Multi-Response Permutation Procedure

1
Multi-Response Permutation Procedure

• Matt Vanlandeghem
• Natascha Israel
• Grant Sorensen

2
MRPP - Introduction

• Nonparametric procedure
• Tests null hypothesis of no difference between
  two or more groups of entities
• Groups determined a priori
• Procedure based on distances among data points
  within groups

3
How MRPP works

• Scatter diagram
• Measure distance among all points within each
  group in diagram
• Take averages of distances for each group
• Calculate observed delta (dobs)
• Weighted average
• Determine if dobs is unusual
• Calculate number of possible permutations (M)
• Calculate p value

4
MRPP - Benefits

• Avoids making distributional assumptions
• No need for normality or equality of variance (or
  variance-covariance matrices)
• Robust to outliers
• If sample size (n) lt number of variables (p)
• Non-parametric approach to MANOVA

5
MRPP - Example

• Freshwater Ecology

6
MRPP - Downfalls

• No direct procedure in SAS
• Most use Euclidean distance
• Computationally strenuous for large data sets
• Number of total combinations
• N!/(n1!n2!)

7

• If M is too big (Mgt106)
• Approximate p values using Pearson type III
  distribution
• Calculate mean (µ dobs), variance (s2 dobs), and
  skewness for delta under null hypothesis
• Standardized test statistic (T) under null
  hypothesis
• T (dobs - µ dobs)/ s2 dobs
• Calculate p value

8
MRPP - Caveats

• Not always the best alternatives to MANOVA
• Test stat can be un-reliable for large data sets
  (n gt20)
• Monte Carlo exercises
• standard parametric tests out performed MRPP when
  data satisfies standard assumptions
• REF

9
MRPP Alt Examples

• Social Sciences
• Multi-response data that tends to violate
  normality
• Data from only a small group of individuals
• Medical sciences
• 20 year study on cancer patients
• Low n but high p
• Data prone to extreme outliers

10
References

• Biondini, M.E., Mielke Jr., P.W., Berry, K.J.
  1988. Data-dependent permutation techniques for
  the analysis of ecological data. Vegetatio 75
  161-168 (1988).
• Cai, L. 2004. Multi-response Permutation
  Procedure as An Alternative to the Analysis of
  Variance an SPSS Implementation. Department of
  Psychology, University of North Carolina.
• Mielke, P.W. Berry, K.J. 1994. Permuation tests
  for common locations among samples with unequal
  variances. Journal of Educational and Behavioral
  Statistics 19217-236.
• Mielke, P.W. Berry, K.J. 2001. Permuation
  methods A distance function approach. New York
  Springer-Verlag.
• Mielke, P.W., Berry K.J., Johnson, E.S. 1976.
  Multi-response permuation procedure for a priori
  classifications. Communications in Statistics
  Theory and Methods 5 1409-1424.