Examples of Correlation Matrix in the following topics:
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- Each row of this actor-by-actor correlation matrix is then extracted, and correlated with each other row.
- Eventually the elements in this "iterated correlation matrix" converge on a value of either +1 or -1 (if you want to convince yourself, give it a try!
- The first panel shows the correlations of the cases.
- The third panel (the "Blocked Matrix") shows the permuted original data.
- The goodness of fit of a block model can be assessed by correlating the permuted matrix (the block model) against a "perfect" model with the same blocks (i.e. one in which all elements of one blocks are ones, and all elements of zero blocks are zeros).
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- The first step in examining structural equivalence is to produce a "similarity" or a "distance" matrix for all pairs of actors.
- This matrix summarizes the overall similarity (or dissimilarity) of each pair of actors in terms of their ties to alters.
- While there are many ways of calculating such index numbers, the most common are the Pearson Correlation, the Euclidean Distance, the proportion of matches (for binary data), and the proportion of positive matches (Jaccard coefficient, also for binary data).
- A number of methods may be used to identify patterns in the similarity or distance matrix, and to describe those patterns.
- Groupings of structurally equivalent actors can also be identified by the divisive method of iterating the correlation matrix of actors (CONCOR), and by the direct method of permutation and search for perfect zero and one blocks in the adjacency matrix (Optimization by Tabu search).
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- In addition, multicollinearity between explanatory variables should always be checked using variance inflation factors and/or matrix correlation plots .
- This figure shows a very nice scatterplot matrix, with histograms, kernel density overlays, absolute correlations, and significance asterisks (0.05, 0.01, 0.001).
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- An adjacency matrix is a square actor-by-actor (i=j) matrix where the presence of pair wise ties are recorded as elements.
- The main diagonal, or "self-tie" of an adjacency matrix is often ignored in network analysis.
- Sociograms, or graphs of networks can be represented in matrix form, and mathematical operations can then be performed to summarize the information in the graph.
- Such data are represented as a series of matrices of the same dimension with the actors in the same position in each matrix.
- Many of the same tools that we can use for working with a single matrix (matrix addition and correlation, blocking, etc.)
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- That is, we might hypothesize that the matrix of information relations would be positively correlated with the matrix of monetary relations - pairs that engage in one type of exchange are more likely to engage in the other.
- Or, it may be that the two relations have nothing to do with one another (no correlation).
- That is, what would the correlation (or other measure) be, on the average, if we matched random actors?
- We note, for example, that there is an observed simple matching of .456 (i.e. if there is a 1 in a cell in matrix one, there is a 45.6% chance that there will be a 1 in the corresponding cell of matrix two).
- Association between Knoke information and Knoke monetary networks by QAP correlation
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- Depending on how the relations between actors have been measured, several common ways of constructing the actor-by-actor similarity or distance matrix are provided (correlations, Euclidean distances, total matches, or Jaccard coefficients).
- One is, what to do with the items in the similarity matrix that index the similarity of an actor to themselves (i.e. the diagonal values)?
- If the data being examined are symmetric (i.e. a simple graph, not a directed one), then the transpose is identical to the matrix, and shouldn't be included.
- If you are working with a raw adjacency matrix, similarity can be computed on the tie profile (probably using a match or Jaccard approach).
- Alternatively, the adjacencies can be turned into a valued measure of dissimilarity by calculating geodesic distances (in which case correlations or Euclidean distances might be chosen as a measure of similarity).
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- Look under the Tools>Matrix Algebra menu.
- If you do know some matrix algebra, you will find that this tool lets you do almost anything to matrix data that you may desire.
- That is, the correlation between an adjacency matrix and the transpose of that matrix is a measure of the degree of reciprocity of ties (think about that assertion a bit).
- This is a mathematical operation that finds a matrix which, when multiplied by the original matrix, yields a new matrix with ones in the main diagonal and zeros elsewhere (which is called an identity matrix).
- Now suppose that we multiply this adjacency matrix times itself (i.e. raise the matrix to the 2nd power, or square it).
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- How do correlation, distance, and match measures index this kind of equivalence or similarity?
- If the adjacency matrix for a network can be blocked into perfect sets of structurally equivalent actors, all blocks will be filled with zeros or with ones.
- Make an adjacency matrix for a simple bureaucracy like this.
- Block the matrix according to the regular equivalence sets; block the matrix according to structural equivalence sets.
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- That is, either an actor was, or wasn't present, and our incidence matrix is binary.
- This is because the various dimensional methods operate on similarity/distance matrices, and measures like correlations (as used in two-mode factor analysis) can be misleading with binary data.
- Block modeling works directly on the binary incidence matrix by trying to permute rows and columns to fit, as closely as possible, idealized images.
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- Hotelling's $T$-square statistic allows for the testing of hypotheses on multiple (often correlated) measures within the same sample.
- A generalization of Student's $t$-statistic, called Hotelling's $T$-square statistic, allows for the testing of hypotheses on multiple (often correlated) measures within the same sample.
- Because measures of this type are usually highly correlated, it is not advisable to conduct separate univariate $t$-tests to test hypotheses, as these would neglect the covariance among measures and inflate the chance of falsely rejecting at least one hypothesis (type I error).
- where $n$ is the sample size, $\bar { x }$ is the vector of column means and $S$ is a $m \times m$ sample covariance matrix.