multiple discriminant analysis-logistic regression.pptx

statistical tool

1. PEM 300 (Advanced Statistics) FLORHEN B. DE LEON-BARA Multivariate Data Analysis

2. Lesson Outline Multiple Discriminant Analysis Logistic Regression : Regression with a Binary Dependent Variable

3. Multiple regression is widely used multivariate dependence technique. its ability to predict and explain metric variables

4. Multiple Discriminant Analysis to identify the group to which an object belongs

5. Discriminant Analysis Purpose: To estimate the relationship between single nonmetric (categorical) dependent variable and metric independent variables Y 1 = X 1 + X 2 + X 3 + …+ X n (Metric) (Nonmetric)

6. Metric Variable Variable with constant unit of measurement Nonmetric Variable Variable with values as label or means of identification Categorical, qualitative, nominal, binary Male Female Yes No

7. Logistic Regression is where dependent variable is nonmetric and limited to binary dependent variables Yes No

8. Discriminant Analysis Analysis involves deriving a variate Capable of handling either two groups or multiple (three or more) groups. Two Classification – two-group discriminant analysis When 3 or more classifications, Multiple discriminant analysis (MDA)

9. Z jk = a + W 1 X 1k + W 2 X 2k + . . . W n X nk Discriminant function Known as the variate of discriminant analysis. Has equation like multiple regression: = Discriminant Z score of discriminant function j for object k = Discriminant weight for independent variable i = intercept Z jk a W i X ik = independent variable i for object k

10. Dependent variable must be nonmetric Minimize the number of categories In converting metric variables to nonmetric scale, use extreme groups to maximize the group differences Rules of Thumb 1 Discriminant Analysis Design

11. Independent variable must identify differences at least 2 groups Sample size must At least 1 observation per group, 20 cases/ group Maximize number of observation/variable w/min. ratio of 5 observations Rules of Thumb 1 Discriminant Analysis Design

12. Assess the equality of covariance matrices with the Box’s M test Examine the independent variables for univariate normality Multicollinearity can markedly reduce the estimated impact of independent variables Rules of Thumb 1 Discriminant Analysis Design

13. Logistic Regression : Regression with a Binary Dependent Variable

14. relies strictly on assumptions of multivariate normality and equal variance–covariance matrices across groups does not face these strict assumptions it is similar to multiple regression two-group discriminant analysis Logistic Regression Discriminant analysis

15. Y 1 = X 1 + X 2 + X 3 + . . . X n Logistic Regression Form of regression to predict and explain a binary (two-group) categorical variable rather than metric dependent measure. (Binary nonmetric) (nonmetric and metric)

16. Method for two-group (binary) dependent variable Sample size focused on the size of each group (10x the n of est. model coefficients) Model sig. test made w/ chi-square test Rules of Thumb 1 Logistic Regression

17. Coefficient are expressed in: original and exponentiated Interpretation of coefficients Direction – directly or indirectly in exponentiated coefficient Magnitude – assessed by exponentiated coefficient Rules of Thumb 1 Logistic Regression

18. Example of Logistic Regression Less affected than discriminant analysis by the variance–covariance inequalities across the groups. Handles categorical independent variables easily, whereas in discriminant analysis the use of dummy variables created problems with the variance–covariance equalities. Empirical results parallel those of multiple regression in terms of their interpretation and the casewise diagnostic measures available for examining residuals. Alternative to discriminant analysis

19. Comparison to Multiple Regression

20. Thank You