discriminate analysis of Biostatistics ppt for MPH Students
- 1. D I S C R I M I N AT E A N A L Y S I S P R E S E N T E D B Y: B H O J R A J G A U TA M R O S H A N T H A PA
- 2. TABLE OF CONTENT • Introduction • Assumptions of discriminate analysis • Discriminate Analysis Model • Types of DA • Steps of Analysis • Hypothesis • Strengths and Weakness • References
- 3. INTRODUCTION • Discriminate analysis is a statistical method used for Classifying a set of observation into predefined groups • In simple, DA helps to understand the relationship between a “dependent variable” and one/ more “independent variables” • It is used to analyze and interpret the differences between two or more groups or categories based on multiple predictor variables DA is sometimes also called as: Discriminate factor analysis Canonical discriminate analysis
- 4. CONTD… • DA is used when the data are normally distributed whereas the logistic regression is used when the data are not normally distributed Dependent variable – categorical Independent variable – intervals or ratio scale
- 5. 5 EXAMPLE Examples includes; i. Dependent variable is person diseased status (1 yes, 2 no) and independent variables are plasma lipid profile, that is total cholesterol (X1) , triglycerides (X2), HDL (X3) and LDL (X4). Since dependent variable is having two categories, so it it an example of two-group DA. Here independent variables are continuous in nature. ii. We want to know whether somebody has lung cancer. Hence, we wish to predict a yes or no outcome. • Possible predictor variables: number of cigarettes smoked a day, coughing frequency and intensity etc.
- 6. WHY DO WE USE DA? • DA has various benefits as a statistical tool and is quite similar to regression analysis • It can be used to determine Which predictor variables are related to the dependent variable To predict the value of the dependent variable given certain values of the predictor variables
- 7. WHEN TO USE DA? • Data must be from different groups • To analysis of differences in groups • For classification of new objects
- 8. ASSUMPTIONS OF DISCRIMINATE ANALYSIS Homogeneous within-group variances Multivariate normality within groups No multi- collinearity Prior probabilities
- 9. DISCRIMINATE ANALYSIS MODEL The discriminate analysis model involves linear combination of the following form: where D = discriminate score b’s = discriminate coefficient or weight X’s = predictor or independent variable • The coefficient, or weight (b), are estimated so that the groups differ as much as possible on the values of the discriminate function • Discriminate analysis– creates an equation which will minimize the possibility of misclassifying cases into their respective groups or categories D = b0+ b1X1+ b2X2+ b3X3+…...+ bkXk
- 10. TYPES OF DA i. Linear discriminate analysis: When the criterion/dependent variable has two categories eg: adopters and non-adopters ii. Multiple discriminate analysis: When three or more categories of dependent variable are involved
- 11. LINEAR DISCRIMINATE ANALYSIS • Given by Ronald Fisher in 1936 • This methods group images of the same classes and separate images of the different classes • This classification involves 2 target categories and 2 predictor variables. These features divide or characterize two or more than two objects or events.
- 12. MULTIPLE DISCRIMINATE ANALYSIS • To discriminate among more than 2 groups • It requires
- 13. STEPS IN ANALYSIS • STEP 1 In step one the independent variables which have the discriminating power are being chosen • STEP 2 A discriminant function model is developed by using the coefficients of independent variables
- 14. STEPS IN ANALYSIS CONTD… • STEP 3 In step three Wilk’s Lambda is computed for testing the significance of discriminant function • STEP 4 In the step four the independent variables which possess importance in discriminating the groups are being found • STEP 5 In step five classification of subjects to their respective group is being made
- 15. STEPS OF DISCRIMINANT ANALYSIS IN SPSS 1. Analyze >> Classify >> Discriminant 2. Select ‘dependent variable’ as your grouping variable and enter it into the Grouping Variable Box 3. Click Define Range button and enter the lowest and highest code for your groups 4. Click Continue. 5. Select your predictors (IV’s) and enter into Independents box and select Enter Independents Together. If you planned a stepwise analysis you would at this point select Use Stepwise Method and not the previous instruction. 6. Click on Statistics button and select Means, Univariate Anovas, Box’s M, Unstandardized and Within-Groups Correlation 7. Continue >> Classify. Select Compute From Group Sizes, Summary Table, Leave One Out Classification, Within Groups, and all Plots 8. Continue >> Save and select Predicted Group Membership and Discriminant Scores 9. OK.
- 16. STATISTICS ASSOCIATED WITH DISCRIMINANT ANALYSIS •Eigen values: • It is the ratio of between groups to within group sum of squares. Higher the eigen value, more will be the appropriateness of the discriminant function. For a two-group DA, there will be one function and one eigen value. It accounts for explained variance in the model. In case of multiple DA, the eigen values will be more but the values will gradually decline. The first eigen value will be largest and most important, the second will be less than the firstone having less explanatory power.
- 17. • Box’s M statistic: It is a test for equality of the covariance matrices of the independent variables across the groups. Here the null hypothesis (Ho) is that the observed covariance matrices are equal across groups. So, a nonsignificant test result (i.e., one with a large p-value) will indicate that the covariance matrices are equal.
- 18. • Wilks’ Lambda: It provides a statistical test to assess discriminating power of the independent variables. If it is significant (revealed by significance of Chisquare), we reject the “HN: No group separability”, and conclude that the discriminant function is statistically significant.
- 20. HYPOTHESIS Discriminant analysis tests the following hypothesis: H0: the group means of a set of independent variable for two or more groups are equal H1: the group means for two or more groups are not equal This group means is referred to as a centroid
- 21. STRENGTHS 1. Classification accuracy: discriminate analysis can be effective when the data is well-separated, and the assumptions of the technique are met. It can produce accurate results when the classes are well-defined and distinct 2. Multiclass classification: Unlike some other classification methods, discriminate analysis can handle multiple classes efficiently. It extends naturally to more than two classes without requiring significant modifications 3. Dimensionally reduction: Discriminant analysis can be used to reduce the number of predictors (independent variables) by creating new variables (discriminant function) that capture most of the information about the group differences 4. Normality assumptions: Discriminant analysis can still perform reasonably well when the normality assumptions is slightly violated, especially with large sample sizes
- 22. WEAKNESS/LIMITATIONS 1. Sensitivity to assumption: 2. Overfitting: 3. Outliers: 4. Non-linear boundaries:
- 23. SIMILARITIES AND DIFFERENCES AMONG ANOVA, REGRESSION AND DISCRIMINATE ANALYSIS ANOVA Regression Discriminate Analysis Similarities Number of dependent variables One One One Number of independent variables Multiple Multiple Multiple Differences Nature of dependent variable Metric Metric Categorical Binary Nature of independent variable Categorical Metric Metric
- 24. REFERENCES • https://www.statisticssolutions.com/discriminant-analysis/ • https://en.wikipedia.org/wiki/Linear_discriminant_analysis • https://www.slideshare.net/slideshow/discriminant-function-analysis-dfa/238649297 • https://www.slideshare.net/slideshow/discriminantfunctionanalysisdfa2009261213041pptx/256616478 • https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/discriminant-analysis • https://www.wallstreetmojo.com/discriminant-analysis/ • https://stats.oarc.ucla.edu/stata/dae/discriminant-function-analysis/
Editor's Notes
- #8: Homogeneous within group variances- variances among group variables are the same levels of predictors Multivariate normality within groups- when all other independent variables are held constant, the independent variable under examination should have a normal distribution No multi-collinearity- predictive power can decrease with an increased correlation between predictor variables Prior probabilities- the probability of an observation coming from a particular group in a simple random sample with replacement