relationship between DFA and MANOVA
Source: Manly, Bryan F.J. Multivariate Statistical Methods: A Primer, Third Edition, CRC Press,
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Tutorial – Week 7 (DFA)
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 is
their relationship to the posterior probabilities?
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 be
classified, then we can use training and test data sets for that analysis. Create
frequency tables to determine the number of cases in each species and sex. Species
group 5 individuals are of unknown sex so exclude all of this species from the frequency
table for sex.
b) Try creating training and test sets for sex. Has the portioning created samples of sizes
that you would expect? Discuss.
c) Convert Group and Sex to factors in your original dataframe. What do you notice about
sex as a factor variable?
d) Perform whatever methods you feel would be appropriate before starting DFA to classify
by species group.
e) Perform DFA by species groups. What proportion of total variance is explained by the
first two DFs? Explain the loadings on DF1.
f) Classify each individual based on your species group DFA model. What percentage of
individuals were correctly classified?
g) Plot individuals for DF1 v DF2 with individuals classified by original species group and
then predicted species group. Interpret. Can you identify the two incorrectly classified
individuals? Plot DF3 v DF4 using both original and predicted species group labels.
h) What would you conclude about this analysis? Include any limitations you would place
i) Run DFA to classify by sex. Species group 5 individuals are of unknown sex so exclude
all of this species from this analysis. As part of your interpretation comment on the prior
probabilities for Sex. Give the total % correctly classified and the %n of each sex
j) See if you can adjust the code from part f) to predict group membership based on only
the first two DF’s. Why might this be useful to consider?
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