Multiple Regression, Multiple Fallacies

It goes without saying that multiple regression is one of most popular and applied statistical methods. Thus, it would be odd if most practitioners among scientists and researchers do not understand and misapply it. And yet, this provocative conclusion seems most likely.

Because a simple bivariate correlation does not disentangle confounding effects, the multiple regression is said to be preferred. The technique attempts to evaluate the strength of an independent (predictor) variable in the prediction of an outcome (dependent) variable, when controlling, i.e., holding constant, every other variables entered (included) as independent variables into the regression model, either progressively step by step or altogether at the same time. The rationale is to get the effect of an independent variable that only belongs to it. But this is a fallacy.
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Structural relationship between g, parental SES, and Achievement : Investigation of the g nexus

The present analysis, using the NLSY97, attempts to model the structural relationship between the latent second-order g factor extracted from the 12 ASVAB subtests, the parental SES latent factor from 3 indicators of parental SES, and the GPA latent factor from 5 domains of grade point averages. A structural equation modeling (SEM) bootstrapping approach combined with a Predictive Mean Matching (PMM) multiple imputation has been employed. The structural path from parental SES to GPA, independently of g, appears to be trivial in the black, hispanic, and white population. The analysis is repeated for the 3 ACT subtests, yielding an ACT-g latent factor. The same conclusion is observed. Most of the effect of SES on GPA appears to be mediated by g. Adding grade variable substantially increases the contribution of parental SES on the achievement factor, which was partially mediated by g. Missing data is handled with PMM multiple imputation. Univariate and multivariate normality tests are carried out in SPSS and AMOS, and through bootstrapping. Full result provided in EXCEL at the end of the article.

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