Source: Manly, Bryan F.J. Multivariate Statistical Methods: A Primer, Third Edition, CRC Press,07/2004.Page 1 of 1Tutorial – Week 7 (DFA)Question 1:a) What is the goal of DFA?b) Describe the relationship between DFA and MANOVA.c) How many DFs are produced through DFA?d) Unless otherwise stated in the model, how are prior probabilities calculated? What istheir relationship to the posterior probabilities?Question 2:Complete exercise 1 at the end of Chapter 8 of Manly using the data set ‘mandiblefull.dat’.As well as classifying individuals by species as stated in Manly, we will also classify by sex.a) If there are more than 20 individuals in each of the sex or species groups to beclassified, then we can use training and test data sets for that analysis. Createfrequency tables to determine the number of cases in each species and sex. Speciesgroup 5 individuals are of unknown sex so exclude all of this species from the frequencytable for sex.b) Try creating training and test sets for sex. Has the portioning created samples of sizesthat you would expect? Discuss.c) Convert Group and Sex to factors in your original dataframe. What do you notice aboutsex as a factor variable?d) Perform whatever methods you feel would be appropriate before starting DFA to classifyby species group.e) Perform DFA by species groups. What proportion of total variance is explained by thefirst two DFs? Explain the loadings on DF1.f) Classify each individual based on your species group DFA model. What percentage ofindividuals were correctly classified?g) Plot individuals for DF1 v DF2 with individuals classified by original species group andthen predicted species group. Interpret. Can you identify the two incorrectly classifiedindividuals? Plot DF3 v DF4 using both original and predicted species group labels.Interpret.h) What would you conclude about this analysis? Include any limitations you would placeon interpretation.i) Run DFA to classify by sex. Species group 5 individuals are of unknown sex so excludeall of this species from this analysis. As part of your interpretation comment on the priorprobabilities for Sex. Give the total % correctly classified and the %n of each sexmisclassified.j) See if you can adjust the code from part f) to predict group membership based on onlythe first two DF’s. Why might this be useful to consider?
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