollinearity problem, it can be seen from the characteristic value of VIF which is smaller than 10. Key words : Local Multicollinearity, Geographically Weighted Principal Components Analysis.
MODELING OF DENGUE HEMORRHAGIC FEVER IN BOGOR USING BAYESIAN SUR-SAR
The purposes of this research are (1) To develop Seemingly Unrelated Regression (SUR) system constructed by correlated Spatial Autoregressive Model (SAR) with Bayesian approach for dynamic analysis of spatial and non-spatial contributions of Dengue Hemorrhagic Fever (DHF) case in Bogor, (2) To evaluate efficiency issues on parameters estimation with SUR system. Markov Chain Monte Carlo (MCMC) sampling scheme was used to estimate all of model parameters with the number of iteration whose burn-in period was discovered. The results indicated that : there was the similar pattern of DHF spread in Bogor during 2009 – 2011, the nearby areas had a significant role to the incidence of DHF in an area in the city of Bogor, and the non-spatial contributions of DHF cases in Bogor during 2009 -2011 included in this model were dynamic. Gain efficiency of parameters estimation on modeling of DHF in Bogor with SAR for each year during 2009-2011 can be obtained if we construct all of SAR with SUR system model.
TEMPERATURE CHANGES IN CLOUD FOREST OF KHAO NAN NATIONAL PARK, SOUTHERN THAILAND DURING 2000 - 2015
Khao-Nan National Park(KNNP) is a part of the Nakhon Si Thammarat mountain range, which is the one of the cloud forest southern Thailand. The characteristic of cloud forest is a plenty of flora especially epiphyte and the presence of clouds even in the dry season. The aim of this study was to investigate temperature pattern and variation at Khao Nan. We downloaded data, for land surface temperatures recorded by MODIS EARTH Satellites every eight days from 2000-2015 in square kilometers grid boxes covering Khao-Nan National Park, to investigate time series of temperature variation. The cubic spline modeling was used for fitting a pattern of LST among day time from satellite image at Khao-Nan National Park. Otherwise, we used GEE for parameter estimate. The result was shown the temperature has similar pattern and variation around Khao-Nan National Park during 2000-2015. Eventually, the conclusion is the temperature have changed during 2000-2005, 2006-2009 and 2010-2015 by using GEE. Key words : Temperature changes, cloud forest, Khao Nan National Park
RANDOM PARAMETER MODELS OF FERTILIZER RESPONSE FOR CORN USING SKEWED DISTRIBUTIONS
Random parameter models have been found to better determine the optimum dose of fertilizer than fixed parameter. However, a major restriction of it is the normality assumption.. The purpose of this study the introduction of random parameter models of fertilizer response using skewed distributions from a Bayesian perspective. The method is applied to data sets of multilocation trials of potassium fertilization on corn. We compare the Linear Plateau, Spillman-Mitscherlich, and Quadratic random parameter models with different random errors distribution assumption, i.e. as normal, skew-normal, Student-t and Skew-t distribution using the Deviance Information Criterion (DIC). The results show that the smallest DIC value is obtained for the normal linear plateau model compare with the other models. The correlation between observed and fitted values was significant. Key words : fertilizer response model, mixed effects, skewed distributions, DIC.
ESTIMATION OF UNEMPLOYMENT RATE USING SMALL AREA ESTIMATION MODEL BASED ON A ROTATING PANEL NATIONAL LABOR FORCE SURVEY
In Indonesia, labor force participation data are collected by Sakernas (National Labor Force Survey). Sakernas is conducted based on a quarterly rotating panel survey. Because of the groups differ according to their time-in-panel and observation strategy, it is possible to the presence of a bias. Besides, there are insufficiency problem of sample size to obtain an adequate precision of direct estimation at the district level. It is necessary to study how to estimate parameter based on a rotating panel survey when sample size is insufficient. Currently, a small area estimation (SAE) model that accomodates the bias component due to the rotation still only assume the effect over time which follows a random walk process, so it is necessary to develop a model that is more general. We propose a SAE model for rotation group level, its combined idea of the time-series multi-level model and the Rao-Yu model. The model will applied to Sakernas data to estimate a quarterly unemployment rate at the district level. Key words : Sakernas, rotating panel survey, time-series multi-level model and Rao-Yu model
