Graphic 1. Some Basics Regarding Factor Models of Correlation Matrices
Mayer, J. D. and Bryan (2021, April 30). Some basics regarding factor models of correlation matrices. Personality Laboratory at the University of New Hampshire. https://mypages.unh.edu/jdmayer/graphics.
Notes: The table illustrates some basic principles regarding how correlations can be modeled in factor analysis. The spanner headings indicate that the first row depicts an example of a one-factor case; the second row, a two-factor case, and the third row depicts a hierachical relation with one factor at the top and subsidiary factors beneath it. Each of the three rows begins with a somewhat different matrix that represents the correlations among the four mental ability tasks, T1 through T4. In this hypothetical example, the four tasks were administered to 1000 participants. Any of the three correlation matrices of Column 1 might have arisen as a consequence.
The middle column of the table depicts the results of a factor analysis of the matrix. The roman numerals designate the first and second factors extracted for the one- and two-factor cases illustrated in the first two rows. The numbers beneath them represent the estimated correlations between the four individual tasks and the factor(s); those correlations are referred to as factor loadings. The final column represents a diagrammatic depiction of the results. More details: The three correlation matrices were factor analyzed using R. The exploratory solutions (top rows) were conducted with the psych package using a principal axis extraction followed, for the two-factor case, by a oblimin rotation. The bottom, hierarchical CFA was conducted in Lavaan using a Maximum Likelihood extraction. Fit statistics were 1.0 for both the CFI and TLI and 0 for the RMSEA.
The R code for the three examples can be found on this website here.
Graphic 2. Loadings of Broad Intelligences on g
The following is an ancillary analysis of the open-source data from Bryan & Mayer, 2020 that illustrates how each of ten broad intelligences loads on a general intelligence factor (g).
Citation in APA Style:
Bryan, V. M., & Mayer, J. D. (2021, April 30). Ten broad Intelligences and their relations to general intelligence: An ancillary analysis of the open-source data from Bryan and Mayer, 2020. Personality Laboratory at the University of New Hampshire. https://mypages.unh.edu/jdmayer/graphics.
Graphic 3. The Four Areas of Personality Function from the Personality Systems Set
Here is an overview of the functional areas of the personality systems framework, as typically envisioned in our work.
Citation in APA Style: Mayer, 2020, "The Four Function Areas of the Personality Systems Set". Online lab graphic from https://mypages.unh.edu/jdmayer/graphics
Graphic 4. People-Centered Versus Thing-Centered Intelligences in the Three-Stratum Model of Intelligence
The following graphic elaborates on the model described in Mayer, J. D. (2018). Intelligences about things and intelligences about people. In R. J. Sternberg (Ed.). The nature of human intelligence (pp. 270-286). Cambridge, England: Cambridge University Press, especially on pp. 272 to 274, and 280.