Shared variance

If brain function measures that correlate with ability test scores occur at different levels of description then it is of interest to discover whether constructs from more than one level share variance that relates to ability test scores. Three examples of this approach follow. All three discuss ways in which the correlation between inspection times and psychometric intelligence may be investigated further. 

Optimization model was built in Excel spreadsheet as proposed. Inputs for the optimization were 30-days average mean return for each share, variance-covariance matrix, and initial investment (at the beginning of each month). Excel add-in Solver was implemented into the macro and used to minimize portfolio s variance at the beginning of the each month. For each optimization. Solver was calibrated as the minimum of... 

If the confounders controlled are broad indicators to a number of important characteristics in the child s home environment, some of which may be relevant to the uptake of lead, and others to explain the child s performance, then controlling for these will remove the shared variance which might in fact be due to lead. By controlling for more specific variables the problem of shared variance is reduced, as the collinearity is likely to be less, but since it is precisely because there is some collinearity in these variables that they are controlled, it does not disappear. This highlights the importance of a priori separation of variables into those thought to be causally related to lead burden, and those thought to be causally related to outcomes. 

Failure to remove variance attributable to other influences (under-control-ling) can result in an apparent lead effect, when in reality the cause is uncontrolled social differences, while removing variance which is in fact attributable to lead is over-controlling, and can result in the failure to find an effect which is really there. Different analytical techniques make different assumptions about shared and residual variance, and the order in which the variance attributable to different covariates is calculated can also influence the way shared variance is treated. 

There is no easy formula to avoid the possibility of over- or undercontrolling in the treatment of confounding variables. Generally, given the complex interacting pattern of influences on body burden and outcomes, control for a small number of variables is more likely to underestimate the effect of confounders, while control for a large number is more likely to overcontrol, because of the removal of shared variance. The control of only broad demographic indicators is more likely to remove shared variance erroneously (and at the same time probably not control for the real confounders), while control for more specific measures is less likely to. Some statistical techniques... 

Over- or under-controlling, and the problem of shared variance... 

Traditionally statistics is a conservative science, and this has a number of implications for lead studies, where the effect looked for is small, and there are a number of other partly-related influences, which are likely to be larger. The cautious convention in multivariate statistics is to attribute any shared variance to the confounder, so if no association is found after control for covariates, there is assumed to be no effect of lead. If a confounder is to some extent a cause of the child s lead burden, as well as being related to the outcome, then variance attributable to lead will be removed along with the social variance, relevant to the outcome. Similarly to control for variables which are consequences of the outcomes will result in over-control. 

Measure r Shared variance, % (r ) Gestational age (GA) GA and parent size GA and substance use GA, parent size, and substance use Substance use... 

Measure Shared variance (%) without other covariate control Shared variance (%) with control of other covariates ... 

We can consider the hydroboration step as though it involved borane (BH3) It sim phfies our mechanistic analysis and is at variance with reality only m matters of detail Borane is electrophilic it has a vacant 2p orbital and can accept a pair of electrons into that orbital The source of this electron pair is the rr bond of an alkene It is believed as shown m Figure 6 10 for the example of the hydroboration of 1 methylcyclopentene that the first step produces an unstable intermediate called a tt complex In this rr com plex boron and the two carbon atoms of the double bond are joined by a three center two electron bond by which we mean that three atoms share two electrons Three center two electron bonds are frequently encountered m boron chemistry The tt complex is formed by a transfer of electron density from the tt orbital of the alkene to the 2p orbital... 

On the other hand, it also shares some of the disadvantages of the Durbin-Watson Statistic. It is also based on a comparison of variances, so that it is of low statistical power. It requires many more samples and readings than the Durbin-Watson statistic does, since each sample must be measured many times. In general, it is not applicable... 

Table 3. Median proportions of variance attributed to additive genetic, nonadditive genetic, shared environmental, and nonshared environmental effects plus error and broad heritability, derived from eight kinships, for seventeen brief strong vocational interest blank scales...

It follows that the allocation of all the permitted extra column dispersion to sample volume dispersion, as defined by Klinkenberg (4) and suggested on page (54), is not permissible. Other sources of dispersion must be taken into account and take a share of the permitted 10% increase in column variance. 

In the following, three scenarios are compared according to their revenue expectations. The basis for the calculation of the variance coefficients is the theory of the diffusion curve13 of innovations. It is assumed that the Austrian market will be satiated by 50% after 10 years. This estimate is based on the analogous market of "Responsible Care". Expected market shares have been used for the calculation of the variance coefficients of the Worst and Best Case scenarios, which assume a 30% and a 70% satiation, respectively (Fig. 37). 

---