AUTOREGRESSIVE MOVING AVERAGE (ARMA) MODEL FOR DETECTING SPATIAL DEPENDENCE IN INDONESIAN INFANT MORTALITY DATA
Infant mortality is an important indicator that must to be monitored seriously. The infant mortality is associated with several determinants, such as the infant’s characteristics, maternal and fertility factors, housing condition, geographical area, and policy. It can also be influenced by the presence of spatial dependence between regency in Indonesia. This is due to the social and economic activity in one regency depend on social and economic activity in other regency, especially with neighboring area. Infant mortality data obtained from Indonesian Demographic and Health Survey (IDHS) published by Statistic Indonesia (BPS). In BPS’s publication, data is always sorted by regency code from the smallest to the largest. Therefore, the closeness of the regency code refers to the closeness of the regency itself. the infant mortality data by regency could be analogized as time series data. So that, the relationship between regency can be seen using Autoregressive Moving Average (ARMA) model. If the parameter at ARMA is significant, we can conclude that there is a spatial dependence on the infant mortality in Indonesia. This paper will focus on discussing whether there is a spatial dependenc in Indonesia’s Infant Mortality Data using ARMA approach. The result is the Autocorrelation Function (ACF) showed a significant effect until lag 3, and Partial Autocorrelation Function (PACF) showed a significant effect until lag 1. Based on Bayesian Information Criterion (BIC), the AR(1) fitted the model well. It shows that the probability of infant mortality in one regency is affected by probability of infant mortality in neighboring regency. Key words : ARMA, spatial dependence, infant mortality, IDHS
PENGGUNAAN JARINGAN SYARAF TIRUAN UNTUK PENDUGAAN MODEL LINEAR TERAMPAT DENGAN KOEFISIEN KERAGAMAN KONSTAN
Secara umum model linear terampat (GLIM) dapat dipetakan secara ekivalen pada Jaringan Syaraf Tiruan (JST) dengan satu lapisan atau disebut juga dengan perceptron. Fungsi aktifasi pada JST sama dengan invers dari fungsi hubung. Pada GLIM dengan komponen acak mempunyai sebaran gamma ekivalen dengan JST tanpa lapisan tersembunyi dengan fungsi galat adalah gamma dan fungsi tujuan adalah fungsi kemungkinan maksimum atau devians. Sedangkan fungsi aktifasi untuk model gamma adalah identitas, resiprokal, atau eksponensial. Makalah ini mengkaji pendugaan model pada data yang mempunyai sebaran gamma dengan metode JST dan seberapa besar perbedaan hasil pendugaannya dibandingkan dengan GLIM. Hasil kajian menunjukkan bahwa JST menghasilkan nilai dugaan yang sama dengan GLIM. Kata kunci : jaringan syaraf tiruan, koefisien keragaman konstan, model gamma
KLASIFIKASI RANCANGAN FAKTORIAL PECAHAN JENUH TIGA TARAF DALAM 27 RUN
Tulisan ini memberikan klasifikasi terhadap gugus rancangan jenuh tiga faktor OA(27, 313) yang berguna dalam penentuan rancangan terbaik untuk diterapkan. Kriteria A3 dan A­4 tidak dapat digunakan karena memiliki nilai yang sama untuk seluruh array. Dengan mengasumsikan hanya ada tiga faktor yang aktif, kriteria projection aberration menggunakan vektor A3(3) mengkelaskan 68 OA yang non-isomorphic ke dalam 54 kelas. Dua array terbaik menurut kriteria ini ditampilkan sebagai rujukan untuk digunakan. Kata kunci: rancangan jenuh, orthogonal array, klasifikasi, projection aberration
PERBAIKAN METODE KRIGING BIASA (ORDINARY KRIGING) MELALUI PEMECAHAN MATRIKS C MENJADI BEBERAPA ANAK MATRIKS NON OVERLAP UNTUK MEWAKILI DRIFT PADA PEUBAH SPASIAL
Persoalan dalam pendugaan spasial dengan menggunakan konsep drift sering kali menemui kendala bila kondisi permukaan yang diduga bersifat anisotropik. Pada kondisi anisotropik kuranglah tepat apabila hanya menggunakan satu model korelogram (variogram). Dalam tulisan ini dicoba area yang diteliti dibagi menjadi beberapa partisi (4 partisi) sehingga disusun empat model variogram untuk keseluruhan area. Dari empat partisi tersebut dicari nilai-nilai total pembobot yang layak agar fungsi penduga menjadi tak bias. Selanjutnya dilakukan perbandingan pendugaan nilai pada titik-titik yang tidak dilakukan pengukuran antara tanpa partisi dengan partisi. Hasil pendugaan menunjukkan bahwa nilai dugaan sama dengan nilai sebenarnya baik yang tak dipartisi maupun yang dipartisi. Akan tetapi, nilai pendugaan yang dihasilkan dari area yang dipartisi lebih baik dibandingkan tanpa partisi.
