Temporal control of behavior and the power law

The performance of rats and pigeons under fixed-interval schedules was studied in two experiments. The duration of postreinforcement pause was a declining proportion of fixed-interval duration. For pigeons this was true both when the duration of the reinforcer was fixed and when it was increased in direct proportion to increases in fixed-interval duration; the longer reinforcer durations did, however, lengthen the postreinforcement pause at higher schedule values. A quantitative analysis of data from Experiments 1 and 2 and from other studies showed that fractional exponent power functions described the relationship between postreinforcement pause and fixed-interval value; similar functions have previously been observed in studies of temporal differentiation. It was concluded that power functions reflect a direct causal, rather than artifactual, relationship between performance and the temporal requirements of reinforcement schedules.     

Axiomatic and numerical conjoint measurement: An evaluation of diagnostic efficacy

Synthetic data are used to examine how well axiomatic and numerical conjoint measurement methods, individually and comparatively, recover simple polynomial generators in three dimensions. The study illustrates extensions of numerical conjoint measurement (NCM) to identify and model distributive and dual-distributive, in addition to the usual additive, data structures. It was found that while minimum STRESS was the criterion of fit, another statistic, predictive capability, provided a better diagnosis of the known generating model. That NCM methods were able to better identify generating models conflicts with Krantz and Tversky's assertion that, in general, the direct axiom tests provide a more powerful diagnostic test between alternative composition rules than does evaluation of numerical correspondence. For all methods, dual-distributive models are most difficult to recover, while consistent with past studies, the additive model is the most robust of the fitted models.Douglas Emery is now at the Krannert Graduate School of Management, Purdue University, West Lafayette, IN, on leave from the University of Calgary.     

Correctness of Kruskal's algorithms for monotone regression with ties

Kruskal has proposed two modifications of monotone regression that can be applied if there are ties in nonmetric scaling data. In this note we prove Kruskal's conjecture that his algorithms give the optimal least squares solution of these modified monotone regression problems. We also propose another (third) approach for dealing with ties.Comments by Dr. J. B. Kruskal have been most helpful.     

Transformation of a three-mode multidimensional scaling solution to indscal form

Relations between Tucker's three-mode multidimensional scaling and Carroll and Chang's INDSCAL are discussed. The possibility is raised that it may be profitable to attempt to transform a three-mode solution to the general form of an INDSCAL solution. Operationally, this involves transforming the three-mode core matrix so that each section is, as nearly as possible, a diagonal matrix. A technique is developed for accomplishing such a transformation, and is applied to two sets of data from the literature. Results indicate that the process is both feasible and valuable, providing useful information on the relative appropriateness of the two models.     

Fitting and testing carroll's weighted unfolding model for preferences

A quadratic programming algorithm is presented for fitting Carroll's weighted unfolding model for preferences to known multidimensional scale values. The algorithm can be applied directly to pairwise preferences; it permits nonnegativity constraints on subject weights; and it provides a means of testing various preference model hypotheses. While basically metric, it can be combined with Kruskal's monotone regression to fit ordinal data. Monte Carlo results show that (a) adequacy of true preference recovery depends on the number of data points and the amount of error, and (b) the proportion of data variance accounted for by the model sometimes only approximately reflects true recovery.This study is based on a doctoral dissertation submitted to the University of Illinois at Urbana-Champaign. The author wishes to thank the members of his dissertation committee—Lawrence E. Jones, Chairman, Charles Lewis, Stephen Golding, Ledyard Tucker, and Nancy Wiggins—for their helpful comments.     

Maintenance of Relationship and Individual Functioning Gains Following Online Relationship Programs for Low‐Income Couples

Initial evidence suggests that gains in relationship functioning from brief, web‐based programs are maintained through one year following the intervention; however, whether these results generalize to a low‐income sample is unclear. Furthermore, previous research from in‐person couple therapy suggests there may be different shapes of maintenance slopes for behavioral versus acceptance‐based techniques. This study contacted 668 individuals who enrolled in online behavioral (ePREP) or acceptance‐based (OurRelationship) programs one year following completion of the program. Multilevel modeling was used to examine linear and quadratic rates of change in the year following the online intervention as well as total amount of change from pretreatment to 12‐month follow‐up for both relationship and individual functioning. The majority of couples who responded continued to be in a relationship with the same partner (68.3%). Examinations of relationship functioning indicated couples in both programs maintained their gains over follow‐up (i.e., no significant linear or quadratic changes), with medium‐to‐large within‐group effect sizes from pre‐ to one‐year follow‐up. There were no significant differences in relationship outcomes between OurRelationship and ePREP. Similarly, examinations of individual functioning outcomes indicated couples maintained their gains over follow‐up or continued to improve. In total, couples experienced small‐to‐medium within‐group effect sizes from pretreatment to one‐year follow‐up, with larger effects for individuals who were initially distressed. These results suggest that online programs create lasting change for low‐income couples in relationship and individual functioning, with minimal differences between behavioral and acceptance‐based orientations.     

