Using logistic regression to estimate delay-discounting functions.

The monetary choice questionnaire (MCQ) and similar computer tasks ask preference questions in order to ascertain indifference, the perceived equivalence of immediate versus larger delayed rewards. Indifference data are then fitted with a hyperbolic function, summarizing the decline in perceived value with delay time. We present a fitting method that estimates the hyperbolic parameter k directly from survey responses. Binary preferences are modeled as a function of time (X2) and a transformed reward ratio (X1), yielding logistic regression coefficients beta 2 and beta 1. The hyperbolic parameter emerges as k = beta 2/beta 1, where the logistic predicted p = .5 (the definition of indifference). The MCQ was administered to 1,073 adolescents and was scored using both standard and logistic methods. The means for In(k) were similar (standard, -4.53; logistic, -4.51), and the results were highly correlated (rho = .973). Simulated MCQ data showed that k was unbiased, except where beta 1 > or = -1, indicating a vague survey response. Jackknife standard errors provided excellent coverage.     

Acculturation and Familiarity With, Attitudes Towards and Beliefs about Genetic Testing for Cancer Risk Within Latinas in East Harlem, New York City

Recent research underscores the need for increasing use of genetic testing for cancer risk in Latinos. This study examined the influence of acculturation on attitudes, beliefs about and familiarity with genetic testing for cancer risk in a community-based sample of Latinas in East Harlem, New York City (N = 103). Multivariate linear regression models analyzed the relationship of acculturation to: (1) familiarity (2) perceived benefits (3) perceived barriers and (4) concerns about abuses of genetic testing for cancer risk. Controlling for sociodemographic factors, results revealed that with increasing acculturation Latinas were more familiar with genetic testing (β = 1.62, SE = 0.72, p = 0.03), more likely to cite perceived benefits (β = 1.67, SE = 0.79, p = 0.04), and less likely to report perceived barriers related to genetic testing (β = −2.76, SE = 1.64, p = 0.10). Study results may help inform the development of culturally-appropriate health education outreach materials and programs targeted to increase awareness, knowledge and understanding about genetic testing for cancer risk within Latinas.     

Syntax for calculation of discounting indices from the monetary choice questionnaire and probability discounting questionnaire

The 27‐item Monetary Choice Questionnaire (MCQ; Kirby, Petry, & Bickel, 1999) and 30‐item Probability Discounting Questionnaire (PDQ; Madden, Petry, & Johnson, 2009) are widely used, validated measures of preferences for immediate versus delayed rewards and guaranteed versus risky rewards, respectively. The MCQ measures delayed discounting by asking individuals to choose between rewards available immediately and larger rewards available after a delay. The PDQ measures probability discounting by asking individuals to choose between guaranteed rewards and a chance at winning larger rewards. Numerous studies have implicated these measures in addiction and other health behaviors. Unlike typical self‐report measures, the MCQ and PDQ generate inferred hyperbolic temporal and probability discounting functions by comparing choice preferences to arrays of functions to which the individual items are preconfigured. This article provides R and SPSS syntax for processing the MCQ and PDQ. Specifically, for the MCQ, the syntax generates k values, consistency of the inferred k, and immediate choice ratios; for the PDQ, the syntax generates h indices, consistency of the inferred h, and risky choice ratios. The syntax is intended to increase the accessibility of these measures, expedite the data processing, and reduce risk for error.     

In the Eye of the Beholder: Alcohol Use and Perceptions Among Student-Patrons of ‘Joints’ in Three Nigerian University Communities

Alcohol use and its associated problems among university students have attracted empirical investigation by researchers and scholars. While many of these studies have reported a very high level of alcohol consumption and highlighted the various problems this portends, alcohol-related perceptions of this vulnerable population, which could be germane to intervention aimed at curtailing the problem, have remained largely under-researched. This cross-sectional survey examined the use and perceptions of alcohol by student-patrons (n = 1,705) of beer parlours or ‘joints’ in three university communities in Southwest Nigeria. Respondents were interviewed using AUDIT, a socio-demographic prototype and an open-ended section on alcohol-related perceptions of the students. Findings indicated that overall, 72% of the respondents perceived that alcohol is good for socializing, 68% perceived that alcohol is good in the aspect of stress reduction, 58% believed that alcohol consumption is indicative of maturity, 36% perceived that alcohol enhances their sexual performance while 39% perceived that alcohol serves to enhance alertness/concentration. Results also showed that gender (β = −. 23; p < .05), paternal alcohol use (β = .36; p < .01), parental socio-economic status (β = .33; p < .01), and residential status of university of respondents (β = .21; p < .05) significantly predicted alcohol use. The study concluded that perceptions about alcohol are very germane to understanding students’ alcohol use and should be reckoned with in designing intervention programmes. The need to adopt a ‘client-centered’ approach to the problem of student drinking behaviour was emphasized.     

On the asymptotic distribution of Pearson’s X 2 in cross-validation samples

In categorical data analysis, two-sample cross-validation is used not only for model selection but also to obtain a realistic impression of the overall predictive effectiveness of the model. The latter is of particular importance in the case of highly parametrized models capable of capturing every idiosyncracy of the calibrating sample. We show that for maximum likelihood estimators or other asymptotically efficient estimators Pearson's X ² is not asymptotically chi-square in the two-sample cross-validation framework due to extra variability induced by using different samples for estimation and goodness-of-fit testing. We propose an alternative test statistic, X _xval ², obtained as a modification of X ² which is asymptotically chi-square with C−1 degrees of freedom in cross-validation samples. Stochastically, X _xval ² ≤ X ². Furthermore, the use of X ² instead of X _xval ² with a χ _C −1² reference distribution may provide an unduly poor impression of fit of the model in the cross-validation sample. This paper is dedicated to the memory of Michael V. Levine. Requests for reprints should be sent to Albert Maydeu-Olivares, Faculty of Psychology, University of Barcelona, P. Valle de Hebrón, 171, 0835 Barcelona, Spain.     

Health-Related Quality of Life in a National Sample of Caregivers: Findings from the Behavioral Risk Factor Surveillance System

Purpose Recent national public health agendas, such as Healthy People 2010, call for improved public health surveillance and health promotion programs for people with disabilities and their caregivers. The goal of this study was to understand the public health impact of caregiving on health-related quality of life (HRQoL) using population-level data. Design & Methods A cross-sectional study design was used. 184,450 adults surveyed during the 2000 national Behavioral Risk Factor Surveillance System survey formed the sample. Binary logistic regression models ascertained differences between caregivers and non-caregivers in reporting reduced (“fair” or “poor”) health. Ordinary least squares regression (OLS) and multinomial logistic regression models examined the influence of caregiving status on HRQoL, measured as categories of healthy days reported in the last 30 days and the number of days reported as physical and mental health not good in the last 30 days. Results Sixteen percent (16%) of the survey respondents were caregivers. There was an interaction effect between caregiving status and age of the caregiver. In the fully adjusted models, caregivers <55 years old had a 35% increased risk of having fair or poor health (odds ratio [OR] = 1.35, 95% confidence interval [CI] 1.28, 1.43) as compared to non-caregivers in that age group, while caregivers 55 years and older had a 3% decreased risk in having fair or poor health (OR = 0.97, 95% confidence interval [CI] 0.92, 1.03) compared to non-caregivers of the same age. In the adjusted models that examined the association of caregiving and healthy days, younger caregivers similarly showed larger deficits in both mental and physical HRQoL compared to older caregivers. For example combining mental and physical days, caregivers <55 had 1.44 fewer healthy days (β = −1.44, standard error (SE) = 0.07), while caregivers 55+ had 0.55 fewer days *β = −0.55, standard error (SE) = 0.13 (compared to non-caregivers in their respective age groups). Implications With increasing population age and the projected increase in caregivers, it is important that we understand the social and public health burden of caregiving and begin to identify interventions to sustain the HRQoL of caregivers. We found that caregivers have a slight to modest decline in HRQoL compared to non-caregivers, and that caregiving affects the HRQoL of younger adults more than older adults. Further research at the population level as to the type and level of burden of caregiving is needed.     

Maximization of sums of quotients of quadratic forms and some generalizations

Monotonically convergent algorithms are described for maximizing six (constrained) functions of vectors x, or matricesX with columns x₁, ..., x _r . These functions are h₁(x)= _k (xA _kx)(xC _kx)^–1, H₁(X)= _k tr (XA _k X)(XC _k X)^–1, h₁(X)= _{k l} (x _l A _kx _l ) (x _l C _kx _l )^–1 withX constrained to be columnwise orthonormal, h₂(x)= _k (xA _kx)²(xC _kx)^–1 subject to xx=1, H₂(X)= _k tr(XA _kX)(XA_kX)(XC_kX)^–1 subject toXX=I, and h₂(X)= _{k l} (x _l A _kx _l )² (x _l C _kX _l )^–1 subject toXX=I. In these functions the matricesC _k are assumed to be positive definite. The matricesA _k can be arbitrary square matrices. The general formulation of the functions and the algorithms allows for application of the algorithms in various problems that arise in multivariate analysis. Several applications of the general algorithms are given. Specifically, algorithms are given for reciprocal principal components analysis, binormamin rotation, generalized discriminant analysis, variants of generalized principal components analysis, simple structure rotation for one of the latter variants, and set component analysis. For most of these methods the algorithms appear to be new, for the others the existing algorithms turn out to be special cases of the newly derived general algorithms.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to Jos ten Berge for stimulating this research and for helpful comments on an earlier version of this paper.     

The psychological side of Hempel’s paradox of confirmation

People often test hypotheses about two variables (X andY), each with two levels (e.g.,X1 andX2). When testing “IfX1, thenY1,” observing the conjunction ofX1 andY1 is overwhelmingly perceived as more supportive than observing the conjunction ofX2 andY2, although both observations support the hypothesis. Normatively, theX2&Y2 observation provides stronger support than theX1&Y1 observation if the former is rarer. Because participants in laboratory settings typically test hypotheses they are unfamiliar with, previous research has not examined whether participants are sensitive to the rarity of observations. The experiment reported here showed that participants were sensitive to rarity, even judging a rareX2&Y2 observation more supportive than a commonX1&Y1 observation under certain conditions. Furthermore, participants’ default strategy of judgingX1&Y1 observations more informative might be generally adaptive because hypotheses usually regard rare events.     

A generalization of coefficient alpha

It is well known that coefficient alpha can be used to estimate the reliability of a test even when the test is split into several parts. It is also known that alpha can severely underestimate test reliability when the several parts have an unequal number of items. A gernalization of alpha,β _k, is proposed to correct this defect. Several properties ofβ _k are also presented. The author gratefully acknowledges the assistance of Dr. Leonard Feldt for reviewing an earlier draft of this paper, and Ms. Rita Karwacki Bode and Mr. Dave Mansell for the analysis of the experimental data reported here. The comments of an unknown referee which contributed substantially to the clarity of the presentation are also gratefully acknowledged.     

A comment on Birnbaum's three-parameter logistic model in the latent trait theory

Birnbaum's three-parameter logistic model for the multiple-choice item in the latent trait theory is considered with respect to the item response information function and the unique maximum condition. It is clarified that with models of knowledge or random guessing nature, which include the three-parameter logistic model, the unique maximum condition is not satisfied for the correct answer, and the item response information function is negative for the interval (− ∞,θ _g ). It is suggested that we should useθ _g as a criterion in selecting optimal items for a specified group of examinees, so that we can practically avoid the possibility of non-unique maxima of the likelihood function on the response pattern given by an examinee in the group. The work described in this paper was partially done while the author was at University of New Brunswick, Canada, in 1968–1970, supported by NRC Grant APA-345 from National Research Council of Canada.     

Interdependent preferences on finite sets

The degree of interdependence of a preference relation ? on a finite subset X of a product set X₁ × X₂ × … × X_n is defined in terms of the highest order of preference interaction among the X_i that must be taken into account in a real-valued, interdependent additive representation for ?. The degree is zero when indifference holds throughout X, and zero or one in the additive conjoint measurement case. A degree of n signifies complete preference interdependence among the X_i.     

Single-letter recognition as a function of exposure duration

The time course of visual letter recognition was investigated in a single-stimulus identification experiment. On each trial, a randomly chosen stimulus letter was presented at 1 of 12 equiprobable positions that were equally spaced around the circumference of an imaginary circle centered on fixation. Exposure duration was varied from 10 to 200 ms, and the letter was followed by a pattern mask. The subject's task was to report the identity of the stimulus letter but refrain from guessing. For the briefest exposures, correct reports never occurred. For longer exposures, the function relating the probability p of recognizing the letter to the duration t of the stimulus exposure was well approximated by an exponential distribution function: p(t) = 1 − exp[−v·(t−t ₀)], where v is the rate of processing and t ₀ is the minimum effective exposure duration. The generality of this finding may be limited to cases in which stimuli are highly discriminable and response criteria are conservative. Extensions to Poisson counter or random walk models are considered for cases in which stimuli are confusable. Received: 1 July 1997 / Accepted: 2 July 1998     

Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: II: A search procedure to locate the greatest lower bound

Finding the greatest lower bound for the reliability of the total score on a test comprisingn non-homogenous items with dispersion matrix Σ _x is equivalent to maximizing the trace of a diagonal matrix Σ _E with elements θ _I , subject to Σ _E and Σ _T =Σ _x − Σ _E being non-negative definite. The casesn=2 andn=3 are solved explicity. A computer search in the space of the θ _i is developed for the general case. When Guttman's λ₄ (maximum split-half coefficient alpha) is not the g.l.b., the maximizing set of θ _i makes the rank of Σ _T less thann − 1. Numerical examples of various bounds are given. Present affiliation of the first author: St. Hild's College of Education, Durham City, England.     

Adolescents’ Social Environment and Depression: Social Networks, Extracurricular Activity, and Family Relationship Influences

The present study examined components of adolescents’ social environment (social network, extracurricular activities, and family relationships) in association with depression. A total of 332 adolescents presenting for a routine medical check-up were self-assessed for social network risk (i.e., smoking habits of best male and female friends), extracurricular activity level (i.e., participation in organized sports teams, clubs, etc.), family relationship quality (i.e., cohesion and conflict), and symptoms of depression (i.e., minimal, mild, moderate/severe). Results of a forward linear regression modeling indicate that social environment components were associated with a significant proportion of the variance in adolescent depression (Adjusted R ² = .177, p ≤ .05). Specifically, adolescent females (β = .166, p < .01) and those having more smokers in their social network (β = .107, p < .05) presented with significantly greater depression symptoms. Conversely, adolescents who engaged in more extracurricular activities (β = −.118, p < .05) and experienced higher quality family relationships (β = −.368, p < .001) presented with significantly lower depressive symptoms. These findings highlight the important role that the social environment plays in adolescent depression, as well as yields new insights into socially-based intervention targets that may ameliorate adolescent depression. These intervention targets may be gender-specific, include positive social network skills training, increase adolescents’ engagement in organized activities, and attend to the quality of their family relationships.     

Distress and Family Functioning in Oncogenetic Counselling for Hereditary and Familial Breast and/or Ovarian Cancers

We conducted a psychological assessment during oncogenetic counseling for hereditary breast/ovarian cancer. Anxiety and depression were assessed with the HAD scale, and family functioning and satisfaction with FACES III. HAD was administered at baseline (t ₁)_, at risk communication (t ₂), at genetic test result communication, or at first surveillance in not tested subjects (t ₃); FACES III was administered at baseline only. We analysed a total of 185 questionnaires administered to the 37 subjects studied. Although not pathological, distress was significantly higher at t ₂ and t ₃ (p = 0.027 and p = 0.039, respectively). Health and marital status were significantly associated with distress. In a disease-free condition, anxiety was higher (p = 0.027) at t _2, and for single status, depression increased from t ₁ to t ₂ (p = 0.026). Families were perceived to be well functioning, and subjects were satisfied with their families. The data collected in this analysis could help to improve the quality of oncogenetic counselling in clinical practice.     

