Download 10.-QAP

QAP: the quadratic
assignment procedure
 Material on QAP is in the Anthropac Reference
Manual: Borgatti, Stephen 1996. Anthropac 4.
Reference Manual. Pp. 85-89
 QAP evaluates the correspondence of cells in
relational matrices
 The matrices may both be observed or one
may be observed and the other expected – that
is the result of theory or prior experience.
 If you expect that children will form play groups of the
same sex, then you would compare an observed childby-child play interaction matrix to a matrix that indicates
whether a pair of children is the same sex or not.
 QAP is a permutation method for correlating whole
proximity matrices.
 The implementation of QAP in Anthropac lets you
correlate matrices or use one matrix as a dependent
variable and the other(s) as independent variable(s) in
a regression.
 If you have profile data on a set of people and you also
have relational data, you can transform the profile data
into a similarity matrix.
 Then you can use QAP to see if, say, attitudes, are
correlated with social relations.
 You can convert a single vector to a relational matrix
using
 DATA>TRANSFORM>MAT>VEC
 QAP calculates the Pearson’s correlation between
corresponding cells of the two matrices.
 It randomly permutes the rows and columns of one of
the matrices and recalculates the correlation 1000+
times.
 QAP produces a statistic, gamma, a measure
of similarity for each permutation of the
observed matrix.
 It also tells you the proportion of permutation
gammas that were as large or larger than the
observed gamma.
 This proportion is equivalent to the probability
of achieving an observed correlation by
chance.
 Read this as a test of the null hypothesis: there is no
relationship between the data and the model.
 A low proportion means the matrices are similar and
that the similarity is unlikely to have occurred by
chance.

Borgatti, Stephen 1996. Anthropac 4. Reference Manual. Pp. 85-89