Cluster Analysis

R has an amazing variety of functions for cluster analysis. In this section, I will describe three of the many approaches: hierarchical agglomerative, partitioning, and model based. While there are no best solutions for the problem of determining the number of clusters to extract, several approaches are given below. Data Preparation Prior to clustering data, you may want to remove or estimate missing data and rescale variables for comparability. # Prepare Data mydata <- na.omit(mydata) # listwise deletion of missing mydata <- scale(mydata) # standardize variables Partitioning K-means clustering is the most popular partitioning method. # Determine number of clusters wss <- (nrow(mydata)-1)*sum(apply(mydata,2,var)) for (i in 2:15) wss[i] <- sum(kmeans(mydata, centers=i)$withinss) plot(1:15, wss, type="b", xlab="Number of Clusters", ylab="Within groups sum of squares") A robust version of K-means based on mediods can be invoked by using pam( ) instead of kmeans( ). Hierarchical Agglomerative

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Wiki: Statistical Methods Basic statistics help: Correspondence Analysis Factor Analysis Some nice explanations: KMO and Bartlett's Test of Sphericity (Factor Analysis) The Kaiser-Meyer-Olkin measure of sampling adequacy tests whether the partial correlations among variables are small. Path Analysis Structural Equation Modeling Software, including AMOS (which looks good, but kind of expensive): have been seeing several papers (both as a reviewer and as a reader of published work) that use AMOS for CFA, path analysis, or SEM models. Hi Matthew, Thanks very much for sending me the messages on the CRTNET listserv related to Amos. Up until version 4.02, when a model included means and intercepts as explicit model parameters, Amos used a different baseline model than most other SEM programs used in computing fit measures like NFI, NNFI, CFI, etc. Best regards, Jim Raftery, A. (1993). Raftery, A. (1995). Thanks for your input!

Метод на най-малките квадрати » Физичен практикум Експерименталните данни често се придружават от някакъв шум. Дори да успеем да постигнем точни и постоянни стойности на контролните величини, измерените резултантни величини винаги варират. Необходим е процес, известен като регресия или пасване на крива, за получаване количествена оценка на тенденцията на измерените експериментални величини. В процеса на пасване на крива се избира такава крива, която да дава добро приближение с експерименталните данни. Идеята на метода е проста. където са стойностите на контролната величина, са съответните измерени стойности на резултатната величина, а е избраната функционална зависимост, която трябва да бъде пасната. Тук ще се спрем на случая на линейна зависимост между една независима контролна величина и една резултатна величина, т.е. тя има вида: Ако формулираме по друг начин задачата си — трябва да прекараме права през набора от експериментални точки, така че сумата (1) да е минимална: Решавайки тази система, получаваме коефициентите на правата: