An alternating least squares method for the weighted approximation of a symmetric matrix

Bailey and Gower examined the least squares approximationC to a symmetric matrixB, when the squared discrepancies for diagonal elements receive specific nonunit weights. They focussed on mathematical properties of the optimalC, in constrained and unconstrained cases, rather than on how to obtainC for any givenB. In the present paper a computational solution is given for the case whereC is constrained to be positive semidefinite and of a fixed rankr or less. The solution is based on weakly constrained linear regression analysis.The authors are obliged to John C. Gower for stimulating this research.     

A maximum likelihood method for latent class regression involving a censored dependent variable

The standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored. This model is generalized by developing a conditional mixture, maximum likelihood method for latent class censored regression. The proposed method simultaneously estimates separate regression functions and subject membership in K latent classes or groups given a censored dependent variable for a cross-section of subjects. Maximum likelihood estimates are obtained using an EM algorithm. The proposed method is illustrated via a consumer psychology application.     

Ecumenism and Global Governance

On 21 June 2018, on his 23rd international journey, Pope Francis travelled to Geneva to commemorate the 70th anniversary of the founding of the World Council of Churches. The Swiss city also hosts a large number of representative international institutions dealing with global governance and the issues of peace, human rights, and migration. After reviewing the main highlights of the journey, this article discusses its significance: to appeal to the common commitment of Christians to proclaim the gospel and its power of salvation in a divided and wounded world. In this way, Pope Francis underlined that in the pluralistic society of today, harmony is not possible if we just ignore faith and focus on what it means to be human while excluding the transcendent. Indeed, it is the gospel that promotes harmony and commitment to a better world.     

Toward a New Concept of Global Morality

The human community faces today the most serious challenges ever to have confronted the planet in the areas of health, environment, and security. Science and technology are essential for responding to these challenges. More is needed, however, because science is not equipped to deal adequately with the values dimensions and the political issues that accompany the challenges. For an adequate response, there must be cooperative effort by scientists and statespersons, informed for moral leadership by the religious wisdom that is available. The religious communities can provide this spiritual dimension, thereby fulfilling their traditional role, but it will require their coming to terms with the character of the scientific and technological base of contemporary culture. The paper lays the conceptual groundwork for understanding these issues.