Judul: Pengembangan kekekaran Model Additive Main Effect – Multiplicative Interaction (AMMI)
Abstrak: AMMI model for interactions in two-way table provide the major mean for studying stability and adaptability through GEI, which modeled by full interaction model. Eligibility of AMMI model depends on the assumption of normally independent distributed error with a constant variance. Nowadays, AMMI models have been developed for any condition of MET data i.e the violence of normality and homegeneity assumptions. We can mention in this class of modelling as MAMMI for Mixed AMMI model and GAMMI for Generalized AMMI model. GAMMI model handles non-normality i.e categorical response variables using an algorithm of alternating regression. While handling the non-homogeneity in mixed-models sense, one may use a model called factor analytic multiplicative for a MAMMI models. Outlier might be found in the data coincides with non-homogeneity variance. A method of handling outlier in additive and multiplicative modeling by applying Robust Alternating Regression (RAR) in FANOVA model. RAR FANOVA model was downweighting outlying scores and loadings in the k-dimensional spaces of scores and loadings, and robust estimator will be minimized under the constraints that are consistent with robust approach of the median of parameters. Application of GAMMI was found in several distribution of exponential family. The most interesting here is Poisson distribution which it has a unique property of equal mean and variance. Many zero observations make some dificulties and fatal consequence in Poisson modeling. We consider to facilitates an analysis of two-way tables of count with many zero observations in AMMI model. We develop GAMMI model for Poisson with zeroes problem, by a statistical framework of RCAM. Some link function apply to the mean of a cell equalling a row effect plus a column effect plus interaction terms are modelled as a reduced-rank regression with rank of 2, then it will be visualized by Biplot through SVD reparameterization. The ZIP-GAMMI model handle the excess-zero and also the overdispersion at once. The interaction structures are extracted from the non-zero cell. ZIP model provide us the probability become zero and the fitted value of the Poisson. The modelling scheme involves two important things: (1) the distribution (and link-function) and (2) the rank of model. Both are confounded, especially if there is overdispersion or excess-zero. Best-model fit can be provided by proper link function with respect to data’s distribution, at the same time it’s also possible by the rank of the model in decomposing the interaction terms. In this case the likelihood ratio test provides us the hypothesis testing.
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Judul: Model ammi terampat untuk data berdistribusi bukan normal
Abstrak: ALFIAN FUTUHUL HADI. Generalized AMMI for Non-Normal Data. Under supervision of AHMAD ANSORI MATTJIK and I MADE SUMERTAJAYA. AMMI (Additive Main Effect Multiplicative Interaction) model for interactions in two-way table provide the major mean for studying stability and adaptability through genotype × environment interaction (GEI), which modeled by full interaction model. Eligibility of AMMI models depends on that assumption of normally independent distributed error with a constant variance. In the study of genotypes’ resistance, disease and pest (insect) incidence on a plant for example, the appropriateness of AMMI model is being doubtful. Transform the observation by power family of Box-Cox transformation is an effort to handle the non-normality. AMMI model then can be applied to the transformed data appropriately following by the use of ordinary least square for estimating parameters. There is another way to handle this non-normality, i.e. by introducing multiplicative terms for interaction in wider class of modeling, Generalized Linear Models. An algorithm of iterative alternating generalized regression of row and column estimates its parameters. This model is known as GAMMI (Generalized Additive Main Effect Multiplicative Interaction) or GBMs (Generalized Bilinear Models). The multiplicative terms of GAMMI models can be visualized through Biplot, as in AMMI. A comparison of the two approaches above is investigated by applying them to a count data of pest population of Poisson distribution, which came from a study of leave pest in soybean genotype, and to study of rice genotype stability of filled grain per panicle (Binomial data). For data averages of filled grain per panicle, AMMI model for transformed data gives interaction matrix estimator slightly difference from of the one given by GAMMI logit-link model. R-square of Procrustes Rotation is less than 20 percent. On the other hand, for transformed data average of pest population, the two approaches do not give significant differences. Data exploration for the last case (the transformed data average of pest population) shows that its distribution character is very similar to Normal distribution. Therefore, it can be concluded that: (1) when the data distribution is close to Normal distribution, results of transformed AMMI and GAMMI are not significantly different; (2) when the data distribution is non Normal, results of the two approaches are quite different. Additional information on log-bilinear, which cannot be obtained from the transformed AMMI model, is odd ratio. This makes the GAMMI model superior compared to effort of transforming normality on Poisson distributed data.
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Judul: Perencanan Lanskap Sunda Kalapa, Jakarta Utara Sebagai Kawasan W isata Sejarah
Abstrak: Perkembangan kota Jakarta dari waktu ke waktu sangatlah cepat, sehingga menyebabkan kota-kota tua banyak yang tergusur untuk dijadikan daerah baru yang lebih modern. Apabila hal tersebut tidak ditanggulangi secara dini maka keberadaan Kota Lama Jakarta akan hilang. Hal inilah yang melatar belakang untuk dilakukan tindakan perlindungan dan revitalisasi kawasan bersejarah Sunda Kalapa.
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