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1 Sun Li Centre for Academic Computing

2 Elementary Data Analysis Group Comparison & One-way ANOVA Non-parametric Tests Correlations General Linear Regression Logistic Models Binary Logistic Model Ordinal Logistic Model Multinomial Logistic Model

3 The Explore procedure Exploratory data analysis Summary statistics Distribution plots Normality plots with tests Analyze Descriptive Statistics Explore The dependent variable must be a scale variable, while the grouping variables may be ordinal or nominal.

4 E.g.: demo.sav Explore the household income for married and unmarried people.

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6 The Crosstabulation table Analysis of cross-classifications To examine the relationship btw two categorical variables Nominal-by-nominal relationships Ordinal-by-ordinal relationships Nominal-by-interval relationships Relative risk measurement Agreement measurement Analyze Descriptive Statistics Crosstabs

7 E.g.: Test and measure the relationship btw the job satisfactions and the number of year with current employer.

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9 T Tests The one-sample T test The paired-samples T test (skip) The independent-samples T test Analyze Compare Means

10 E.g.: 1. Test if the average household income equals to 75k. 2. Test if the average household income for married and unmarried people has no significant difference.

11 One-way analysis of variance to test the hypothesis that the means of two or more groups are not significantly different. E.g.: Test if the average household income for the five education groups are different. If there is significant difference, identify which groups have the major difference.

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14 Non-parametric tests Two-independent samples tests Tests for several independent samples Analyze Nonparametric Tests 2 Independent Samples K Independent Samples

15 Two-independent samples tests: Test if the household income varies btw married and unmarried people. Mann-Whitney and Wilcoxon tests--

16 The two-sample Kolmogorov-Smirnov test

17 K-independent samples tests: Test if the household income varies among people with different educations. Using the median test to detect the difference:

18 Using Kruskal-Wallis to Test Ordinal Outcomes

19 Correlation Analyze Correlation Bivariate correlation: Describe relationship btw two variables. Partial correlation: Describe relationship btw two variables while controlling for the effects of one or more additional variables. Distances: (skip) Similarities/dissimilarities btw pairs of variables/cases.

20 E.g.: Compute the correlation coefficient btw the household income and the price of primary vehicle.

21 E.g.: Compute the correlation coefficient btw the household income and the price of primary vehicle after controlling factor age, marriage status and education.

22 The GLM Univariate procedure Analyze General Linear Model Univariate Analyze Regression Linear In SPSS, there are two menus about linear regressions under pull-down menu Analyze. The difference btw the two menus is that Linear function under Regression treats every predictor to be continuous variables, while in General Linear Model, there are options to define categorical predictors and continuous predictors.

23 Factors: Categorical predictors should be selected as factors in the model. Fixed-effects factors are generally thought of as variables whose values of interest are all represented in the data file. Random-effects factors are variables whose values in the data file can be considered a random sample from a larger population of values. They are useful for explaining excess variability in the dependent variable. Covariates: Scale predictors should be selected as covariates in the model. E.g.: grocery_1month.sav Use the GLM Univariate procedure to fit a model with fixed and random effects to the amounts customers spent in grocery stores.

24 E.g.: A grocery store chain surveyed a set of customers concerning their purchasing habits. Given the survey results and how much each customer spent in the previous month, the store wants to see the factors. Variable storeid shop for style usecoup amtspent Variable information Store id Who shop for: 1 = self 2 = self and spouse 3 = self and family Shopping style: 1 = biweekly, in bulk 2 = weekly, similar items 3 = often, what s on sale Use coupons: 1 = no 2 = from newspaper 3 = from mailings 4 = from both Amount spent last month

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27 Hays, W. L Statistics, 3rd ed. New York: Holt, Rinehart, and Winston. Brown, M. B., and A. B. Forsythe. 1974b. Robust tests for the equality of variances. Journal of the American Statistical Association, 69:, Milliken, G., and D. Johnson Analysis of Messy Data: Volume 1. Designed Experiments. New York: Chapman & Hall. Neter, J., W. Wasserman, and M. H. Kutner Applied Linear Statistical Models, 3rd ed. Homewood, Ill.: Irwin. Siegel, S., and N. J. Castellan Nonparametric statistics for the behavioral sciences. New York: McGraw-Hill, Inc.. Conover, W. J Practical Nonparametric Statistics, 2nd ed. New York: John Wiley and Sons. Horton, R. L The General Linear Model. New York: McGraw-Hill, Inc..

