Upper bound on the number of GARPconsistent subpopulations and clustering.
Description
The cpUpper
function computes a CrawfordPendakur type upper bound on the number of GARPconsistent subpopulations, and performs clustering of the data.
Usage
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Arguments
x 
data frame or matrix containing the observed quantities, where each row corresponds to an observation and the columns are types of goods, or an object of class 
p 
data frame or matrix (of same dimensions as x) containing the corresponding prices, 
times 
number of times the algorithm is run (the final result is the best of 
afriat.par 
the Afriat parameter, a real number in [0,1], which allows a certain level of error in the optimization of choices ; default is 1, ie. no optimization error allowed, 
method 
character string: 
object 
an object of class 
... 
additional arguments passed to the 
Details
For each run of the algorithm, a random permutation of the observations is drawn, and one by one each observation is associated with the biggest cluster that can include it while preserving consistency with the GARP rationality axiom. If no cluster is compatible with a given observation a new cluster is created to accomodate it.
Three methods are available:
"fastfloyd"
(default) uses an iterative variant of the FloydWarshall algorithm, in which the check of consistency of the current observation with a given cluster is done in a single step of the FloydWarshall algorithm. Much faster than "floyd"
.
"deep"
uses a single run of recursive depthfirst search with tabu list for each check of an observation against a given cluster. Faster than "fastfloyd"
on large datasets (eg. > 5000 observations).
"floyd"
uses the algorithm described in Crawford and Pendakur (2013): at each step the complete FloydWarshall algorithm is run to check whether each cluster can accomodate the current observation. Much slower than the two other algorithms.
Value
cpUpper
returns an object of class upperBound
which contains the following elements:

numeric vector with length equal to number of observations, containing the cluster number of each observation, 

numeric vector containg the numbers of observations allocated to each cluster, 

numeric vector containing the history of numbers of clusters found during multiple runs of the algorithm. 

upper bound on the number of types, 

Afriat parameter used in the algorithm. 
Note
Warning: cpUpper
can be very slow for large datasets (eg. more than 1000 observations).
Author(s)
Julien Boelaert jubo.stats@gmail.com
References
Crawford, I. and Pendakur, K. (2013). How many types are there? The Economic Journal, 123(567):7795.
See Also
See cpLower for the lower bound on number of types.
Examples
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