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.
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.
While Rushton (1999) demonstrates, using PCA, that g and black-white differences were related, with Flynn Effect (FE) gains over time showing no relationship with the aforementioned variables, Flynn (2000) has challenged Rushton in arguing that Wechsler’s subtest loadings on the Raven test, an universally recognized measure of fluid g, showed positive correlations with both black-white differences and FE gains. Up to now, Flynn’s estimates of g fluid (Gf) has not been scrutinized. I will show presently that the Flynn’s g-fluid (call it, fluid reasoning) and Rushton’s g-crystallized (call it, consolidated knowledge) anomaly was solely due to a single statistical artifact, namely, g_Fluid vector unreliability. By adding additional samples, I created a new, updated Wechsler’s subtest Gf loadings. The present analysis comes to the conclusion that g_Fluid was not in fact correlated with FE gains. Furthermore, this Gf variable has been correlated with other variables as well, such as, heritability (h2), shared environment (c2), nonshared environment (e2), adoption IQ gains, inbreeding depression (ID), and mental retardation (MR). I will also discuss these findings in light of Kan’s (2011) thesis against the hereditarian hypothesis.
In his classic work, Educability and Group Differences, Arthur Jensen presented a number of lines of evidence in defense of his thesis that the Negro-White difference in psychometric intelligence had a congenital component. On the basis of full sibling correlations and relations, Jensen offered the following arguments:
(a1) The full sibling correlations for Blacks and Whites are comparable; (a2) unshared environmental hypotheses, such as nutritional ones, would predict otherwise (pg. 338-339).
(b1) The full sibling correlations for Blacks and Whites are comparable; (b2) a shared environmental hypothesis of group differences would predict otherwise, assuming that the within population heritablities were the same (pg. 108-109).
(c1) The average absolute difference between full siblings is no greater for Blacks than for Whites; (c2) unshared environmental hypotheses, such as nutritional ones, would predict otherwise (pg. 338-339).
(d1) When matching Blacks and Whites on IQ, one sees differential sibling regression, a differential regression which does not decrease with increasing IQ; (d2) an environmental hypothesis of group differences would not predict this (pg. 118-119). Continue reading
Hu (2013, September, 5; 2013, July, 5; 2013, August, 18) has raised some interesting points. I will comment on a few of them here and present several new analyses.
Cultural Loading, Heritability, and the BW gap
As Meng Hu noted, Kan et al. (2011) showed that subtest cultural-loadings, as they estimated them, correlated both with the magnitude of the B/W subtest gaps and with subtest heritability estimates. The authors interpreted these associations as support for a GxE hypothesis of individual differences and offered a model similar to that proposed by Flynn and Dickens (2001). Moreover, Kan et al. (2011) saw the associations between cultural-load and heritability and between cultural-load and the magnitude of the BW gap as problematic for what they termed a biological g model. Below, I will show that g-loadings fully mediate the association between cultural loadings and the two other variables noted and therefore that what is in need of explanation is only the association between cultural-loadings and g-loadings. I will then proceed to offer an account for this.
First, I looked to see if g-loadings mediated the association between the BW gap and cultural loadings. They did. Then I looked to see if cultural-loadings mediated the association between the BW gap and g-loadings. They did not fully. The results are shown below. As reliability estimates were not presented for all subtests, I ran the analysis with and without reliability corrections. Continue reading
The present analysis is an extension of Spitz’s earlier (1988) study on the relationship between mental retardation (MR) lower score and subtest heritability (h2) and g-loadings. These relationships were found to be positive. But Spitz himself haven’t tested the possibility that MR (lower) score could be related with shared (c2) or nonshared (e2) environment. I use the WAIS and WISC data given in my earlier post, and have found that MR is not related with c2 and e2 values. These findings nevertheless must be interpreted very carefully because the small number of subtests (e.g., 10 or 11) is a very critical limitation.
I analyze two studies who provide the necessary data for studying the test-retest effects, namely, Watkins (2007), Schellenberg (2004, 2006). Both used the Wechsler’s subtests, and the correlations between the IQ changes among those subtests with g-loadings are negative, in line with earlier studies on this topic.
A correlation between the g factor and indices of heritability (h2) gives support for the genetic g hypothesis but, on the other hand, the interpretation may appear questionable if g correlates with shared (c2) and/or non shared (e2) environment to the same extent. The results from the present meta-analysis tend to support the hereditarian hypothesis.
Studies of the nature of the Flynn Effect are usually done in developed countries (e.g., Rushton, 1999; Wicherts, 2004; Nijenhuis, 2007; for an ‘Overview of the Flynn Effect’, see Williams, 2013). There are two recent data on two developing countries (Khaleefa, 2009; Liu, 2012). The reported numbers on subtests gains can be studied using either MCV or PC analysis. Next, we will see that shared (c²) and non-shared (e²) environments, as measured by Falconer’s formula, are unrelated to heritability (h²) of the WAIS and WISC subtests. Culture load, heritability, g-loadings, and black-white differences tend to form a common cluster (on PC1) that is different from the pattern of loadings shown by shared and non-shared environment.
The french adoption study, by Capron & Duyme (1989, Table 2; 1996, Table 3), attempted to show that IQ can be improved by adoption. Their numbers displayed an IQ gain of 15 or even 20 points (WISC-R). To recall, Jensen (1997) analyzed Capron and Duyme adoption data (1996) with N=38, a study often cited by environmentalists as evidence against the hereditarian hypothesis. In Adoption Data and Two g-Related Hypotheses, Jensen shows that IQ difference owing to the adoption of children from low-SES parents by high-SES families is not g-loaded while at the same time the IQ difference owing to low-SES versus high-SES biological families loaded in fact on the g factor or PC1. Plus, the SES-difference of adopted families correlated at only 0.099 with SES-difference of biological families.