Discriminant Analysis
Data: The ustudy.sav data file includes data collected from two independent samples of faculty from two types of universities. The variables are as follows:
* ACADRNK: academic ranking, with 1 being assistant, 2 associate, and 3 full professor;
* UNIV: type of university , with 1 being a state and 2 a private university; * YRSPHD: number of years since earning a Ph.D.; * SALARY: salary, in $ thousands; * PUBLCTN: number of publications. Scope: • To determine variates (linear combinations of IVs, also called discriminant functions) that discriminate best between the given levels of the DV Variables: • dependent variable: a nonmetric variable (DV) with two (two-group DA) or more (multiple DA) levels (groups) • independent variables: metric variables (IV1, IV2, etc.) Notes: • DA is the opposite of MANOVA • The number of discriminant functions equals the number of groups in the DV minus
1 • These discriminant functions are then used to classify objects described in terms of their IV characteristics into the given groups of the DV (membership prediction) Procedure: Open an SPSS data file and: 1. select Analyze / Classify / Discriminant;
2. move the nonmetric DV in the "Grouping Variable" area and define its levels using Define Range (Min. / Max.);
3. move the metric IVs in the "Independents" area;
4. click on "Statistics" and check the Unstandardized under "Function Coefficients"; then, click Continue; 5. finally, click OK. Output: The output includes: • Wilks' Lambda table: indicates the significance for each discriminant function; • Canonical Discriminant Function Coefficients table: provides the coefficients ("weights") needed to build the discriminant functions; • Functions at Group Centroids table: provides the group centroids; use them to calculate the cutting scores to be used when predicting group membership. EXERCISE Using the ustudy.sav data file, run a discriminant analysis to determine if type of university can be predicted by the following faculty characteristics: number of years since Ph.D., salary, and number of publications. 1. What is the dependent variable? What type of data does the DV have? How many groups?
2. What are the independents? What type of data do the IVs have?
3. How many discriminant functions should you expect? Explain.
4. Check the Wilks' Lambda table. Is the model significant? Explain.
5. Write the discriminant function using the coefficients provided in the Canonical Discriminant Function Coefficients table. (The general equation is Z = Constant + W1 * YRSPHD + W2 * SALARY + W3 * PUBLCTN. You just need to identify the coefficients. Note: Make sure you use the unstandardized, not the standardized discriminant coefficients that are also provided in a separate table!)
6. Check the Functions at Group Centroids table. What are the centroids Z1 and Z2 for the two types of universities?
7. Calculate the cutting score ZC. (Consider that the sizes of the two groups are equal so that you can use the formula ZC = (Z1+Z2) / 2.
8. A colleague of mine who got her Ph.D. 3 years ago now earns $40K per year. So far, she has published 6 papers in academic journals. Where would you say my colleague teaches: a private or a state university? (Calculate the person's discriminant score. Then, compare it with ZC.)
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