Robust estimation for ordinal regression.

Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot.Breakdown point; Diagnostic plot; Influence function; Ordinal regression; Weighted maximum likelihood; Robust distances;

Note sur les verbes météorologiques

Pourquoi les phénomènes météorologiques sont-ils souvent exprimés par des phrases qui n’ont pas la structure normale argument-prédicat (cf. il pleut)? La réponse est à chercher dans la manière dont ces phénomènes sont perçus et vécus dans l’expérience : il s’agit d’événements dans lesquels il est très artificiel de distinguer l’événement même d’un être ou objet auquel cet événement arrive. Une critique est faite des tentatives de réduire ces cas à des structures propositionnelles standards. Les phrases météorologiques qui semblent avoir une structure propositionnelle standard (le vent souffle, alld. der Wind weht, jap. ame ga furu) sont à leur manière aussi étranges que il pleut.Why is it that atmospheric phenomena are often expressed by sentences without a standard argument-predicate structure (cf. it's raining)? The answer to this is to be seeked in the way these phenomena are experienced: they are perceived as events in which it is highly artificial to distinguish the event proper from some being or object to which the event happens. Former attemps to reduce this case to standard propositional structures are criticized. It is shown that atmospheric sentences which seem to display a standard propositional structure (the wind is blowing, German der Wind weht, Japanese ame ga furu) are in their own way as strange as it's raining

Detection of influential observations on the error rate based on the generalized k-means clustering procedure

Cluster analysis may be performed when one wishes to group similar objects into a given number of clusters. Several algorithms are available in order to construct these clusters. In this talk, focus will be on the generalized k-means algorithm, while the data of interest are assumed to come from an underlying population consisting of a mixture of two groups. Among the outputs of this clustering technique, a classi cation rule is provided in order to classify the objects into one of the clusters. When classi cation is the main objective of the statistical analysis, performance is often measured by means of an error rate ER(F; Fm) where F is the distribution of the training sample used to set up the classi cation rule and Fm (model distribution) is the distribution under which the quality of the rule is assessed (via a test sample). Under contamination, one has to replace the distribution F of the training sample by a contaminated one, F(eps) say (where eps corresponds to the fraction of contamination). In that case, the error rate will be corrupted since it relies on a contaminated rule, while the test sample may still be considered as being distributed according to the model distribution. To measure the robustness of classification based on this clustering proce- dure, influence functions of the error rate may be computed. The idea has already been exploited by Croux et al. (2008) and Croux et al. (2008) in the context of linear and logistic discrimination. In this setup, the contaminated distribution takes the form F(eps)= (1-eps)*Fm + eps*Dx, where Dx is the Dirac distribution putting all its mass at x: After studying the influence function of the error rate of the generalized k- means procedure, which depends on the influence functions of the generalized k-means centers derived by Garcia-Escudero and Gordaliza (1999), a diagnostic tool based on its value will be presented. The aim is to detect observations in the training sample which can be influential for the error rate

PENGARUH METODE MORAL REASONING TERHADAP PENANAMAN KARAKTER NASIONALISME SISWA SD DALAM PEMBELAJARAN TEMATIK

Penelitian ini bertujuan untuk mengetahui pengaruh metode moral reasoning terhadap penanaman karakter nasionalisme siswa SD dalam pembelajaran tematik. Jenis penelitian ini adalah quasi experiment dengan desain nonequivalent control group design. Subjek penelitian ini adalah siswa kelas V di SD N Ngebel Kasihan. SD N Ngebel memiliki dua kelas, kelas V A sebagai kelompok kontrol menggunakan metode storytelling dan kelas V B sebagai kelompok eksperimen menggunakan metode moral reasoning. Teknik pengumpulan data yang digunakan adalah observasi dan wawancara. Analisis data yang digunakan adalah uji-t dengan taraf signifikansi 0,05. Hasil penelitian menunjukkan bahwa ada perbedaaan yang signifikan antara penanaman karakter nasionalisme dengan metode moral reasoning dan metode storytelling. Perbedaaan tersebut terlihat di semua subkarakter nasionalisme yang mencakup nilai Ketuhanan Yang Maha Esa dengan hasil uji t 0,155, nilai Kemanusiaan yang Adil dan Beradab dengan hasil uji t 0,129, nilai Persatuan Indonesia dengan hasil uji t 0,405, nilai Kerakyatan yang Dipimpin oleh Hikmat Kebijaksanaan dalam Permusyawaratan/Perwakilan dengan hasil uji t 0,529, dan nilai Keadilan Sosial Bagi Seluruh Rakyat Indonesia dengan hasil uji t 0,608

