What is the Multinomial-Logistic Regression Classification Algorithm and How Does One Use it for Analysis?

Logistic regression measures the relationship between the categorical target variable and one or more independent variables It deals with situations in which the outcome for a target variable can have two or more possible types. The Multinomial-Logistic Regression Classification Algorithm is useful in identifying the relationships of various attributes, characteristics and other variables to a particular outcome.

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2. Multinomial Logistic Regression

3. Terminologies Introduction & Example Standard input/tuning parameters & Sample UI Sample output UI Interpretation of Output Limitations Business use cases What Are All Covered

4. Terminologies

5. Terminologies Target variable usually denoted by Y , is the variable being predicted and is also called dependent variable, output variable, response variable or outcome variable (Ex : One highlighted in red box in table below) Predictor, sometimes called an independent variable , is a  variable that is being used to predict the target  variable ( Ex : variables highlighted in green box in table below ) Age Marital Status Gender Satisfaction level 58 married Female High 44 single Female Low 33 married Male Medium 47 married Female High 33 single Female Medium 35 married Male High 28 single Male Low

6. Introduction & Example

7. Introduction Objective : Logistic regression measures the relationship between the categorical target variable and one or more independent variables It deals with situations in which the outcome for a target variable can have two or more possible types Thus , logistic regression makes use of one or more predictor variables that may be either continuous or categorical to predict the target variable classes Benefit : Logistic regression model output helps identify important factors ( Xi ) impacting the target variable (Y) and also the nature of relationship between each of these factors and dependent variable

8. Example : Multinomial Logistic Regression : Input Let’s conduct the Multinomial Logistic Regression analysis on following variables : Job satisfaction level Age Marital Status Gender Income Low 58 married Male 46,399 Medium 44 single Male 47,971 Low 33 married Female 52,618 High 47 married Male 28,717 Medium 33 single Female 41,216 Medium 35 married Female 34,372 Low 28 single Male 64,811 Medium 42 divorced Female 53,000 High 58 married Female 41,375 Low 43 single Male 53,778 Low 41 divorced Male 44,440 Medium 29 single Female 51,026 Independent variables (X i ) Target Variable (Y)

9. Example : Multinomial Logistic Regression : Output 1 Coefficient P value High Age 1.54 0.05 Income -0.34 0.03 Male 0.67 0.02 Low Age -2.34 0.05 Income 0.56 0.01 Male -1.23 0.04 Coefficients High satisfaction with reference to medium satisfaction: Age - Multinomial logit (Natural log of the proportion of High to that of Medium here) estimate for 1 year increase in  age for high job satisfaction relative to medium job satisfaction when other independent variables are held constant = 1.54 Male - Multinomial logit estimate for comparing male to females for high job satisfaction relative to medium job satisfaction when other variables are held constant = 0.67 Interpretation

10. Example : Multinomial Logistic Regression : Output 2 Classification Accuracy : (50+ 10 + 70) / (50+ 10 + 70+ 4+4+5+4+6+7) = 81% The prediction accuracy is useful criterion for assessing the model performance Model with prediction accuracy >= 70% is useful Classification Error = 100- Accuracy = 19% There is 19% chance of error in classification Low Medium High Low 50 4 4 Medium 4 70 5 High 6 7 10 Actual versus predicted Predicted Actual

11. Standard input/tuning parameters & Sample UI

12. Standard input parameters & Sample UI

13. SAMPLE OUTPUT UI

14. Sample output 1 : Model Summary Actual versus predicted Predicted Actual Coefficient matrix : Low Medium High Low 50 4 4 Medium 4 70 5 High 6 7 10 Coefficient P value High Age 1.54 0.05 Income -0.34 0.03 Male 0.67 0.02 Low Age -2.34 0.05 Income 0.56 0.01 Male -1.23 0.04

15. Age Marital Status Gender Income Job satisfaction level Predicted class Probability 58 married Female 46,399 Low Low 0.7 44 single Female 47,971 High High 0.9 33 married Male 52,618 Low Low 0.8 47 married Female 28,717 Low High 0.7 33 single Male 41,216 High Low 0.6 35 married Male 34,372 High High 0.5 28 single Female 64,811 Low Low 0.4 42 divorced Male 53,000 Low Low 0.3 58 married Female 41,375 High Low 0.2 43 single Male 53,778 High High 0.1 Sample output 2 : Predicted class & probability

16. Sample Output 3 : Classification Plot Lesser the overlap among three classes in the plot above , better the classification done by model Thus, output will contain predicted class column, confusion matrix and classification plot

17. Interpretation of Output

18. Interpretation of Important Model Summary Statistics Accuracy: If Accuracy >= 70% : Model is well fit on provided data and predicted classes are reasonably accurate If Accuracy < 70% : Model is not well fit on provided data and predicted classes are likely to contain high chances of error Coefficients and p value : If value of coefficient is positive and p value <0.05 , variable is positively correlated with target variable If value of coefficient is negative and p value <0.05 , variable is negatively correlated with target variable If p value > 0.05 , variable is unimportant in terms of predicting target variable classes

19. Limitations

20. Limitations It is applicable only when target variable is categorical Sample size must be at least 1000 in order to get reliable predictions Level 1 of the target variable should represent the desired outcome. i.e. if desired class is yes in response/non response target variable then Yes has to be recoded into 1 and No into

21. Business Use Cases

22. Use case 1

23. Use case 1 : Sample Input Dataset Responder ID Qualification income Age Gender Occupation Done voting in past Preferred party 1039153 Bcom 105000 18 M Accountant yes ABC 1069697 12 th Pass 192000 20 F Office Supervisor No XYZ 1068120 BSC 310000 30 F Pathologist yes PQL 563175 10 th Pass 100000 45 M Labour yes XYZ 562842 ME 357228 25 M Software Developer No PQL 562681 MSC 413000 28 F Statistician yes XYZ 562404 BSC Nill 34 F Home maker No PQL

24. Use case 1 : Output : Predicted Class Output : Each record will have a predicted class along with probability assigned as shown below : Responder ID Qualification Income Age Gender Occupation Done voting in past Predicted party Probability 1039153 Bcom 105000 18 M Accountant yes ABC 0.7 1069697 12 th Pass 192000 20 F Office Supervisor No XYZ 0.9 1068120 BSC 310000 30 F Pathologist yes PQL 0.8 563175 10 th Pass 100000 45 M Labour yes XYZ 0.7 562842 ME 357228 25 M Software Developer No PQL 0.6 562681 MSC 413000 28 F Statistician yes XYZ 0.5 562404 BSC Nill 34 F Home maker No PQL 0.4

25. Use case 1 : Output : Sample Class profile Predicted Party Average Annual income Average Age ABC 86,467 30 XYZ 60,935 25 PQL 1,05,400 35 As can be seen in the table above, there is distinctive characteristics of population associated with each preferred party : For instance, females are inclined towards XYZ whereas males tend to prefer ABC Responders with high income and age prefer to vote for PQL whereas XYZ party is preferred by lowest income and age group Fresh voters are likely to vote for party XYZ whereas those who have done voting in past are inclined towards ABC party Gender Predicted Party Male Female ABC 60 4 XYZ 10 78 PQL 14 15 Past voting status Predicted Party Yes No ABC 58 6 XYZ 15 7 3 PQL 11 1 9

26. Use case 2

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