Variable selection is an important topic in linear regression analysis. In practice, a large number of predictors usually are introduced at the initial stage of modeling to attenuate possible modeling biases. stepwise deletion and subset selection are usually used which can be computationally expensive and ignore stochastic errors in the variable selection process. In addition, the best subset selection of variables suffers from several disadvantages, the most severe of which is its a lack of stability. In this article, penalized likelihood approaches are proposed to handle these kinds of problems. The proposed methods select variables and estimate coefficients simultaneously. Some of penalty functions are used to produce sparse solutions. Based on the RMSE and Generalized Information Criterion (GIC) criteria, it was found that the factors affecting Indonesian mathematics scores, where LASSO produces 11 important variables for the model while SCAD has 6 variables which mean that the LASSO model is more complex than SCAD. The MCP produces a simpler model with 5 important variables but has excessive biassed. The results also showed that the SCAD penalty function had the best performance compared to LASSO, Ridge and MCP. Ridge penalty has a worst performance based on all criteria.

The Generalized linear mixed model (GLMM) is an extension of the generalized linear model by adding random effects to linear predictors to accommodate clustered or over dispersion. Severe computational problems in the GLMM modelling cause its use restricted for only a few predictors. When many predictors are available, the estimators become very unstable. Therefore, the procedure for selecting relevant variables is essential in modelling. The use of penalty techniques for selecting variables in mixed models is still rarely applied. In this article, the penalized Lasso approach proposed to handle these kinds of problems. The proposed methods select variables and estimate coefficients simultaneously in GLMM. Based on the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and standard error criteria, it was found that glmmLasso has a better performance than GLMM. For the factors affecting Indonesian’s student scores, where glmmLasso produces three significant covariates for the GLMM model while GLMM without penalized Lasso has five covariates, which means that the GLMM model is more complicated than glmmLasso. Gender, school quality based on National Examination (UN) scores and the opportunity for students to investigate to test their ideas are essential covariates as factors that influence the rating of Indonesian students.

Penelitian ini bertujuan guna menguji pengaruh model pembelajaran Problem Based Learning (PBL) berbantuan Google Classroom terhadap kemampuan pemecahan masalah matematis siswa. Penelitian ini menerapkan metode quasi-experiment dengan posttest-only control group design. Teknik pengambilan sampel menggunakan cluster random sampling dan simple random sampling. Instrumen penelitian yang diterapkan ialah tes kemampuan pemecahan masalah matematis pada materi perbandingan trigonometri yang telah diuji validitas dan reliabilitasnya. Berdasarkan hasil analisis data dengan uji-t didapatkan nilai thitung sebesar 5,074 dan ttabel sebesar 1,995 sehingga tolak H0 pada taraf signifikansi α = 0,05 dengan nilai Cohen’s effect size sebesar 1,213 yang termasuk dalam kategori besar dengan persentase 88%. Dapat disimpulkan bahwa terdapat pengaruh signifikan dari model pembelajaran PBL berbantuan Google Classroom terhadap kemampuan pemecahan masalah matematis siswa.

Penelitian ini membahas tentang penerapan model pembelajaran SAVI (Somatik, Auditori, Visual, Intelektual) terhadap kemampuan memecahkan masalah matematika ditinjau dari kemampuan awal matematika siswa kelas X SMK. Penelitian ini menggunakan metode kuasi eksperimen dengan Post-Test Only Non-equivalent Control Group Design . Pengambilan sampel dengan teknik cluster random sampling . Kelas eksperimen terdiri atas 36 siswa, yang mendapat pelatihan terdiri dari model pembelajaran SAVI dan kelas kontrol terdiri dari 32 siswa yang menggunakan model pembelajaran konvensional.Instrumen yang digunakan adalah tes kemampuan awal matematika dan tes kemampuan pemecahan masalah yang dikembangkan oleh peneliti dan memiliki tingkat validitas dan reliabilitas sangat tinggi. Berdasarkan hasil pengujian menggunakan uji ANAVA RAK diperoleh model pembelajaran SAVI dan konvensional yang dilakukan tidak memberikan dukungan dalam pengaduan Selain itu, berdasarkan tingkat kemampuan awal matematika terkait dengan kemampuan memecahkan masalah matematika siswa. Kemudian, dengan Uji Duncan (DMRT) memperoleh hasil model SAVI dengan kemampuan awal matematika yang lebih baik dari model konvensional dalam kemampuan memecahkan masalah matematika siswa.

Crime rate is the number of reported crimes divided by total population. Several factors could contribute the variability of crime rates among areas. This study aims to model the relationship between crime rates among regencies and cities in the East Java Province (Indonesia) and some potentially explanatory variables based on Statistics Indonesia publication in 2020. The crime rate in the East Java Province was consistently at the top three after DKI Jakarta and North Sumatra during 2017 to 2019. Therefore, it is interesting for us to study further about the crime rate in the East Java. Our preliminary analysis indicates that there is an overdispersion in our sample data. To overcome the overdispersion, we fit Generalized Poisson and Negative Binomial regression. The ratio of deviance and degree of freedom based on Negative Binomial is slightly smaller (1.38) than Generalized Poisson (1.99). The results indicate that Negative Binomial and Generalized Poisson regression, compared to standard Poisson regression, are relatively fit to model our crime rate data. Some factors which contribute significantly (α=0.05) for the crime rate in the East Java Province under Negative Binomial as well as Generalized Poisson regression are percentage of poor people, number of households, unemployment rate, and percentage of expenditure.