I am very proud of this paper, which proposes a systematic method for testing whether theories putatively explain empirical phenomena. Congrats to the whole team, thanks to @Noah_van_Dongen for pulling it over the finish line.
10 years after we created Registered Reports, the thing critics assured us would never (in a million years) happen has happened: @Nature is offering them.
The Registered Reports initiative just went up a gear and we are one step closer to eradicating publication bias and reporting bias from science.
Congratulations to all involved in achieving this milestone.
A universe of infinitely many quantitative variables is considered, from which a sample ofn variables is arbitrarily selected. Only linear least-squares regressions are considered, based on an infinitely large population of individuals or respondents. In the sample of variables, the predicted value of a variablex from the remainingn − 1 variables is called the partial image ofx, and the error of prediction is called the partial anti-image ofx. The predicted value ofx from the entire universe, or the limit of its partial images asn → ∞, is called the total image ofx, and the corresponding error is called the total anti-image. Images and anti-images can be used to explain “why” any two variablesx j andx k are correlated with each other, or to reveal the structure of the intercorrelations of the sample and of the universe. It is demonstrated that image theory is related to common-factor theory but has greater generality than common-factor theory, being able to deal with structures other than those describable in a Spearman-Thurstone factor space. A universal computing procedure is suggested, based upon the inverse of the correlation matrix.
This article examines the methodological foundations of exploratory factor analysis (EFA) and suggests that it is properly construed as a method for generating explanatory theories. In the first half of the article it is argued that EFA should be understood as an abductive method of theory generatio …