Testing equality of generalized variances of k multivariate normal populations

Generalized variance is a measure of dispersion of multivariate data. Comparison of dispersion of multivariate data is one of the favorite issues for multivariate quality control, generalized homogeneity of multidimensional scatter, etc. In this article, the problem of testing equality of generalized variances of k multivariate normal populations by using the Bartlett's modified likelihood ratio test (BMLRT) is proposed. Simulations to compare the Type I error rate and power of the BMLRT and the likelihood ratio test (LRT) methods are performed. These simulations show that the BMLRT method has a better chi-square approximation under the null hypothesis. Finally, a practical example is given.     

Analyzing the Dimensionality of Place Attachment and Its Relationship with Residential Satisfaction in New Cities: The Case of Sadra,Iran

Social Indicators Research - During the recent decades, new cities have been set up around Iranian main cities, after exclusive pre-planning and investigations. However, no significant research...     

Typology of causes of poverty: The perception of Iranian farmers

Causal attributions are important mediators of future behaviour because once a cause is assigned; a commensurate action can be taken. The aims of this research were to find how Iranian farmers attribute the causes of poverty, to provide a typology of attribution of causes of poverty as perceived by Iranian farmers and to compare socio-economic characteristics and contextual conditions of farmers based on their causal attribution of poverty type. Findings revealed that 50% of respondents had structuralistic, almost 30% had individualistic, and about 20% hold fatalistic attitudes towards the causes of poverty. Farmers with individualistic attitudes towards the causes of poverty had higher quality of life, well-being, level of agricultural technology, agricultural production, used insurance more often, they had more land, income, access to agricultural extension services and practiced sustainable agriculture more often. Farmers with fatalistic attitudes towards the causes of poverty had the worst condition with regard to the above variables. However, those who had structuralistic attitudes, stood somewhere between the two previous groups. Based on findings, a number of poverty alleviation recommendations are made.     

Combining Qualitative and Quantitative Methods in the Measurement of Rural Poverty: The Case of Iran

Poverty reduction is one of the major challenges confronting mankind and a principal obstacle to well-being for a large proportion of the world’s population. New paradigms of development as advocated by Chambers and others focus strongly on poverty reduction. Poverty is increasingly recognised as a multifaceted concept that can be elucidated through both qualitative and quantitative analysis. In researching poverty it is desirable to recognise both the value position of researchers and the values of local people. This paper uses qualitative and quantitative data and considers both outsiders’ and insiders’ views through the use of participatory approaches in selected rural areas of Iran. A poverty index is constructed and validated in a six-stage process. On the basis of the findings, a number of recommendations are made about appropriate approaches to the investigation of poverty.     

Confidence intervals for product of powers of the generalized variances of k multivariate normal populations

In this paper, some confidence intervals (CIs) for the product of powers of the generalized variances of k multivariate normal populations with possibly different dimensions are proposed. The performance of these CIs in terms of the coverage probabilities and average lengths were evaluated via a Monte Carlo simulation study. The results were found to be satisfactory. To demonstrate utility of the proposed CIs, applications on three real data sets were provided.     

Replacement Decisions for Potentially Hazardous Substances

As public awareness of environmental hazards increases, a growing concern for corporations is the potential negative environmental impact of their products and the chemicals these products contain. In this study, we analyze the optimal decisions of a firm when a substance within its product is identified as potentially hazardous. Although the substance is not currently regulated, regulation may occur in the future. Therefore, the firm must devise a strategy for the development and implementation of a replacement substance. In an environment where replacement costs can be millions of dollars, regulation is uncertain, and both consumer and non‐governmental organization pressures exist, a carefully developed plan that balances costs and risks is critical for a firm. Our results demonstrate that as long as a threat of regulation exists, a firm should always dedicate resources toward developing a replacement substance. However, it is not always optimal for a firm to implement a developed replacement. Regarding competitive dynamics, we find that competition between firms can offset a low chance of a shift in consumer perception about a substance and compel firms to replace; however, competition can lead to inefficient outcomes in which firms incur avoidable costs to implement ahead of potential regulation.     

Performance evaluation of likelihood-ratio tests for assessing similarity of the covariance matrices of two multivariate normal populations

Abstract

In analyzing two multivariate normal data sets, the assumption about equality of covariance matrices is usually used as a default for doing subsequence inferences. If this equality doesn’t hold, later inferences will be more complex and usually approximate. If one detects some identical components between two decomposed non equal covariance matrices and uses this extra information, one expects that subsequence inferences can be more accurately performed. For this purpose, in this article we consider some statistical tests about the equality of components of decomposed covariance matrices of two multivariate normal populations. Our emphasis is on the spectral decomposition of these matrices. Hypotheses about the equalities of sizes, shapes, and set of directions as components of these two covariance matrices are tested by the likelihood ratio test (LRT). Some simulation studies are carried out to investigate the accuracy and power of the LRT. Finally, analyses of two real data sets are illustrated.