Cohen’s Linearly Weighted Kappa is a Weighted Average of 2×2 Kappas

An agreement table with n∈ℕ_≥3 ordered categories can be collapsed into n−1 distinct 2×2 tables by combining adjacent categories. Vanbelle and Albert (Stat. Methodol. 6:157–163, 2009c) showed that the components of Cohen’s weighted kappa with linear weights can be obtained from these n−1 collapsed 2×2 tables. In this paper we consider several consequences of this result. One is that the weighted kappa with linear weights can be interpreted as a weighted arithmetic mean of the kappas corresponding to the 2×2 tables, where the weights are the denominators of the 2×2 kappas. In addition, it is shown that similar results and interpretations hold for linearly weighted kappas for multiple raters.     

The Influence of Clinical Variables on the Psychological Adaptation of Adolescents after Solid Organ Transplantation

This study assessed the influence of clinical and socio-demographic variables on the psychological adaptation of transplanted adolescents. Twenty-six transplanted adolescents and 25 healthy adolescents, aged 13–17, and their parents participated in the study. The following domains were measured: social competence, emotional/behavioral problems, self-concept, self-esteem and subjective well-being. The findings revealed that transplanted boys presented significantly less social competence (U = 26,000, p < .05) and more externalizing problems (U = 25,000, p < .05), social problems (U = 25,000, p < .05) and attention problems (U = 17,500, p < .01) than healthy boys. In contrast, transplanted girls displayed significantly more internalizing problems (U = 47,000, p < .05) and lower physical self-concept (U = 49,500, p < .05) than healthy girls. Hierarchical regression analysis showed clinical variables, especially waiting-list time, significantly predicted attention problems (β = .364, p < .05) and negative affect (β = .632, p < .05) in transplanted adolescents. Also, male (β = −0.554, p < .01) and younger (β = −0.444, p < .01) transplanted adolescents were at risk for attention problems. Our data suggest the importance of the waiting-list time for transplanted adolescents. Efforts to reduce the pretransplant phase would help adolescents achieve better psychological adaptation at long-term posttransplant.     

DELAY‐AMOUNT TRADEOFFS IN CHOICES BY PIGEONS AND RATS: HYPERBOLIC VERSUS EXPONENTIAL DISCOUNTING

An adjusting‐delay procedure was used to study the choices of pigeons and rats when both delay and amount of reinforcement were varied. In different conditions, the choice alternatives included one versus two reinforcers, one versus three reinforcers, and three versus two reinforcers. The delay to one alternative (the standard alternative) was kept constant in a condition, and the delay to the other (the adjusting alternative) was increased or decreased many times a session so as to estimate an indifference point—a delay at which the two alternatives were chosen about equally often. Indifference functions were constructed by plotting the adjusting delay as a function of the standard delay for each pair of reinforcer amounts. The experiments were designed to test the prediction of a hyperbolic decay equation that the slopes of the indifference functions should increase as the ratio of the two reinforcer amounts increased. Consistent with the hyperbolic equation, the slopes of the indifference functions depended on the ratios of the two reinforcer amounts for both pigeons and rats. These results were not compatible with an exponential decay equation, which predicts slopes of 1 regardless of the reinforcer amounts. Combined with other data, these findings provide further evidence that delay discounting is well described by a hyperbolic equation for both species, but not by an exponential equation. Quantitative differences in the y‐intercepts of the indifference functions from the two species suggested that the rate at which reinforcer strength decreases with increasing delay may be four or five times slower for rats than for pigeons.