A time series analysis of the relation between motor skill acquisition and sleep in infancy

To systematically examine the relation between motor milestone onset and disruption of night sleep in infancy, three families kept microgenetic, prospective, daily checklist diaries of their infants’ motor behavior and sleep (197-313 observation days; 19,000 diary entries). Process control and interrupted time series analyses examined whether deviations from the moving average for night wakings and evening sleep duration were temporally linked to motor skill onset and tested for meaningful differences in individual sleep patterns before and after skill onset. Model assumptions defined skill onset as first day of occurrence or as mastery and moving average windows as 3, 7, or 14 days. Changes in infants’ sleep patterns were associated with changing expertise for motor milestones. The temporal relation varied depending on infant and sleep parameter. Intensive longitudinal data collection may increase our understanding of micro-events in infant development.     

Parents’ postnatal depressive symptoms and their children's academic attainment at 16 years: Pathways of risk transmission

The aim of the study was to examine whether parents’ increased postnatal depressive symptoms predicted children's academic attainment over time and whether the parent–child relationship, children's prior academic attainment, and mental health mediated this association. We conducted secondary analyses on the Avon Longitudinal Study of Parents and Children data (12,607 mothers, 9,456 fathers). Each parent completed the Edinburgh-Postnatal Depression Scale at 8 weeks after the child's birth (predictor) and a questionnaire about the mother–child and father–child relationship at 7 years and 1 month (mediator). The children's mental health problems were assessed with the teacher version of the Strengths and Difficulties Questionnaire at 10–11 years (mediator). We used data on the children's academic attainment on UK Key Stage 1 (5–7 years; mediator) and Key Stage 4 (General Certificate of Secondary Education 16 years) (outcome). We adjusted for the parents’ education, and child gender and cognitive ability. The results revealed that parents’ depressive symptoms at 8 weeks predicted lower academic performance in children at 16 years. Mothers’ postnatal depressive symptoms had an indirect effect through children's mental health problems on academic outcomes at 16 years via negative mother–child relationship, and prior academic attainment. There was a significant negative indirect effect of fathers’ postnatal depressive symptoms on academic attainment at 16 years via negative father–child relationship on child mental health. The findings suggest that the family environment (parental mental health and parent–child relationship) and children's mental health should be potential targets for support programmes for children of depressed parents.     

Assessing depressive symptoms with the Borg centiMax Scale® in a Swedish sample of patients and students

The Borg centiMax Scale, is a psychophysically composed general intensity ratio scale, which could enable more precise inter- and intraindividual comparisons of the intensity of depressive symptoms. In the present study, the properties of the centiMax scale were examined in 38 patients with clinical depression and 109 students. Additionally, preliminary centiMax cut-off scores for mild, moderate and severe depression were estimated. The psychometric properties of the centiMax were found to be satisfactory regarding internal consistency, convergent, discriminative and predictive validity. Moreover, the centiMax was demonstrated to provide meaningful comparisons of symptom intensity, which makes it possible to evaluate the relative importance of individual symptoms in a profile and make more precise comparisons within and between individuals. With regard to intraindividual comparisons, patients rated , for example, the intensity of feeling “guilt” twice as strong as feelings of “being punished,” and the intensity of “loss of pleasure” almost three times as strong as “being punished.” With regard to interindividual comparisons, patients rated e.g., the intensity of “being punished” as 12 times stronger than controls, and the intensity of “worthlessness” about nine times stronger. In conclusion, the centiMax was shown to be reliable and valid for assessing depressive symptoms. The centiMax with level anchored ratio data, appears to be highly advantageous as it permits rather precise values of symptom intensity for intra- and interindividual comparisons that could be useful in the diagnostic process and in treatment planning.     

Relative effects of breastfeeding intention and practice on maternal responsiveness

Our objective was to examine the differential effects of antenatal breastfeeding intention (BI) and breastfeeding practice (BP) on maternal postnatal responsiveness. We conducted a secondary analysis of longitudinal data from a subsample of 962 mother–infant dyads from a U.K.-based birth cohort study the Avon Longitudinal Study of Parents and Children. Exposures were BI and BPs measured at 32 weeks of gestation and 18 months’ postpartum. The outcome was maternal responsiveness assessed at 12 months’ postpartum. We used logistic regression analyses unadjusted and adjusted for confounders. Intention to breastfeed was associated with increased odds of postnatal maternal responsiveness independent of BP, adjusted odds ratio (OR) = 2.34, 95% CI [1.42, 3.86]. There was no evidence that BP was an independent predictor of maternal responsiveness, OR = 0.93, 95% CI [0.55, 1.57]. Life-course epidemiology analyses demonstrated that maternal responsiveness is most positive when both BI and BP are present. This is the first population-based study to provide evidence that BI during pregnancy is more strongly associated with maternal postnatal responsiveness than is BP. Further research is needed to understand the determinants of BI in pregnancy and its relationships with maternal responsiveness.