PENINGKATAN KETERAMPILAN BERDISKUSI DENGAN MODEL PEMBELAJARANPROJECT CITIZEN PADA SISWA KELAS X2 SMA WIDYA KUTOARJO

Penelitian ini bertujuan untuk meningkatkan keterampilan berdiskusisiswa kelas X2 SMA Widya Kutoarjo dengan model pembelajaranproject citizen. Peningkatan dilaksanakan secara proses dan produk dengan menerapkan model pembelajaranproject citizen. Penelitian ini merupakan penelitian tindakan kelas yang dilakukan diSMA Widya Kutoarjo. Subjek penelitian ini adalah siswa kelasX2yang terdiri atas29 siswa. Penelitian ini terdiri dari tiga siklus. Setiap siklus terdiri dari empat tahap yaitu;perencanaan(planning), pelaksanaan tindakan(acting), observasi(observing) dan refleksi (reflecting). Penelitian ini dilakukan secara kolaboratif antara peneliti bersama guruBahasa Indonesia. Teknik pengumpulan data yang digunakan dalam penelitian ini berupa observasi, penilaian keterampilan berdiskusi, angket, wawancara dengan guru dan siswa, pedoman penskoran yang dianalisis secara kualitatif. Data yang diperoleh dianalisis secara deskripsi kualitatif yang didukung oleh data kuantitatif. Hasil penelitian ini menunjukkan bahwapembelajaranproject citizendapat meningkatkan keterampilanberdiskusi padasiswa kelas X2 SMA Widya Kutoarjo. Peningkatanketerampilan berdiskusi siswa tampak pada kualitas proses pembelajaran yang ditunjukkan oleh keaktifan, interaksi, sikap, dan antusias siswa ketika melakukan diskusi menggunakan model pembelajaranproject citizensehinggadapat menciptakan suasana diskusiyangaktif dan menyenangkan bagi siswa. Peningkatan secara produk dapat dilihat dari peningkatan skor dari hasil sebelum pelaksanaan tindakan dan setelah pelaksanaan tindakan. Rata-rata skor pada saat sebelum pelaksanaan tindakan sebesar6,68berkatergorikurang, rata-rata skor pada siklus I sebesar 15,51berkategori kurang baik, rata-rata skor pada siklus II sebesar 24,31 berkategori cukup baik,dan rata-rata skor pada siklus III sebesar32,65berkategori baik. Kenaikan skor rata-rata mulai dari pratindakan hingga siklus III adalah sebesar 25,97

Impact of contamination on empirical and theoretical error

Classification analysis allows to group similar objects into a given number of groups by means of a classification rule. Many classification procedures are available : linear discrimination, logistic discrimination, etc. Focus in this poster will be on classification resulting from a clustering analysis. Indeed, among the outputs of classical clustering techniques, a classification rule is provided in order to classify the objects into one of the clusters. More precisely, let F denote the underlying distribution and assume that the generalized kmeans algorithm with penalty function is used to construct the k clusters C1(F), . . . ,Ck(F) with centers T1(F), . . . , Tk(F). When one feels that k true groups are existing among the data, classification might be the main objective of the statistical analysis. Performance of a particular classification technique can be measured by means of an error rate. Depending on the availability of data, two types of error rates may be computed: a theoretical one and a more empirical one. In the first case, the rule is estimated on a training sample with distribution F while the evaluation of the classification performance may be done through a test sample distributed according to a model distribution of interest, Fm say. In the second case, the same data are used to set up the rule and to evaluate the performance. Under contamination, one has to replace the distribution F of the training sample by a contaminated one, F(eps) say (where eps corresponds to the fraction of contamination). In that case, thetheoretical error rate will be corrupted since it relies on a contaminated rule but it may still consider a test sample distributed according to the model distribution. The empirical error rate will be affected twice: via the rule and also via the sample used for the evaluation of the classification performance. To measure the robustness of classification based on clustering, influence functions of the error rate may be computed. The idea has already been exploited by Croux et al (2008) and Croux et al (2008) in the context of linear and logistic discrimination. In the computation of influence functions, the contaminated distribution takes the form F(eps) = (1 − eps)*Fm + eps* Dx, where Dx is the Dirac distribution putting all its mass at x. It is interesting to note that the impact of the point mass x may be positive, i.e. may decrease the error rate, when the data at hand is used to evaluate the error