Spearman's law of diminishing returns: A statistical artifact?

Do Cognitive-Achievement Relations Vary by General Ability Level?

Cognitive-achievement relations research has been instrumental in understanding the development of academic skills and learning difficulties. Most cognitive-achievement relations research has been conducted with large samples and represent average relations across the ability spectrum. A notable gap in the literature is whether these relations vary by cognitive ability levels (IQ). This study examined cognitive-achievement relations across different general ability levels (Low, Average, and High) to fill this gap. Based on Spearman's Law of Diminishing Returns, it would be expected that general intelligence would be a stronger predictor of academic skills at lower levels of IQ, and more specific abilities would be stronger predictors of academic skills at higher levels of IQ. To test this, multi-group path analysis and structural equation modeling were used to examine whether integrated models of cognitive-reading relations are differentiated by IQ levels in the Woodcock-Johnson III and Woodcock-Johnson IV standardization samples. Global and broad cognitive abilities were used as predictors of basic reading skills and reading comprehension for elementary and secondary school students. The magnitude of prediction differed across ability groups in some cases, but not all. Importantly, the variance explained in basic reading skills and reading comprehension tended to be larger for the Low group compared to the Average and High groups. When variance accounted for by general intelligence was removed from the broad abilities, the effects of the broad abilities were similar across ability groups, but the indirect effects of g were higher for the Low group. Additionally, g had stronger relative effects on reading in the Low group, and broad abilities had stronger relative effects on reading in the Average and High groups. The implications and limitations of this study are discussed.

Reduced attention toward faces, intentionality and blame ascription in violent offenders and community-based adults: Evidence from an eye-tracking study

People typically have a strong bias in attention toward faces to help them understand social interactions. Nonetheless some people, like incarcerated offenders and psychopaths, exhibit deficits in "face reading," which may impair their interpretations, especially in case of attribution allocation in harmful events. In these cases, the ascription of intentionality is key in understanding the allocation of blame and structuring social information processing. Consequently, in the current study, in addition to typically studied intentionality and blame ascription levels (subfactors of hostile attributions), we also propose a new indicator of hostile attributions: intentionality/blame isomorphism, indicating reduced differentiation between those two factors. Violent prison inmates (N = 63) and community-based adults without previous history of incarceration (N = 63) took part in an eye-tracking study. In line with our hypotheses, offenders exhibited reduced attention orienting to faces as well as greater intentionality/blame isomorphism. In the case of both groups, people looked longer at the faces of the harm doer compared with the harm receiver. Additionally, greater intentionality/blame isomorphism predicted reduced attention to faces; however, when group status was included in the model, it became the only significant predictor of the attention to faces. Future studies should examine the origins of these gaze and attribution patterns and investigate consequences related to social perception and interactions of people prone to violence.

Diminishing returns as a function of the association between within-individual average performance and variance

It has been demonstrated that the worst performance rule (WPR) effect can occur as a result of statistical dependencies in the data. Here, we examine whether this might also be the case for Spearman's law of diminishing returns (SLODR). Two proposed SLODR criteria are the skewness of the estimated latent ability factor and the correlation between this latent ability and within-individual residual variance. Using four publicly available datasets, covering quite different dimensions of behavior, we show that both these criteria are affected by the correlation between within-individual average performance and variance on the test scores. However, the influence of this correlation on the two criteria goes in opposite directions, which suggests that it generally might be difficult to get results that unambiguously support SLODR. These results might have far-reaching implications for the literature, to the extent that various research findings attributed to human cognitive functioning might in fact be due to trivial statistical dependencies in data. This is an important issue to address for future research.

Diminishing returns as a function of disturbance

According to Spearman's law of diminishing returns (SLODR), IQ test scores are more g saturated among those with low, compared to those with high, ability. The present simulation shows that such difference in saturation can be observed if test scores are affected by a disturbing factor, for example, low motivation, illness, or linguistic confusion, that varies in magnitude between individuals. More contemporary criteria of SLODR can also be satisfied if test scores are affected by disturbance, especially if the disturbance variable is negatively skewed. This indicates a possible threat against the validity of findings supporting SLODR and points at the importance for researchers to try to eliminate the influence of such disturbing factors from their studies.

Heteroscedastic Latent Trait Models for Dichotomous Data

Effort has been devoted to account for heteroscedasticity with respect to observed or latent moderator variables in item or test scores. For instance, in the multi-group generalized linear latent trait model, it could be tested whether the observed (polychoric) covariance matrix differs across the levels of an observed moderator variable. In the case that heteroscedasticity arises across the latent trait itself, existing models commonly distinguish between heteroscedastic residuals and a skewed trait distribution. These models have valuable applications in intelligence, personality and psychopathology research. However, existing approaches are only limited to continuous and polytomous data, while dichotomous data are common in intelligence and psychopathology research. Therefore, in present paper, a heteroscedastic latent trait model is presented for dichotomous data. The model is studied in a simulation study, and applied to data pertaining alcohol use and cognitive ability.