@ARTICLE{26583223_545349694_2021, 
	author = {Aleksei Korneev and Anatoly Krichevets and Konsatantin Sugonyaev and Dmitry Ushakov}, 
	keywords = {, structure of intelligence, linear structural modeling, moderated confirmatory factor analysisSpearman's law of diminishing returns},
	title = {Moderated Confirmatory Factor Analysis and Non-Linear Effects in Intelligence Testing},
	journal = {Psychology. Journal of Higher School of Economics},
	year = {2021},
	volume = {18},
	number = {4},
	pages = {718-747},
	url = {https://psy-journal.hse.ru/en/2021-18-4/545349694.html},
	publisher = {},
	abstract = {In this work we discuss the advantages and limitations in using moderated confirmatory factor analysis (MCFA) in studies of intelligence structure in the context of Spearman's Law of Diminishing Returns (SLODR). A simple one-factor model was estimated on large samples of simulated data and real results of intelligence tests using MCFA. The simulated data represent large datasets (about 10,000 "respondents" in each dataset) and simulate some specific situations: the SLODR effect, the heteroscedasticity of the residuals (an increase in error along with an increase in the general IQ factor), asymmetry in the distribution of the g-factor, and a high density of easy tasks in the test. The real data consist of the results of IQ testing of 11,388 adult respondents. The model was estimated on each of the datasets, with factor scores obtained by the principal component analysis used as a moderator. Factor loadings and residuals were moderated, both separately and simultaneously. The results showed that (1) the simultaneous moderation of factor loadings and residuals may give inadequate results in some cases; (2) the SLODR effect can be expressed by various combinations of the distribution asymmetry of factor scores and  an increase in error variances along the g-factor; (3) within the framework of classical psychometrics, it is probably impossible to distinguish between the real SLODR effect and the false one generated by the selection of respondents; (4) two known sources of asymmetry of distributions in intelligence testing - unequal density of tasks of varying difficulty and selection of respondents are easily detected in simulated pure form, but it is not so easy to do with the real data. (5) It may be difficult to interpret directly the results of MCFA due to its closeness and opacity: it is shown that the moderation of the error variance can be replaced by the analysis of regression residuals, and the interpretation of the moderation of factor loadings can be improved if it is accompanied by an analysis of the asymmetries of the distributions of variables and factor scores.},
	annote = {In this work we discuss the advantages and limitations in using moderated confirmatory factor analysis (MCFA) in studies of intelligence structure in the context of Spearman's Law of Diminishing Returns (SLODR). A simple one-factor model was estimated on large samples of simulated data and real results of intelligence tests using MCFA. The simulated data represent large datasets (about 10,000 "respondents" in each dataset) and simulate some specific situations: the SLODR effect, the heteroscedasticity of the residuals (an increase in error along with an increase in the general IQ factor), asymmetry in the distribution of the g-factor, and a high density of easy tasks in the test. The real data consist of the results of IQ testing of 11,388 adult respondents. The model was estimated on each of the datasets, with factor scores obtained by the principal component analysis used as a moderator. Factor loadings and residuals were moderated, both separately and simultaneously. The results showed that (1) the simultaneous moderation of factor loadings and residuals may give inadequate results in some cases; (2) the SLODR effect can be expressed by various combinations of the distribution asymmetry of factor scores and  an increase in error variances along the g-factor; (3) within the framework of classical psychometrics, it is probably impossible to distinguish between the real SLODR effect and the false one generated by the selection of respondents; (4) two known sources of asymmetry of distributions in intelligence testing - unequal density of tasks of varying difficulty and selection of respondents are easily detected in simulated pure form, but it is not so easy to do with the real data. (5) It may be difficult to interpret directly the results of MCFA due to its closeness and opacity: it is shown that the moderation of the error variance can be replaced by the analysis of regression residuals, and the interpretation of the moderation of factor loadings can be improved if it is accompanied by an analysis of the asymmetries of the distributions of variables and factor scores.}
}