ANALISIS KONJOIN: METODE FULL PROFILE DAN CBC UNTUK MENELAAH PERSEPSI MAHASISWA TERHADAP PILIHAN PEKERJAAN
Tulisan ini membahas perbandingan analisis konjoin metode full profile dan metode CBC. Metode full profile merupakan metode yang klasik dan cukup mudah diterapkan terutama dalam pembuatan disain pengumpulan dan analisis data, tetapi cukup merepotkan dalam tahap pengumpulan data. Sedangkan Metode CBC, walaupun agak sulit dalam disain pengumpulan dan analisis datanya tetapi pada saat pengumpulan datanya relatif lebih mudah dan dipandang lebih alamiah. Penerapan kedua metode ini dalam menelaah faktor yang paling dipertimbangkan oleh mahasiswa dalam memilih pekerjaan memberikan hasil yang relatif sama. Faktor utama yang berpengaruh terhadap pilihan pekerjaan mahasiswa adalah besarnya gaji pertama dan kesesuaian bidang pekerjaan dengan latar belakang pendidikannya.
Penggerombolan adalah proses mengelompokkan objek ke dalam kelompok-kelompok yang memiliki kemiripan. Beberapa masalah yang sering dijumpai dalam analisis gerombol yaitu skala pengukuran peubah tidak sama dan jumlah objek besar serta jumlah gerombol tidak diketahui. Salah satu pendekatan untuk menangani masalah ini tanpa mentransformasi peubah-peubah tersebut adalah dengan menggunakan metode Two Step Cluster. Penelitian ini bertujuan sebagai penerapan metode Two Step Cluster dengan menggerombolkan desa/kelurahan yang berada di Jawa Barat. Hasil penggerombolan dengan metode TwoStep Cluster, gerombol awal yang dihasilkan pada tahap pertama adalah sebanyak delapan gerombol, sedangkan gerombol optimal yang dihasilkan pada tahap dua adalah sebanyak tiga gerombol. Gerombol satu tidak dapat dikatakan sebagai suatu gerombol, karena anggota-anggota didalamnya merupakan objek-objek yang memencil ekstrim dan tidak dapat dimasukkan ke dalam gerombol lainnya. Desa/kelurahan yang termasuk gerombol dua memiliki karakteristik pedesaan. Desa/kelurahan tersebut memiliki lahan terluas, jumlah rumah tangga pertanian terbanyak, namun belum berkembang dalam bidang industri serta komunikasi dan informasi. Sehingga untuk meningkatkan potensi desa pada gerombol ini, yang harus diperhatikan adalah peubah-peubah yang tingkat perkembangannya masih rendah. Gerombol tiga memiliki karakteristik desa yang berstatus perkotaan. Desa/kelurahan pada gerombol ini memiliki jarak terdekat ke pusat kota, cukup maju dalam bidang industri, komunikasi dan informasi, namun memiliki angka pengangguran tertinggi.
KLASIFIKASI GENOTIPE PADA DATA TIDAK LENGKAP DENGAN PENDEKATAN MODEL AMMI
Percobaan multilokasi mempunyai peranan penting dalam perkembangbiakan tanaman dan penelitian agronomi. Kajian mengenai interaksi antara genotipe dan lingkungan diperlukan dalam penyeleksian genotipe yang akan dilepas. Metode statistika yang biasa digunakan untuk mengolah data hasil percobaan multilokasi salah satunya adalah AMMI (Additive Main effect and Multiplicative Interaction). Metode ini menggabungkan analisis ragam aditif bagi pengaruh utama perlakuan dengan analisis komponen utama pada pengaruh interaksinya. Pendekatan AMMI juga sangat baik digunakan untuk uji multilokasi tanpa ulangan. AMMI adalah analisis yang membutuhkan data yang lengkap. Jika ada data yang hilang, maka harus dilakukan pendugaan terhadap data tersebut. Pada kasus data tidak lengkap, diperlukan suatu metode pendugaan data untuk mempermudah analisis. Metode yang dapat digunakan antara lain connected data dan algoritma EM-AMMI untuk menduga data yang tak lengkap.
Tulisan ini mendeskripsikan status kesuburan tanah menggunakan biplot. Data yang digunakan merupakan lokasi rencana pencetakan sawah baru di daerah Merowi, Kalimantan Barat. Data terdiri dari 17 seri tanah dan 14 sifat-sifat tanah. Hasil telaah menunjukkan bahwa daerah tersebut dapat dikelompokkan dalam empat kelompok dengan status kesuburan relatif sama yaitu kelompok pertama terdiri dari seri Seringkong, Sekayam, Pemodis, dan Merowi dengan ciri utama pH dan basa-basa dapat ditukar relatif tinggi; kelompok kedua terdiri dari Kualadua, Sebungkuh dan Robokan dengan ciri utama kadar kalium dan bahan organik relatif tinggi; kelompok ketiga terdiri dari Semayang, Ketanan, Tanjungpinang, dan Senajam dengan ciri utama pH dan basa-basa dapat ditukar relatif rendah; kelompok keempat terdiri dari Tanjungbunga, Seke, Tunggalbhakti, Tataikuju, Potua dan Kembayan dengan ciri utama kadar kalium dan bahan organik relatif rendah.
