MULTIPLE REGRESSION ANALYSIS APPLIED TO RESIDENTIAL PROPERTIES

An interesting and promising innovation in the assessment of property for tax purposes is the application of multiple regression analysis. Sales prices are regressed on various housing characteristics, and models developed from sold properties are used to generate value estimates for unsold properties. Two important issues relating to the development of such models are (1) the extent to which real estate markets are stable in terms of structural relationships over time, and (2) the extent to which sales prices reflect actual market values. The first issue is important because it affects how current sales must be before they can be used in model development, as well as the amount of information the assessor must collect and maintain on properties. The second issue is important because it concerns the amount of measurement error in the models and the extent to which the assessor/analyst can unambiguously interpret residual variance. These issues are investigated by comparing regression models developed from a sample of properties in Eugene, Oregon, which sold in each of two well separated time periods.     

SENSITIVITY ANALYSIS WITH INTERACTION EFFECTS

The purpose of this paper is to extend the sensitivity analysis methodology as it applies to linear programming. The methodology developed herein is concerned with those changes in a technological coefficient that cause simultaneous changes in the relevant cost coefficients of the objective function. By proceeding from the definitions of feasibility and optimality, the authors develop formulas for determining bounds on the extent to which a technological coefficient, which has a predetermined effect on the corresponding cost coefficient, can vary without changing the optimal set of activities. After the formulas are developed, their use is demonstrated on a product-mix problem. This technique is of interest because changes in the rate at which an input is utilized can be expected to change the cost per unit of a resulting product. This interdependence should be recognized whenever a sensitivity analysis is performed on a technological coefficient of either a cost minimization or a contribution margin maximization problem.     

Digit ratios (2D:4D) as predictors of risky decision making for both sexes

Many important decisions involve financial risk, and substantial evidence suggests that women tend to be more risk averse than men. We explore a potential biological basis of risk-taking variation within and between the sexes by studying how the ratio between the length of the second and fourth fingers (2D:4D) predicts risk-taking. A smaller 2D:4D ratio has been linked to higher exposure to prenatal testosterone relative to estradiol, with men having lower ratios than women. In financially motivated decision-making tasks, we find that men and women with smaller 2D:4D ratios chose significantly riskier options. We further find that the ratio partially explains the variation in risk-taking between the sexes. Moreover, for men and women at the extremes of the digit-ratio distribution the difference in risk-taking disappears. Thus, the 2D:4D ratio partially explains variation in financial risk-taking behavior within and between sexes and offers evidence of a biological basis for risk-taking behavior.     

Assessing the Concept of the ‘Insecure‐Other’ Category in the Cassidy–Marvin Scheme: Changes Between 4 and 6 Years in the English and Romanian Adoptee Study

We set out to explore the meaning of the attachment categories in the Cassidy/Marvin strange situation procedure, as employed in the home, using data from a longitudinal study of children adopted into UK families up to the age of 42 months from Romanian institutions, and of adopted children without the experience of institutional care––both groups being assessed at 4 and 6 years of age. Inter‐rater reliability was found to be good. Security (meaning the use of the parent as a secure base and no negative behavior on reunion) was the modal categorical rating in both the institution‐reared and comparison groups, but the category of anomalous non‐normative behavior (meaning a lack of any ordered attachment behavior as covered by the standard ratings), previously labeled ‘insecure‐other’, was more common in the institution‐reared children. Because this was unassociated with the usual manifestations of insecurity (such as avoidance or resistance) and because it was largely evident in interactions with the stranger, it is concluded that the adjective ‘insecure’ was not appropriate. Although this ‘insecure‐other’ category was associated with disinhibited attachment as reported by parents (meaning a lack of differentiation among adults, a willingness to go off with strangers and a lack of checking back with parents in anxiety‐provoking situations), it did not prove to be a good index of disinhibited attachment because changes over time in the ‘insecure‐other’ category were not associated with changes in the rate of disinhibited attachment. Also, whereas the rate of ‘insecure‐other’ fell markedly in the institution‐reared group between 4 and 6 years of age, it rose in the comparison group, raising queries over its meaning.     

