The Calculate Square Root of Matrix process outputs a data set containing columns of the square root of a matrix calculated by Singular Value Decomposition. The input matrix is defined by the columns of the Input Data Set specified as Matrix Variables. This analytical process can be used to calculate the SVD root of a custom kinship matrix that was not computed using the Relationship Matrix process for input into the Q-K Mixed Model process. When used for this purpose, the input K matrix variables must form a square, symmetric matrix that define the covariance of the random effect that you want to fit in the Q-K mixed model. The square root computation of the estimated kinship covariance matrix is necessary for accurately fitting the correct covariance structure according to how the Q-K Mixed Model process computes the model. This process is necessary only if the matrix to be used as the K random component was calculated in an external program, otherwise it can be calculated in the Relationship Matrix process. The output K matrix square root variables can then be specified in the Q-K Mixed Model process to ensure that the correct covariance structure is formed.
Note: The output data set containing the square root matrix variables from this process should be merged with the SNP data set in preparation for using the Q-K Mixed Model process. If the input data set already contains columns of SNP data, these variables should be retained in the output data set.
One data set is required to run the Calculate Square Root of Matrix process. This Input Data Set, contains all of the marker data. The morocco_kmatrix.sas7bdat data set, shown below, represents a 193 x 193 matrix of Identity By Descent (IBD) values calculated between individuals from genome-wide SNP using data from a study of gene expression variation and SNP associations in southern Morocco (Idaghdour, Czika, et al., 2010)
For detailed information about the files and data sets used or created by JMP Life Sciences software, see Files and Data Sets.
The output of the Calculate Square Root of Matrix process includes one output data set that contains the square root of the input matrix and a set of Action Buttons. The data set is accessed from a tabbed Results window.
This process was run for the data sets shown above. The morocco_kmatrix_svd.sas7bdat output data set (shown below) represents the square root of the morocco_kmatrix.sas7bdat input data set and is ready for use as input for the Q-K Mixed Model process.
The action button surfaced on the Results window, enables you to launch the Q-K Mixed Model process with the results of the Calculate Square Root of Matrix process preloaded, for further analysis.