Partial Correlation Diagram

The Partial Correlation Diagram process helps you infer association and potential causal relationships between a set of variables . This process fits so-called covariance selection models (also known as graphical Gaussian models ), in which partial correlations ( the correlation between two variables adjusted for all other variables) are estimated, and then plots each variable as a node. The nodes are then connected with line segments, whose size and color are determined by the partial correlations. Additional graphs are also available, along with options for controlling them.

Note : Although a strong partial correlation is not the same as a causal relationship, it can suggest one.

Method

Let the partial correlation matrix be R . The eigenvalue decomposition is applied to R .

R= E*Diag(M)*E

where E is the eigenvector matrix, and M is the diagonal matrix of eigenvalues.

The X and Y position of each node is determined by the following:

X = Sqrt(Abs(M[1]))*E[,1]

Y = Sqrt(Abs(M[2]))*E[,2]

M[1] and M[2] are the 1st and 2nd eigenvalue, respectively. E[,1] and E[,2] are the 1st and 2nd eigenvector, respectively.

What do I need?

One Input Data Set is required to run the Partial Correlation Diagram process. Because the Distance Matrix and Clustering process calculates the distance between the observations (rows), a wide -formatted data set (in which the rows comprise each of the variables) is normally used as the input data set. If you are working with a tall data set and you want to compute distance between columns, first run the Transpose Rectangular process.

An example data set, the adsl_diit.sas7bdat data set, shown below, was generated by transposition of the adsl_dii.sas7bdat data set included with JMP Clinical (see Nicardipine ). Patients are listed in columns, adverse events are listed in rows. There are 911 columns for 906 patients and 350 rows listing events.

For detailed information about the files and data sets used or created by JMP Life Sciences software, see Files and Data Sets .

Output/Results

The output generated by this process is summarized in a Tabbed report. Refer to the Partial Correlation Diagram output documentation for detailed descriptions and guides to interpreting your results.