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===Velicer's Minimum Average Partial test (MAP)===
Velicer's (1976) MAP test<ref name=Velicer/> “involves a complete principal components analysis followed by the examination of a series of matrices of partial correlations” (p. 397). The squared correlation for Step “0” (see Figure 4) is the average squared off-diagonal correlation for the unpartialed correlation matrix. On Step 1, the first principal component and its associated items are partialed out. Thereafter, the average squared off-diagonal correlation for the subsequent correlation matrix is computed for Step 1. On Step 2, the first two principal components are partialed out and the resultant average squared off-diagonal correlation is again computed. The computations are carried out for k minus one steps (k representing the total number of variables in the matrix). Finally, the average squared correlations for all steps are lined up and the step number that resulted in the lowest average squared partial correlation determines the number of components or factors to retain (Velicer, 1976). By this method, components are maintained as long as the variance in the correlation matrix represents systematic variance, as opposed to residual or error variance. Although methodologically akin to principal components analysis, the MAP technique has been shown to perform quite well in determining the number of factors to retain in multiple simulation studies.<ref name =Ruscio/><ref name=Garrido>Garrido, L. E., & Abad, F. J., & Ponsoda, V. (2012). A new look at Horn's parallel analysis with ordinal variables. Psychological Methods. Advance online publication. doi:10.1037/a0030005</ref> However, in a very small minority of cases MAP may grossly overestimate the number of factors in a dataset for unknown reasons.<ref>{{cite journal | last1 = Warne | first1 = R. T. | last2 = Larsen | first2 = R. | year = 2014 | title = Evaluating a proposed modification of the Guttman rule for determinig the number of factors in an exploratory factor analysis
===Parallel analysis===
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