9533 BQA Exam 6 Multiple Discriminant Analysis This filename is: ad8213bea1912c9c003d0d967181ad4c65e2fc36.doc Revised: Tuesday, February 24, 2009 0 words For all exams, write on one side only, use paper without torn edges, and number the pages. For all Excel and SPSS and other computer output, avoid splitting a table across multiple pages if possible, and repeat the row and/or column labels as a header if splitting is necessary. Start with this document. Leave intact each of the questions and numbers. Paste the requested output and/ or requested answers below the question part. For some questions, I left part of my output as a hint. Delete this partial output before pasting in yours. Do this analysis using SPSS (or SAS or other statistical package) and Word (or Word Perfect or another word processor). Submit via email before class starts on the due date. Use the correct filename when submitting your work. The file name should be "exam06nnn.doc" (where "nnn" is your last name). Do not include the quotes in the filename. Special caution: When SPSS creates a large text object, as with Matrix and Manova output, the border window may not be large enough to see all the output. Always check this, that you can see what is the end of the text output. You can select the object, and then drag the handle at the bottom down until lots of blank space is visible. Then drag back up to show all the text. 1) 2) Duplicate the "small sample" example from the textbook. Do this to check you are getting the right output, but don't turn it in. [No response needed for this part.] Do a MDA and canonical correlation analysis of the data in the file exam06_MDA_2009_sleep.xls. Data for 62 mammals are from the article "Sleep in Mammals: Ecological and Constitutional Correlates" by Allison, T. and Cicchetti, D. (1976), Science, November 12, vol. 194, pp. 732-734. Variables are: species of animal body weight in kg brain weight in g Encephalization Quotient = (brain weight) / (12 * (body weight)^(2/3) = relative brain size slow (EEG) wave ("nondreaming") sleep (hrs/day) paradoxical (REM or "dreaming") sleep (hrs/day) total sleep (hrs/day) (sum of slow wave and paradoxical sleep) maximum life span (years) gestation time (days) predation index (1-5) 1 = minimum (least likely to be preyed upon), 5 = maximum sleep exposure index (1-5) 1 = least exposed, 5 = most exposed overall danger index (1-5) (based on the above two indices and other information) 1 = least danger (from other animals), 5 = most danger (from other animals) [No response needed for this part.] 3) Conduct the MDA analysis. The DV is the overall danger index (5 levels) and IV are all other variables except for the predation and sleep exposure indices. Unless specified otherwise, use Prior Probabilities from group sizes and pooled covariance matrix (within groups). Use alpha = 0.05 unless otherwise specified.
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a) Paste below (as a picture) the descriptive statistics for all variables (N, Min, Max, Mean, SD, Skewness, and Kurtosis). b) Do the MDA using Wilks' Lambda Method, stepwise with probability to enter/exit of 0.3 and 0.3001, Specify cross-validated classification output (leave one out classification). Include Plots for combined groups and territorial map. Paste below (pictures) the "Variables in the Analysis" and "Variables not in the Analysis." Which variables are not included in the model (and therefore not useful in the discrimination)? c) How many of observations have missing data for one or more of the DV and IV? How many of these observations have missing data only in the variables excluded from the stepwise procedure above? d) Paste the Eigenvalues output below and the Wilks' Lambda (picture). How many of the canonical correlations are statistically significant (alpha = 0.05)? e) Paste the classification results. What is the cross-validated classification What accuracy? is the nave classification accuracy (without a statistical model)? 4) Now repeat the analysis using "enter independents together" (all the IV vars are used) and specifying the 5 IV bodyweight brain paradoxical total lifespan. Also, request Box's M test for equality of covariance matrices within groups. a) What are the cross-validated and "regular" classification accuracies? b) Paste below the test results for Box's M test. Describe the null hypothesis. Give a summary statement for the test result. c) Run the analysis again the same way, except for using separate covariance matrix estimates for each group. What is the resulting classification accuracy? Compare this with the accuracy with a single pooled covariance matrix estimate. d) This will be our final model. Paste below the Structure Matrix (loadings) and give an interpretation (explanation) of the first 2 CV. e) Paste below the "All-Groups Scatter Plot." Which groups are most effectively separated by CV1 only? Explain its general effect in predicting group membership. f) Which groups are most effectively separated by CV2 only? Explain its general effect in predicting group membership.
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At most 2 of the CV can be regarded as statistically significant. I get a p-value of 0.486 for CV3 CV4, which is no more than attributable to chance. This suggests that any predictive value from CV3 and CV4 is due to overfitting. Repeat the analysis, saving the discriminant scores. Hint: Here is my syntax:
/* save scores separate cov matrix for vars in model */ DISCRIMINANT /GROUPS=danger(1 5) /VARIABLES=bodyweight brain paradoxical total lifespan /ANALYSIS ALL /SAVE=SCORES /PRIORS SIZE /STATISTICS=CROSSVALID TABLE /PLOT=COMBINED /CLASSIFY=NONMISSING SEPARATE .
Then repeat the analysis using just the first 2 scores and separate covariance matrices. a) Paste below the classification result. Compare this classification accuracy with that using all 5 IV with separate covariance matrices and with all 5 and a pooled covariance matrix. Note that only the first 2 CV are statistically significant, and the p-value for CV 3 and 4 combined is near 0.5 indicating they contribute no more predictive benefit that what would result from chance. 6) Another data reduction method is factor analysis, with one use to extract most of the variation in a set of variables with a much smaller number of factors. Let's see how many factors would be retained and how effective those would be in classification. a) Do a PC factor analysis on the 5 IV bodyweight brain paradoxical total lifespan. Paste below the Total Variance Explained. How many factors would be retained using the e-value > 1 method? b) Repeat the PC factor analysis, keeping 2 factors, varimax rotation, saving the (regression) scores. (Here the term "regression" means the sum of products, as used to calculate y-hat in regression. It has nothing to do with the statistical method of regression.) Paste below the Rotated Component Matrix and the Component Plot in Rotated Space. c) Interpret (explain) these 2 factors in terms of the 5 IV. Compare these factors with the 2 CV from the MDA above. d) Now use these 2 saved factor scores as IV in the MDA, using separate covariance matrices. Paste below the Classification Results and All-Groups Scatter Plot. What is the classification accuracy with the 2 factors? e) Compare the classification accuracy using 2 CV with that using 2 factors. Does one accuracy necessarily have to be larger than the other? (Explain why either way.) Is there a limit to how much they can differ? (Explain your answer.)
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Paste below (as mono-spaced text) the syntax used for all the steps. Edit out the syntax that was not used and put the commands in the order of the requested output.
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