The number of paths and cycles in a digraph

An algorithm is presented for constructing from the adjacency matrix of a digraph the matrix of its simplen-sequences. In this matrix, thei, j entry,i j, gives the number of paths of lengthn from a pointv _i to a pointv _j ; the diagonal entryi, i gives the number of cycles of lengthn containingv _i . The method is then generalized to networks—that is, digraphs in which some value is assigned to each line. With this generalized algorithm it is possible, for a variety of value systems, to calculate the values of the paths and cycles of lengthn in a network and to construct its value matrix of simplen-sequences. The procedures for obtaining the two algorithms make use of properties of a line digraph—that is, a derived digraph whose points and lines represent the lines and adjacency of lines of the given digraph.The research reported here was supported by Grant NSF-G-17771 from the National Science Foundation. We wish to thank Professor Frank Harary for suggesting certain ways of improving an earlier draft of this paper.     

A note on a matrix criterion for unique colorability of a signed graph

A signed graph,S, is colorable if its point set can be partitioned into subsets such that all positive lines join points of the same subset and all negative lines join points of different subsets.S is uniquely colorable if there is only one such partition. Developed in this note is a new matrix, called thetype matrix ofS, which provides a classification of the way pairs of points are joined inS. Such a classification yields a criterion for colorability and unique colorability.The work reported here was supported by Grant MH 10834 from the National Institute of Mental Health.     

Whither the Epidemic? Psychoactive Drug-Use Career Patterns of College Students1

Reported nonmedical use and intentions for future use of eight groups of psychoactive drugs were conceptualized and arrayed to represent a person's usage career. Intentions closely predicted usage eight months later. Changes in careers were analyzed from data obtained in surveys of all students at a univeristy in 1968 and three follow-up surveys of the class of 1972. In 1968, the most common order of extent of use of the drug groups was: beer, hard liquor, tobacco, cannabis, depressants, amphetamines, hallucinogens, and narcotics. Students' starting, usage, and intent patterns for the drugs displayed hierarchical, Guttman-like, scalability in approximately this order. Intentions to progress to new drugs on the scale were strong in all classes in 1968. In the class of 1972, however, despite growing experience with the less common drugs as they went through college, intentions to return to more common drugs grew and intentions to progress to new ones decreased, relative to both themselves as freshmen and to equivalent level classes in 1968. The pattern of these changes suggests that it is hazardous to extrapolate from early usage and intent data in predicting the long-term course of usage.     

An item response theory analysis of DSM-IV personality disorder criteria across younger and older age groups

Many of the Diagnostic and Statistical Manual of Mental Disorders, 4th edition (DSM-IV; American Psychiatric Association, 1994) personality disorder (PD) diagnostic criteria focus on a younger social and occupational context. The absence of age-appropriate criteria for older adults forces researchers and clinicians to draw conclusions based on existing criteria, which are likely inadequate. To explore which DSM-IV PD criteria contain age group measurement bias, the authors report 2 analyses of data on nearly 37,000 participants, ages 18-98 years, taken from a public data set that includes 7 of the 10 PDs (antisocial, avoidant, dependent, histrionic, obsessive-compulsive, paranoid, and schizoid). The 1st analysis revealed that older age groups tend to endorse fewer PD criteria than younger age groups. The 2nd analysis revealed that 29% of the criteria contain measurement bias. Although the latent variable structure for each PD was quite similar across younger and older age groups, some individual criteria were differentially endorsed by younger and older adults with equivalent PD pathology. The presence of measurement bias for these criteria raises questions concerning the assessment of PDs in older adults and the interpretation of existing data.     

Recognizing young children in need of mental health assessment: Development and preliminary validity of the early childhood screening assessment

The Early Childhood Screening Assessment (ECSA) is a primary care screening measure developed to identify very young children (1½–5 years old) who need further emotional or behavioral assessment. The ECSA was developed specifically to meet the logistical constraints of primary care settings. This study assessed the preliminary psychometric properties of the ECSA by comparing it with extant validated measures of young children's emotional and behavioral development, comparing it with a diagnostic interview, and measuring test‐retest reliability. In the study, 309 mothers in two primary care clinics completed the ECSA and the Child Behavior Checklist (CBCL; T. Achenbach & L. Rescorla, 2000). A subset (n = 69) also completed the Diagnostic Interview for the Preschool Age (DIPA; M. Scheeringa & N. Haslett, 2010). ECSA score correlated significantly and strongly with the CBCL Total Problem T score (Spearman's rho = 0.86, p ? .01). The ECSA was 86% sensitive and 83% specific in identifying DIPA diagnoses. Internal consistency of the ECSA was 0.91. Test‐retest reliability at 10 days was excellent (Spearman's rho = 0.81, p ? .01). The ECSA is an easy‐to‐use screening measure that demonstrates strong convergent validity, criterion validity, and test‐retest reliability in the pediatric setting. It shows potential as a feasible and psychometrically strong tool for busy primary care providers to identify preschoolers who need further socioemotional assessment.     

Relationship influences on teachers' perceptions of academic competence in academically at-risk minority and majority first grade students

This study examined the associations among child demographic variables, teacher perceptions of parent-teacher and student-teacher relationship quality, and teacher perceptions of children's academic abilities in an ethnically diverse sample of 607 academically at-risk first grade children. Relative to relationships with African American children and parents, teachers rated their relationships with White and Hispanic children and parents more positively. Measures of relationship quality added unique variance to teachers' perceptions of children's abilities, controlling for parent educational level and measured ability. Relationship variables fully mediated the association between African American status and teachers' perceptions of children's abilities. Implications of the findings for teacher in-service and professional development and for parent involvement programs are discussed.     

A paired compositions model for round-robin experiments

Investigation of the effects of a series of treatment conditions upon some social behaviors may require observation of a set of subjects which have been mutually paired, in round-robin fashion. Data arising from such experiments are difficult to analyze, partly because they do not fit neatly into standard designs. A paired compositions scaling model due to Bechtel is adapted to provide a linear model for such round-robin experiments. Both fixed and mixed versions of the model are considered and some results of a Monte Carlo study of the mixed model are reported. The model is applied to illustrative data from the field of physiological psychology.     

Improving the metric quality of questionnaire data

A procedure is proposed whereby questionnaire data, which is usually ordinal in nature and often error-ridden, may be transformed to reduce the error variance in the data and to improve the metric properties of the individual variables. The technique is suggested by a result of Eckart and Young. The properties of the method are investigated by means of a Monte Carlo study. Various matrices were generated representing the usual concept of true scores. These matrices were distorted using two levels of random errors and two kinds of categorization. The distorted matrices were in turn transformed by the proposed methods and compared to the true scores. In all cases an overall measure of similarity reveals the transformed matrices are better approximations to the true scores than the untransformed data. Some properties of the transformation are discussed and some possible applications of the general technique are suggested.