Blocked-Error-R 2: A Conceptually Improved Definition of the Proportion of Explained Variance in Models Containing Loops or Correlated Residuals

Bentler and Raykov (2000, Journal of Applied Psychology 85: 125–131), and Jöreskog (1999a, http://www.ssicentral.com/lisrel/column3.htm, 1999b http://www.ssicentral. com/lisrel/column5.htm) proposed procedures for calculating R ² for dependent variables involved in loops or possessing correlated errors. This article demonstrates that Bentler and Raykov’s procedure can not be routinely interpreted as a “proportion” of explained variance, while Jöreskog’s reduced-form calculation is unnecessarily restrictive. The new blocked-error-R ² (beR ²) uses a minimal hypothetical causal intervention to resolve the variance-partitioning ambiguities created by loops and correlated errors. Hayduk (1996) discussed how stabilising feedback models – models capable of counteracting external perturbations – can result in an acceptable error variance which exceeds the variance of the dependent variable to which that error is attached. For variables included within loops, whether stabilising or not, beR ² provides the same value as Hayduk’s (1996) loop-adjusted-R ². For variables not involved in loops and not displaying correlated residuals, beR ² reports the same value as the traditional regression R ². Thus, beR ² provides a conceptualisation of the proportion of explained variance that spans both recursive and nonrecursive structural equation models. A procedure for calculating beR ² in any SEM program is provided.     

Diastolic dysfunction

Diastolic dysfunction of the heart is characterized by normal left ventricular contractility and normal ejection fraction, however ventricular relaxation is impaired. In systolic dysfunction, ventricular contractility and ejection fraction are reduced, in addition to impaired relaxation. The prevalence of diastolic dysfunction is increased in the elderly, especially those who have had inadequately treated hypertension. Both diastolic and systolic dysfunction may result in similar clinical signs and symptoms. Therefore, echocardiography is needed to make the distinction. Left atrial (LA) enlargement, assessed by left atrial volume indexed to body surface area, appears to be the best measure to assess diastolic function. LA enlargement is likely when indexed LA volume is > or = 34-40 mL/m2. B-type natriuretic protein appears to be useful for the diagnosis, assessment and prognosis of heart failure, but it does not distinguish between the two types of dysfunctions. Several drug treatments that have effects on the mechanism of diastolic dysfunction are under investigation.     

Vasectomy bonuses and completed family size in India

This paper discusses the consequences in rural India of a certain rational household decision function on the number of children born in the family when birth control opportunities are available. Households are assumed to choose whether or not to practice birth control after each child is born on the basis of maximising expected utility as a function of the consumption per head and the number of members in the family. Uncertainty arises on account of the different evaluation of children of different sexes. The model is then used to predict how completed family size would change if a government agency paid bonuses for smaller families.     

Revenue Sharing with Heterogeneous Investments in Sports Leagues: Share Media,Not Stadiums

This study examines revenue sharing in sports leagues where franchises engage in multiple types of investments. Previous literature typically treats revenues and investments as homogeneous, but we add to the literature by differentiating between investment types and revenue sources. This is important because investment in talent leads to winning, which is a zero-sum game for the league and therefore owners have an incentive to limit talent investment. However, other investments, such as stadiums, are not a zero-sum game, and therefore the implications of revenue sharing are different for the league. We provide sufficient conditions under which it is more efficient to share media revenue compared to stadium revenue. We conclude by providing applications of this model.