Child custody issues and co‐occurrence of intimate partner violence and child maltreatment: controversies and points of agreement amongst practitioners

The situation of families undergoing separation in a context of co‐occurrence of intimate partner violence (IPV) and child maltreatment raises certain issues related to child custody. The results presented in this paper were collected and analysed within the framework of a qualitative study aiming to identify the principal points of agreement and the main controversies amongst practitioners in several different types of organizations. Focus groups were held with a total of 43 practitioners from six different settings concerned with child custody in cases of co‐occurrence of IPV and child maltreatment. Although they agreed on the importance of ensuring the safety of victims of violence, their views diverged on three points: (1) the importance of preserving the father–child relationship; (2) collaboration between voluntary organizations and semi‐voluntary or legal agencies; and (3) consideration of cultural differences.     

BAYESIAN SUBSET SELECTION AND MODEL AVERAGING USING A CENTRED AND DISPERSED PRIOR FOR THE ERROR VARIANCE

This article proposes a new data‐based prior distribution for the error variance in a Gaussian linear regression model, when the model is used for Bayesian variable selection and model averaging. For a given subset of variables in the model, this prior has a mode that is an unbiased estimator of the error variance but is suitably dispersed to make it uninformative relative to the marginal likelihood. The advantage of this empirical Bayes prior for the error variance is that it is centred and dispersed sensibly and avoids the arbitrary specification of hyperparameters. The performance of the new prior is compared to that of a prior proposed previously in the literature using several simulated examples and two loss functions. For each example our paper also reports results for the model that orthogonalizes the predictor variables before performing subset selection. A real example is also investigated. The empirical results suggest that for both the simulated and real data, the performance of the estimators based on the prior proposed in our article compares favourably with that of a prior used previously in the literature.     

DENSITY ESTIMATION FOR CLUSTERED DATA

The commonly used survey technique of clustering introduces dependence into sample data. Such data is frequently used in economic analysis, though the dependence induced by the sample structure of the data is often ignored. In this paper, the effect of clustering on the non-parametric, kernel estimate of the density, f(x), is examined. The window width commonly used for density estimation for the case of i.i.d. data is shown to no longer be optimal. A new optimal bandwidth using a higher-order kernel is proposed and is shown to give a smaller integrated mean squared error than two window widths which are widely used for the case of i.i.d. data. Several illustrations from simulation are provided.     

Estimation of relaxation time distributions in magnetic resonance imaging

Magnetic resonance imaging techniques can be used to measure some biophysical properties of tissue. In this context, the T₂ relaxation time is an important parameter for soft‐tissue contrast. The authors develop a new technique to estimate the integral of the distribution of T₂ relaxation time without imposing any constraint other than the monotonicity of the underlying cumulative relaxation time distribution. They explore the properties of the estimation and its applications for the analysis of breast tissue data. As they show, an extension of linear discriminant analysis is found to distinguish well between two classes of breast tissue.     

Random regression models for human immunodeficiency virus ribonucleic acid data subject to left censoring and informative drop-outs

Objectives in many longitudinal studies of individuals infected with the human immunodeficiency virus (HIV) include the estimation of population average trajectories of HIV ribonucleic acid (RNA) over time and tests for differences in trajectory across subgroups. Special features that are often inherent in the underlying data include a tendency for some HIV RNA levels to be below an assay detection limit, and for individuals with high initial levels or high ranges of change to drop out of the study early because of illness or death. We develop a likelihood for the observed data that incorporates both of these features. Informative drop-outs are handled by means of an approach previously published by Schluchter. Using data from the HIV Epidemiology Research Study, we implement a maximum likelihood procedure to estimate initial HIV RNA levels and slopes within a population, compare these parameters across subgroups of HIV-infected women and illustrate the importance of appropriate treatment of left censoring and informative drop-outs. We also assess model assumptions and consider the prediction of random intercepts and slopes in this setting. The results suggest that marked bias in estimates of fixed effects, variance components and standard errors in the analysis of HIV RNA data might be avoided by the use of methods like those illustrated.     

Consistent Estimation of the Structural Distribution Function

Motivated by problems in linguistics we consider a multinomial random vector for which the number of cells N is not much smaller than the sum of the cell frequencies, i.e. the sample size n . The distribution function of the uniform distribution on the set of all cell probabilities multiplied by N is called the structural distribution function of the cell probabilities. Conditions are given that guarantee that the structural distribution function can be estimated consistently as n increases indefinitely although n / N does not. The natural estimator is inconsistent and we prove consistency of essentially two alternative estimators.