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TOOLS > STATISTICS > MATRIX (QAP) > QAP-REGRESSION

PURPOSE Regress a dependent matrix on one or more independent matrices, and assess significance of the r-square and regression coefficients.

DESCRIPTION The procedure is principally used to model a social relation (matrix) using values of other relations.

The algorithm proceeds in two steps.  In the first step, it performs a standard multiple regression across corresponding cells of the dependent and independent matrices.

In the second step, it randomly permutes rows and columns (together) of the dependent matrix and recomputes the regression, storing resultant values of r-square and all coefficients.  This step is repeated hundreds of times in order to estimate standard errors for the statistics of interest.  For each coefficient, the program counts the proportion of random permutations that yielded a coefficient as extreme as the one computed in step 1. The primary requirement for conducting a multiple regression quadratic assignment procedure is that all the variables in the regression have to be one-mode, two-way matrices.  That is, they must all be NxN networks.  Person-by-object or Person-by-event matrices can be converted to NxN matrices using Data>Affiliations.

PARAMETERS
Dependent variable:
Name of dataset containing the observed or dependent data:  the matrix whose values are to be predicted. Data type: Square Matrix.

Independent variables:
Names of datasets containing the independent or predictor matrices. To include more than one dataset using the browse button highlight all required files by pressing Ctrl and clicking with the mouse. If the file names are typed they should be separated by commas with no spaces. File names that contain spaces should be enclosed in quotation marks.  Data type: Square Matrices.

Number of random permutations: (Default = 500)
Number of regressions to compute between the data matrix and the randomly permuted structure matrix.  The larger the number of permutations, the better the estimates of standard error and "significance", but the longer the computation time.

Treat diagonals as valid? (Default = No)
If Yes, the values along the main diagonals of each matrix are included in the computations.  Otherwise, they are treated as missing.

Random number seed:
The random number seed sets off the random permutations.  UCINET generates a different random number as default each time it is run.  This number should be changed if the user wishes to repeat an analysis.  The range is 1 to 32000.

LOG FILE Two tables are output.  The first looks like this:

R-Square One-Tailed Probability
0.023   0.618
The table gives the observed r-square along with the proportion of random trials yielding an r-square as large or larger than the observed.

The second table is as follows:

Unstandardized Two-Tailed
Independent  Coefficient  Probability
Intercept     0.385965    0.178
R1   -0.007519    0.866
R2   -0.150376    0.170
R3    0.000000    0.838

This table gives the Unstandardized regression coefficient for each independent variable, including the intercept, along with the proportion of random trials yielding a coefficient with an absolute value as large or larger than the observed.  In this example, all the coefficients have non-significant probabilities, indicating that the observed values are well within the range of random variation.,

TIMING O(N^2).

COMMENTS The program ignores missing values.

REFERENCES None.