Some aspects of bivariate regression subject to linear constraints

This paper considers a two-equation linear model when a subset of the parameters in one of the equations is subject to zero constraints. Inference procedures are presented both in the Bayesian and sampling theory framework. Specifically, posterior distributions and confidence distributions of the parameters, as well as various test procedures, are derived and illustrated with examples. The effect of the zero constraints on these procedures are discussed, and a comparison of the Bayesian with the sampling results is given.     

Occupation and the journey-to-work: Some further analysis

This paper examines the impact of occupation upon commuting distances in the Toronto Census Metropolitan Area (CMA). Specifically, from the residential and job location patterns of each occupational group a “minimum distance” indicator of the degree of job-residence access of each occupational group is developed with the aid of a linear programming transportation model. The differences in “minimum distance” that must be travelled by the members of each occupational group are explained. The actual distances travelled to work by the members of each occupational group are then investigated and attempts are made to separate the determinants of each occupational group's average journey-to-work distance into two main factors—job residence access and propensity to commute. On the basis of the locational patterns, the analysis suggests that job residence access was generally greater for blue-collar workers than for white-collar workers. Although occupation did have an impact, then, on journey-to-work distance through its influence upon locational patterns of job and residence, little evidence of its effect on the propensity to commute was found. Rather, the results suggest that the main determinant of this factor was sex since female workers exhibited a far lower disposition to commute than did their male counterparts.     

Company size,environmental regulation and ecological modernization: further analysis at the level of the firm

In the paper published in Business Strategy and the Environment (7, (3)) entitled ‘Sector variation and ecological modernization: towards an analysis at the level of the firm’, the authors situated their analysis of firms within the framework of ecological modernization. They indicated the part which sector variability plays in firms positioning themselves towards environmental issues. In this paper, the authors extend their analysis to consider the effects that environmental regulation and company size have on the levels of environmental motivation demonstrated by companies and what this reveals about the prospects for a move towards ecological modernization. © 1998 John Wiley & Sons, Ltd and ERP Environment.     

Conditional regression analysis

This article deals with the question of whether the inclusion of multiplicative terms to model conditional effects in multiple regression is legitimate. The major arguments in the controversy relating to this subject are reviewed. The main conclusion is that most of the objections against multiplicative terms are based on misinterpretations of the coefficients of conditional models. For the often-ignored possible numerical problems in the estimation of these models, due to multicollinearity, an indirect estimation technique is proposed. The potentials of conditional regression analysis are demonstrated on a concrete example.     

Some aspects of testing non-nested hypotheses

This paper examines some aspects of testing non-nested hypotheses. An inequality between the Cox and Atkinson statistics is noted, and the necessary and sufficient condition for the Atkinson test to be consistent is derived. A new test procedure is also outlined. The rest of the paper illustrates the various test statistics, their properties, and relationships for competing linear regression models.     

On multiple regression analysis

The sums of squares associated with the independent variables in a multiple regression equation depend on the order in which these variables are introduced. Two methods have been proposed in the literature to avoid this inconvenience: "forward selection" or "backward elimination".
With forward selection the independent variables are introduced in successive stages. The order is not predetermined but at each stage that variable is taken as the next one which produces the highest reduction in the residual sum of squares of the dependent variable.
With backward elimination on the other hand, we start with the complete regression equation and eliminate the independent variables from it in the order in which they produce the smallest increases in the residual sum of squares.
This paper describes a simple and convenient computational lay-out which can be used for both procedures. In forward selection we start with the matrix of product sums, and in bacward elimination we work from the inverse matrix.
In addition these techniques are applied to a variety of practical examples in order to see what results they lead to and what pitfalls may be encountered.     

Some computational aspects of a trimloss problem

In dit artikel wordt het probleem van de afvalbeperking behandeld, dat bij het snijden van papier en andere materialen optreedt. Het blijkt, dat in het geval dat de schrijvers bestudeerden, de lineaire programmerings-matrix sterk kon worden vereenvoudigd door toepassing van een gemakkelijk hanteerbaar criterium.
Voorts wordt ingegaan op het vinden van de begin-oplossing en het verdere verloop van het iteratieproces     

Some economic aspects of industrial democracy*

Laurence Hunter argues that although there has been some reference to economic questions in the debate on industrial democracy, they have not received the attention that they deserve. Rather than to provide answers, the purpose of his article is to highlight the importance of the questions, in the hope that others might be encouraged to accept the presented challenge.     

Some aspects of analysis of variance and covariance theory for a certain multivariate complex gaussian distribution

Summary In this paper we consider some aspects of analysis of variance and covariance theory for the complex normal distribution introduced byGoodman (1963). The properties which we consider are similar to those in the real case.Goodman (1963), andKhatri (1965) have studied several other properties of the complex normal model and have pointed out the similarity between the real and the complex case.     

Robustness issues in multilevel regression analysis

A multilevel problem concerns a population with a hierarchical structure. A sample from such a population can be described as a multistage sample. First, a sample of higher level units is drawn (e.g. schools or organizations), and next a sample of the sub‐units from the available units (e.g. pupils in schools or employees in organizations). In such samples, the individual observations are in general not completely independent. Multilevel analysis software accounts for this dependence and in recent years these programs have been widely accepted. Two problems that occur in the practice of multilevel modeling will be discussed. The first problem is the choice of the sample sizes at the different levels. What are sufficient sample sizes for accurate estimation? The second problem is the normality assumption of the level‐2 error distribution. When one wants to conduct tests of significance, the errors need to be normally distributed. What happens when this is not the case? In this paper, simulation studies are used to answer both questions. With respect to the first question, the results show that a small sample size at level two (meaning a sample of 50 or less) leads to biased estimates of the second‐level standard errors. The answer to the second question is that only the standard errors for the random effects at the second level are highly inaccurate if the distributional assumptions concerning the level‐2 errors are not fulfilled. Robust standard errors turn out to be more reliable than the asymptotic standard errors based on maximum likelihood.     

Bayesian regression analysis using poly-t densities

Poly-t densities are defined by the property that their kernel is a product, or ratio of products, of Student-t kernels. These multivariate densities arise as Bayesian posterior densities for regression coefficients, under a surprising variety of specifications for the prior density and the data generating process. Although no analytical expression exists for the integrating constant and moments of these densities, these parameters are obtained through numerical integration in a number of dimensions given by the number of Student-t kernels in the numerator, minus one. The paper reviews how poly-t densities arise in regression analysis, and summarizes the results obtained for a number of models.     

Some characterizations of distributions by regression models for ordinal response data

Summary Let a random variableX be classified intok classes. By doing so, a new random variable is obtained, measured on ordinal scale. If this variable is a response variable in certain regression models for ordinal response data, the distribution ofX is characterized by the models. In this paper, characterizations of the distribution ofX by the proportional odds model and the proportional hazards model are given.     

Testing for serial correlation in simultaneous equation models: Some further results

In this paper approximate counterparts of the exact tests earlier proposed by the authors are examined. Type 1 error probabilities and test powers are estimated and compared using Monte Carlo experiments. The effect on the Type 1 error probabilities of the misspecification which results when serial correlation is present elsewhere in the system is also investigated.