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MULTIVARIATE STATISTICAL MODELS’ SYMBOLS

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MULTIVARIATE STATISTICAL MODELS’ SYMBOLS

  1. 1. MULTIVARIATE STATISTICAL MODELS’ SYMBOLS Multivariate Regression Discriminant Analysis Multivariate Discriminat Analysis Factor Analysis Principal Components Analysis Canonical Correlation Analysis Variance Analysis Models ANCOVA-MANCOA
  2. 2. Relationships x y Two-way arrow Explains just relationship between variable x and y. It doesn’t tell the causality. x y One-way arrow Explains causality between independent variable x and dependent variable y. x1 y x2 Interaction Explains both of two independent variables have influence on dependent variable y. x1 x2 y x1 x2 Recursive Models Explains causality flows in only one direction.
  3. 3. Symbols ofVariables MANIFEST. Represents continuos variable. LATENTVARIABLE. Represents latent variable. Represents categorical (qualitative) variable. Represents categorical (qualitative) variable that has three categories.
  4. 4. Student t Although Student t test is not a multivariate statistical analysis, it underlies the linear dependent multivariate statistical models. 1st group of independent variable X 2nd group of independent variable X x dependent variable Y y independent categorical (2 categories) dependent continuous
  5. 5. Multiple Regression Analysis x1 x2 xp y independent continuous variables dependent continuous variable . . .
  6. 6. Discriminant Analysis x1 x2 xp independent continuous variables dependent categorical variable that has two categories . . . y
  7. 7. Multivariate Discriminant Analysis x1 x2 xp independent continuous variables dependent categorical variable that has categories higher than two . . . y
  8. 8. Factor Analysis x1 x2 x3 x4 Latent Latent independent continuous variables latent variables
  9. 9. Principal Components Analysis x1 x2 x3 x4 Latent Latent independent continuous variables latent variables
  10. 10. Canonical Correlation Analysis x1 x2 Latent x3 x4 x5Latent x6 x7 independent continuous variables independent continuous variables there is a relationship between latent variables
  11. 11. VarianceAnalysis Models
  12. 12. One-Way ANOVA y independent categorical variable has to have minimum 3 categories x
  13. 13. InteractiveTwo-Way ANOVA y independent categorical variable has to have minimum 2 categories x2 x1
  14. 14. One-Way MANOVA y1 y2 yp independent categorical variables that have to have more than two categories (here as an example the dependent variable x has 5 categories) dependent continuous variables . . . y3 x
  15. 15. Two-way MANOVA independent categorical variables has to have minimum 2 categories x2 x1 y1 y2 yp dependent continuous variables . . . y3
  16. 16. Two-Way MANOVA with interaction independent categorical variables has to have minimum 2 categories x2 x1 y1 y2 yp dependent continuous variables . . . y3 x3
  17. 17. ANCOVA x2 x1 covariate factor y one categorical + one continuosu covariate variable dependent continuous variable

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