A Profile
Liu Reference "whole network analysis handouts" and "social network analysis Introduction", summarizes some of the QAP.
In social network analysis, there is a method used to study the relationship between the relationship, popular terms, is to study the correlation and regression of two square. This method is called QAP (Quadratic Assignment Procedure, the secondary program is assigned). It two square value of the similarity of each comparison cell is given the correlation coefficient between the two matrices, and the coefficients are non-parametric test, it permutation matrix on the basis of data.
QAP is different from other standard statistical procedures that are not independent of each other between the respective values of the matrix, and therefore in many standard statistical procedures can not be parameter estimation and statistical tests, or calculates the standard deviation of error. For this problem, scholars have used a randomization test method (randomization test) to test, QAP belong to one of them.
Two randomized Procedure
Examples are given, if there are two matrices of 5 5 * (not independent of each other, i.e. non-1 0), to verify the correlation between, with the QAP following methods:
Matrix A:
- 1 0 0 0
1 - 1 0 0
0 1 - 1 1
0 0 1 - 1
0 0 1 1 -
Matrix B:
- 0 1 1 1
0 - 0 1 1
1 0 - 0 1
1 1 0 - 0
1 1 1 0 -
First of all values of each matrix as a long vector, each vector comprising a 5 * 4 = 20 numbers (not diagonal, n-dimension is n (n-1)), two vectors may be calculated the correlation coefficient between R = cov (a, B) / sqrt (D (a) * D (B)), i.e., the covariance divided by the product of the square root of variance only. These two vectors is calculated correlation coefficient is -0.8165, strong correlation, and negative correlation.
This correlation is observed, the question is this factor in the statistical sense whether significant? To study the problem can not actually use standard statistical methods, because it is contrary to the presuppositions (independent). We want to pursue the essence of the problem is that the correlation coefficient is calculated in the random case, coefficient than the observed large or small?
In practice, for any random matrix (one of them instead of two) label replacement (rows and columns at the same time replacement), up to 5! Species replacement pattern. Matrix and then another after the replacement of non-replacement of the correlation coefficient matrix is solved. The correlation coefficient statistics for each case. Statistical results: strong positive correlation of 3.3%, the median level of 26.7% and other related, 40% unrelated, 26.7% moderate negative correlation, 3.3 strong negative correlation (-0.8165). It can be concluded: The correlation coefficient was observed and randomly assigned to coefficients obtained, only a small probability is the same, therefore, has a strong negative correlation between these two minimum probability matrix is random, i.e. it two matrices strong negative correlation does exist!
If the size of the matrix is relatively large, then the replacement will be carried out hundreds of times, the statistical distribution of the correlation coefficient after the permutation, more observable correlation coefficient in the position of the distribution of the total, to see falls accepted domain. Suppose significance level of 0.05, then the correlation coefficient if the substitution ratio of greater than or equal to the observed correlation coefficient is less than or equal to 0.05, then in the statistical sense, between the surface of two matrices studied strong correlation, or said correlation coefficient between the two is unlikely to be caused by random.
Interpretation of three parts
The reason for the rows and columns corresponding simultaneous substitution in order not to destroy data, making the argument matrix and dependent variables are interdependent matrix row and column. It lists the relationship between the permutation test and routine testing:
| Permutation test |
Routine inspection |
| The relationship between the variables test the relationship, does not care about the overall distribution, non-parametric test |
The relationship between test property variables, random sample, the overall normal distribution, parametric tests, test results can be generalized to the overall |
Substantially, a QAP can be understood as a control on the basis of the known matrix structure, by changing the label of a particular point in another matrix, causing the differences in the structure of the two matrices to verify the significance of the original structure. QAP is a good way to structure relationships can be ruled out false.
Four QAP regression analysis
The top section talking about the correlation analysis of two matrices, if the study is the relationship between multiple regression matrix with a matrix, then we should use QAP regression analysis. Regression and correlation analysis similar, except that the following points:
- Coefficient of correlation of two matrices -> matrix and a plurality of request matrix coefficients and multivariate regression coefficient of determination
- One-tailed test -> two-tailed test
The above summary is part of, if wrong, please correct me!