PENERAPAN RANTAI MARKOV PADA PENGEMBANGAN UJI KETERDUGAAN KUNCI (Markov Chain Technique in Key Predictability Test Development)
One Time Key (OTK) system with key from alphabetical sequences is one of symmetric encryption algorithm that used in Indonesia to protect secret information. Alphabetic sequences in OTK system must be cryptographically secure pseudorandom sequences. OTK system in Indonesia only tested by overlapping m-tuple test developed by Marsaglia (2005). Overlapping m-tuple test doesn’t check the unpredictability of alphabetical sequences, it just tests distribution form and indpendency of alphabetical sequences. So, an alphabetical sequence in OTK system cannot be used in cryptography application by the reason of unpredictability sequence is unknown. Because some of Pseudorandom Number Generator (PRNG) algorithm based on block cipher algorithm that has markovian properties, markov chain model used to detect predictability alphabetical sequences. Data in this study consists of two data sources i.e. simulation data that generated from four classes PRNG and OTK system keys in 2005 that used in three communication units of foreign ministry. Simulation data is used to develop key predictability test methodology by find predictability threshold value based on characteristic of match level. OTK system keys will be predictability tested by comparing characteristic of match level with threshold value that is obtained from simulation data. The first result of this study shows the alphabetical sequence generated by first, second and fourth PRNG class can't be modeled with first-order markov chain until third-order. The third PRNG class, except PRNG LCG1, LCG2, coveyou, rand and randu, also can't be modeled with first order markov chain until third-order. Sequence generated by LCG2, coveyou, rand and randu are not fit for use in cryptography because it has a high probability to be modeled by high orders of markov chain (above the order of three). The second result obtains predictability threshold value with markov chains based on the minimum and maximum match level on the second-order and third-order. The last result shows the size of training data must be greater than the size of the observation data with the best ratio between the size of training data with observational data is 100: 10. The results of testing using 10 times repeated shows that the match level average of the OTK system key match on the all of three-order less than 4.5 x 10-2, so the OTK system the is feasible to secure information in three communication units. Keywords: One Time Key (OTK), markov chain, PRNG, probability transition, match level
Copyright (c) 2016 FORUM STATISTIKA DAN KOMPUTASI
PENGARUH PEMILIHAN ARAH ACUAN 00 DAN ARAH ROTASI PADA ANALISIS KORELASI DAN REGRESI LINIER-SIRKULAR (STUDI KASUS: PETA KAWASAN RAWAN BENCANA LETUSAN GUNUNG
The measurement results doesn't only consist of data with linear attributes, but also data with circular attributes. The circular data has a uniqueness that is not owned by the linear data, circular data is independent of the choice of 0o reference and rotation direction. The uniqueness of circular data analysis is tested in linear circular correlation and linear circular regression. The results of correlation analysis proved that the selection of the reference direction 0o can be done subjectively because the linear circular correlation results show the same value 0.899 for all possible selection of 0o reference and rotation direction. For linear circular regression, the model constructed has a same coefficient of determination that is 0.808 and the same b0, which is 5.231 for all possible selection of 0o reference and rotation direction. Similarly, statistics from the error of linear circular regression analysis have the same value, minimum = -2.693, quartile 1 = -0.835, median = -0.171, quartile 3 = 0.548, maximum = 8.421. Alleged circular linear regression parameters, namely b1 and b2, forming a cycle that each has in common b1 = -1.226 E-07-2.728 cos (α) - 2.655 sin (α) and b2 = 3.061 E-07-2.655 cos (α ) + 2.728 sin (α) where α is the position of the 0o reference direction in degrees on each model. Keywords : Directional Statistics, Circular Statistics, Linear-Circular Regression, Linear Circular Correlation
JARINGAN SYARAF TIRUAN DAN ALGORITMA GENETIKA DALAM PEMODELAN KALIBRASI (STUDI KASUS : TANAMAN OBAT TEMULAWAK)
The problems in prediction of calibration model are multicolinearity and the number of variables is larger than the number of observations. Principal Component Analysis-Artificial Neural Network-Genetic Algorithm (PCA-ANN-GA) models were applied for the relationship between sample of concentration which is limited and transmittance data which is in large dimensions. A large number of variables were compressed into principal components (PC’s). From these PC’s, the ANN was employed for prediction of concentration. The principal components computed by PCA were applied as inputs to a backpropagation neural network with one hidden layer. The models was evaluated using GA for the best network structure on hidden layer. Root Mean Square Error (RMSE) for 80% training set and 20% testing set are 0.0314 and 0.5225, respectively. Distribution of data according to the percentage of training data and testing data were also very influential to obtain the best network structure with the smallest RMSE achievement. The best model for these methods is two layers Neural Network with eight neuron in the hidden layer.