Testing regression lack of fit without replication: a tutorial around Minitab's XLOF procedures

The tutorial is concerned with two types of test for the general lack of fit of a linear regression model, as found in the Minitab software package, and which do not require replicated observations. They aim to identify non-specified curvature and interaction in predictors, by comparing fits over the predictor region divided into two parts. Minitab's regression subcommand XLOF which gives the tests is only briefly documented in the manual and, unlike virtually all other statistical procedures in the software, it is not standard and cannot be readily found in textbooks. The two types of test are described here; they concern the predictors one-at-a-time and the predictors all-at-once. An example of their use is given. A suite of macros is available which reproduces the results of the XLOF tests in much more detail than is given by the XLOF subcommand.     

“Entering the developmental spiral the work of Michael F. Basch applied to clinical social work

Entering the developmental spiral through affect attunement reactivates and revitalizes the thrust to continue development when it has been fixated, distorted or derailed. Achieving affect attunement is a vital dimension of the healing process. Basch describes how affect stimulates and controls the ordering and pattern matching function of the brain, motivating behavior and relationships. These theories are examined in selected vignettes illustrating the manner in which we seek to free individuals from stalemate in relationships, destructive behavior or depressive states.     

AN ALGORITHM FOR THE CONSTRUCTION OF OPTIMAL OR NEAR-OPTIMAL CHANGE-OVER DESIGNS

This paper presents an algorithm for the construction of optimal or near optimal change-over designs for arbitrary numbers of treatments, periods and units. Previous research on optimality has been either theoretical or has resulted in limited tabulations of small optimal designs. The algorithm consists of a number of steps:first find an optimal direct treatment effects design, ignoring residual effects, and then optimise this class of designs with respect to residual effects. Poor designs are avoided by judicious application of the (M, S)-optimality criterion, and modifications of it, to appropriate matrices. The performance of the algorithm is illustrated by examples.     

Membranes, mitochondria and amoebae: shape models

Most real-world shapes and images are characterized by high variability- they are not rigid, like crystals, for example—but they are strongly structured. Therefore, a fundamental task in the understanding and analysis of such image ensembles is the construction of models that incorporate both variability and structure in a mathematically precise way. The global shape models introduced in Grenander's general pattern theory are intended to do this. In this paper, we describe the representation of two-dimensional mitochondria and membranes in electron microscope photographs, and three-dimensional amoebae in optical sectioning microscopy. There are three kinds of variability to all of these patterns, which these representations accommodate. The first is the variability in shape and viewing orientation. For this, the typical structure is represented via linear, circular and spherical templates, with the variability accomodated via the application of transformations applied to the templates. The transformations form groups: scale, rotation and translation. They are locally applied throughout the continuum and of high dimension. The second is the textural variability; the inside and outside of these basic shapes are subject to random variation, as well as sensor noise. For this, statistical sensor models and Markov random field texture models are used to connect the constituent structures of the shapes to the measured data. The third variability type is associated with the fact that each scene is made up of a variable number of shapes; this number is not assumed to be known a priori. Each scene has a variable number of parameters encoding the transformations of the templates appropriate for that scene. For this, a single posterior distribution is defined over the countable union of spaces representing models of varying numbers of shapes. Bayesian inference is performed via computation of the conditional expectation of the parametrically defined shapes under the posterior. These conditional mean estimates are generated using jump-diffusion processes. Results for membranes, mitochondria and amoebae are shown.     

The impact of unionization,right-to-work laws,and female labor force participation on earnings inequality across states

This study examines the effect of unionization, right-to-work laws, and participation of women in the labor force on income inequality. Two distinct models are developed using 1970 and 1980 census data on the 50 states in the U.S. First, an income inequality model is specified as a beta distribution of the second kind to estimate Gini measures of income inequality. Second, these Gini estimates are used in a simultaneous equations model. The 1970 results indicate that higher unionization rates decreased inequality while right-to-work laws increased inequality. In 1980, the measure of inequality was lower in states with higher female labor force participation. We thank an unknown referee and the editor for comments and criticisms that greatly improved the paper. The usual caveat applies.     

ASKING THREATENING QUESTIONS AND SITUATIONAL FRAMING:

Although surveys are extensively used in sociology, there has been a relative neglect of the effect of task definition upon results obtained. The present article examines the effects of one such task variable, length and specificity of the cue, on response sets concerning the frequency and quantity of alcohol consumed. In one survey format, respondents were asked to report the average number of days drinking per month, and the average number of drinks consumed on each of these occasions. In the second format, questions concerning the monthly frequency of alcohol consumption and quantity consumed were decomposed by twelve drinking locations. The results indicate dramatic increases both in terms of frequency and quantity between the two questionnaire formats. Implications of these results are discussed within the framework of the methodological phenomena of telescoping and the social psychological tendency to under-report threatening behaviors.     

The impact of child care on fertility in urban Thailand

Women’s labor force participation in Thailand, particularly in the modem sector, recently has increased in conjunction with rapid declines in fertility. This paper examines whether a relationship exists between child care considerations and fertility decision making among Bangkok women. Although the two-child family has become the norm in recent years, and although most respondents said that ideally they would like to have two children, a high proportion of women surveyed said they planned to only have one child. Women’s work status and type of employment is found to strongly affect the likelihood of having a second birth: those who work at jobs that not only are low-paying but are located in a formal setting are least likely to have a second child. The type of child care for the first child also has an impact: those whose first child is in a less preferred situation are less likely to have a second. Variables measuring the need for and type of child care are found to have greater consequences for fertility than do usual measures of socioeconomic status.     

On the existence and uniqueness of maximizers of two likelihood functions

While applying theclassical maximum likelihood method for a certain statistical inference problem, Smith and Weissman [5] have noted that there are conditions under which the likelihood function may be unbounded above or may not possess local maximizers. Ariyawansà and Templeton [1] have derived inference procedures for this problem using the theory of structural inference [2,3,4]. Based on numerical experience, and without proof, they state that the resulting likelihood functions possess unique, global maximizers, even in instances where the classical maximum likelihood method fails in the above sense. In this paper, we prove that under quite mild conditions, these likelihood functions that result from the application of the theory of structural inference are well-behaved, and possess unique, global maximizers. This research was supported in part by the Applied Mathematical Sciences subprogram of the U.S. Department of Energy under contract W-31-109-Eng-38 while the author was visiting the Mathematics and Computer Science Division of Argonne National Laboratory, Argonne, Illinois.