28 Logistic Models Binary logistic model: dichotomous response outcomes e.g.: presence or absence of an event π i = E( yi xi ) logit( π ) = log( π /(1 π )) = g( π ) = α + β X Ordinal logistic model: ordinal response variable with more than two ordered categories e.g.: a 5-point Likert scale g(pr( Y i X )) = αi + β ' X, i = 1,..., k Multinomial logistic model: nominal response variables with more than two categories e.g.: different types of programs in school Pr( Y = i X ) log = αi + β ' i X, i = 1,..., k Pr( Y = k + 1 X )

29 Using binary logistic regression to assess credit risk E.g.: bankloan.sav Analyze Regression Binary Logistic If you are a loan officer at a bank, then you want to be able to identify characteristics that are indicative of people who are likely to default on loans, and use those characteristics to identify good and bad credit risks. We have information on 850 past and prospective customers. The first 700 cases are customers who were previously given loans. Use these 700 customers to create a logistic regression model. Then use the model to classify the 150 prospective customers as good or bad credit risks.

30 Variable name age ed employ address income Variable information Age in years Level of education 1= didn t complete high school 2= high school degree 3= college degree 4= undergraduate 5= postgraduate Years with current employer Years in current address Household income in thousands debtinc Debt to income ratio (*100) creddebt othdebt default Credit card debt in thousands Other debts in thousands Previously defaulted 1= Yes 0 = No

31 Step 1: select the first 700 obs for logistic model Data Select Cases

32 Step 2: construct logistic model

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34 Step 3: identify possible outlying obs Scatter plot: predicted probability vs Cook s D statistics

35 Step 4: draw ROC curve and find the optimal cut-off point Analyze ROC Curve

36 Step 5: predict credit risk Select the rest 150 obs and compute predicted probability with model coefficients

37 Using Multinomial Logistic Regression to Classify Telecommunications Customers E.g.: telco.sav A telecommunications provider has segmented its customer base by service usage patterns, categorizing the customers into four groups. If demographic data can be used to predict group membership, you can customize offers for individual prospective customers. Analyze Regression Multinomial Logistic

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40 Using Ordinal Regression to Build a Credit Scoring Model g(pr( Y i X )) = αi + β ' X, i = 1,..., k E.g.: german_credit.sav A creditor wants to be able to determine whether an applicant is a good credit risk, given various financial and personal characteristics. From their customer database, the creditor (dependent) variable is account status, with five ordinal levels: no debt history, no current debt, debt payments current, debt payments past due, and critical account. Potential predictors consist of various financial and personal characteristics of applicants, including age, number of credits at the bank, housing type, checking account status, and so on.

41 Analyze Regression Ordinal

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43 Hays, W. L Statistics, 3rd ed. New York: Holt, Rinehart, and Winston. McCullagh, P., and J. A. Nelder Generalized Linear Models, 2nd ed. London: Chapman & Hall. Cox, D. R., and E. J. Snell The Analysis of Binary Data, 2nd ed. London: Chapman and Hall. Hosmer, D. W., and S. Lemeshow Applied Logistic Regression, 2nd ed. New York: John Wiley and Sons. Kleinbaum, D. G Logistic Regression: A Self-Learning Text. New York: Springer-Verlag. Norusis, M SPSS 13.0 Advanced Statistical Procedures Companion. Upper Saddle-River, N.J.: Prentice Hall, Inc..

44 Advanced Models 30 May Friday 10am-12pm Training Library Level 5 Curve Estimation Non-linear Regression Survival Analysis Linear Mixed Model Time-series Data Analysis

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