Influential observations in principal component analysis:a case study

A number of results have been derived recently concerning the influence of individual observations in a principal component analysis. Some of these results, particularly those based on the correlation matrix, are applied to data consisting of seven anatomical measurements on students. The data have a correlation structure which is fairly typical of many found in allometry. This case study shows that theoretical influence functions often provide good estimates of the actual changes observed when individual observations are deleted from a principal component analysis. Different observations may be influential for different aspects of the principal component analysis (coefficients, variances and scores of principal components); these differences, and the distinction between outlying and influential observations are discussed in the context of the case study. A number of other complications, such as switching and rotation of principal components when an observation is deleted, are also illustrated.     

Dropouts and continuers in Gamblers Anonymous: Part 3: Some possible specific reasons for dropout

This is the third part of a study of dropouts from Gamblers Anonymous, the overall design, aims and rationale of which are outlined in part one. Dropouts who had attended more than one meeting were asked about many specific aspects of their experience in Gamblers Anonymous. These reports are compared with similarly obtained reports from a group of continuing attendees who had not gambled for more than one year in an attempt to explore the viability of many specific hypotheses as to the possible factors in dropout.     

Effect of blocking on estimation of response surface

The conditions under which experimental trials are performed may not, in general, be homogeneous. However, it may be possible to achieve a greater degree of homogeneity by carying out limited groups—or block—of trials. In this case, when fitting a response surface model, the least squares estimates of the model's parameters will generally depend on how the response surface design is blocked. The purpose of this article is to demonstrate the effects of the blocks on estimating the mean response, on the prediction variance and on the optimum of the response surface. These are all shown to be affected by the sizes of the blocks and the allocation of experimental runs to the blocks. In particular, the prediction variance increases as a result of blocking. In the special case of an orthogonally blocked design, the least squares estimates of the fitted model's parameters remain unchanged by the block effect, except possibly for the intercept. The increase in the prediction variance in this case depends only on the sizes of the blocks. A numerical example is also given.     

Familial spinal shape

It has been proposed that there is a familial relationship in the shape of the spine. This paper describes a pilot study investigating familial shape in the sagittal plane (side view), using three data sets of normal Leeds schoolchildren. The study is exploratory in nature, because only small samples were available. Data acquisition was by means of the Quantec system, which obtains surface shape measurements and extracts a line representing the spinal curve. The coordinates of the spine line in the sagittal plane are then used to investigate familial correlations of spinal shape. The spine lines first undergo some preprocessing, including Procrustes rotations to remove location, rotation and size effects. Smoothed principal component analysis of the curves provides suitable shape variables, and familial correlations between curves are then investigated. The covariates of sex and height are also investigated in the analysis. It does appear that there could be some evidence for familial correlations in sagittal spinal shape, although a further large-scale study is required. Finally, a discussion of the approach and other alternatives is considered.     

A Tale of Two Border Cities: Community Context,Ethnicity, and Homicide*

Objective. Using Poisson‐based negative binomial regression, we estimate the effect of neighborhood factors on homicides in two cities (San Antonio, Texas and San Diego, California) that have large Mexican‐origin populations. Methods. Three independent data sources (official homicide police reports, medical examiner records, and the U.S. Census) are used to construct the dependent homicide, and independent neighborhood, variables. Census tracts represent the unit of analysis, which serve as a proxy for neighborhoods. Given the spatial nature of the data, spatial estimation procedures were also modeled. Results. Spatial proximity to violence, neighborhood disadvantage, and affluence (in San Antonio) consistently buffered homicide across neighborhoods, even in heavily populated Latino neighborhoods. Conclusions. Spatial embeddedness and neighborhood characteristics are important for improving our understanding about ethnic neighborhood variations in levels of violence. Comparative approaches across places, namely, Latino‐dominated cities, can yield considerable insight into how the local context intersects race/ethnicity and violent crime.     

The Benefits of Congruence

This study examined the relation between 3 aspects of congruence (vocational, leisure, and skill utilization) and 6 well-being (or strain) measures (occupational satisfaction, work satisfaction, anxiety, burnout, somatic complaints and self-esteem). The study was conducted among 120 participants (lawyers, psychologists, and physicians). Findings were that (a) correlations among the congruence aspects ranged between .24 and .36, (b) all correlations between each of the congruence aspects and each of the well-being measures were in the expected direction, and (c) all 3 congruence aspects showed an additive effect on all well-being measures. Thus, supportive evidence for the benefits of congruence in its broader meaning was found.