Statistical Software “SAMMIF” Okayama Univ. of Science Graduate School, Okayama Univ. Kurashiki Univ. of Science and the Arts Okayama Univ. Yuichi MORI Yoshiro YAMAMOTO Shingo WATADANI Yoshimasa ODAKA Tomoyuki TARUMI Yutaka TANAKA SAMMIF Project Sensitivity Analysis in Multivariate Methods based on Influence Functions

KJCS-97 ， Outline of our presentation About SAMMIF –Motivation and process of developments. –Ideas in SAMMIF. –General procedure and flow of “SAMMIF”. Demonstration of “SAMMIF” –Exploratory factor analysis. open/closed book data (Mardia et al, 1979) Discussion and Future plans

KJCS-97 ， Motivation for development Sensitivity analysis procedures using influence functions and their analogues; SAM （ Tarumi and Tanaka, 1986 ）, SAF/B （ Odaka, Watadani and Tanaka, 1991 ）, SAF/S （ Inoue, Odaka and Tanaka, 1991 ）, SAM II （ Mori and Tarumi, 1993 ）, SACS （ Watadani and Tanaka, 1994 ）, etc. –developed for a specified family of multivariate methods separately, –most of them run on MS-DOS (BASIC) platform. Necessary to develop a new program; –unifying any multivariate method where influence functions or their analogues are available, –reinforcing GUI under the Windows environment.

KJCS-97 ， Sensitivity analysis Data Multivariate method Influence of the i-th observation ? Results θ ＾ Data the i-th obs. Results ( i ) θ ( i ) ＾ Multivariate method i ＝ 1,..., n

KJCS-97 ， Empirical Influence Function Introduce perturbation to the cdf F,, where is the cdf of a unit point mass at x. Empirical Influence Function ( EIF ),.

KJCS-97 ， Empirical Influence Function Influence of k observations –approximation of,. Influence of one observation Influences of subsets, influential individually, similar influence patterns. Canonical Variate Analysis Cook’s Local Influence

KJCS-97 ， Sensitivity analysis based on influence functions Data n obs. Data n obs. EIF Vectors, More than one Vectors, More than one Parameters Observable measures Observable measures Summarizing them into scalar measures Summarizing them into scalar measures Influence of multiple obs. Influence of multiple obs. Applying CVA or PCA to EIF Applying CVA or PCA to EIF

KJCS-97 ， Flow of SAMMIF Data entry Prior analysis Single-case diagnostics Multiple-case diagnostics Posterior analysis Comparison (Pre / Post) 1) Data 2) Pre Estimate ordinarily using all observations. 3) Diagnostics 3-1) SD Compute EIFs and summarize them to influence measures. 3-2) MD Apply CVA or PCA to EIFs. 4) Post Estimate without observations of interest. 5) Comp Compare results in 4) with in 2).

KJCS-97 ， Flow of SAMMIF Data entry Prior analysis Single-case diagnostics Multiple-case diagnostics Posterior analysis Comparison (Pre / Post) 1) Data 2) Pre Estimate ordinarily using all observations. 3) Diagnostics 3-1) SD Compute EIFs and summarize them to influence measures. 3-2) MD Apply CVA or PCA to EIFs. 4) Post Estimate without observations of interest. 5) Comp Compare results in 4) with in 2). Influence measures 1) Influence on the estimate ; (a) Euclidean norm, (b) Generalized Cook's distance. 2) Influence on the precision; (c) COVRATIO-like measure. 3) Influence on the goodness-of-fit; (d) Change of X 2, (e) Change of goodness-of-fit index (GFI), (f) Change of root mean square residual (RMR). Influence measures 1) Influence on the estimate ; (a) Euclidean norm, (b) Generalized Cook's distance. 2) Influence on the precision; (c) COVRATIO-like measure. 3) Influence on the goodness-of-fit; (d) Change of X 2, (e) Change of goodness-of-fit index (GFI), (f) Change of root mean square residual (RMR).

KJCS-97 ， Features of SAMMIF (Version0.8) Developing tool: MS-Visual Basic Language: English / Japanese Included method: Factor analysis –Sensitivity analysis in Exploratory FA –Sensitivity analysis in Confirmatory FA Features (other than Windows functions) : –Clicablemap-type flowchart, –Graphical displays, –Brief tutorial, Hint options, –Standard / detail outputs, –Intermediate reports, savable outputs.

KJCS-97 ， Example (Demonstration) Factor analysis –Basic model, f :common factor ， e:unique factor ， : mean vector :Factor loading matrix –Covariance matrix of x, Estimated parameters Example –Method: Exploratory factor analysis –Data: “open/closed book data (Mardia et al, 1979)”, –88 observations, 5 variables.

KJCS-97 ， Demonstration of “SAMMIF” Demonstration of “SAMMIF” Demonstration of “SAMMIF” Demonstration of “SAMMIF” Method: Exploratory factor analysis Data: “open/closed book data (Mardia et al, 1979)” 88 observations, 5 variables.

KJCS-97 ， Discussion and Future plans SAMMIF –provides important information easily, –for diagnostic checking of the data. Future plans –Include other multivariate methods: LISREL type covariance structure analysis, PCA, Canonical correlation analysis, etc. –Other type of perturbation scheme –Improve convenience: for both beginners and experts, various options, Interface with other software, enrichment of helps and consultation.

KJCS-97 ， SAMMIF Sensitivity Analysis in Multivariate Methods based on Influence Functions Contact to Yuichi MORI Okayama University of Science Dept. Socio-Information Distribution Exe files Brief tutorial file Sample data Manual (in HTML) English / Japanese Publication On the Web okayama-u.ac.jp ous.ac.jp kusa.ac.jp January, 1998