A new goodness-of-fit measure for probit models: Surrogate R2

Probit models are used extensively for inferential purposes in the social sciences as discrete data are prevalent in a vast body of social studies. Among many accompanying model inference problems, a critical question remains unsettled: how to develop a goodness-of-fit measure that resembles the ordinary least square (OLS) R² used for linear models. Such a measure has long been sought to achieve ‘comparability’ of different empirical models across multiple samples addressing similar social questions. To this end, we propose a novel R² measure for probit models using the notion of surrogacy – simulating a continuous variable $S$ as a surrogate of the original discrete response (Liu & Zhang, Journal of the American Statistical Association, 113, 845 and 2018). The proposed R² is the proportion of the variance of the surrogate response explained by explanatory variables through a linear model, and we call it a surrogate R². This paper shows both theoretically and numerically that the surrogate R² approximates the OLS R² based on the latent continuous variable, preserves the interpretation of explained variation, and maintains monotonicity between nested models. As no other pseudo R², McKelvey and Zavoina's and McFadden's included, can meet all the three criteria simultaneously, our measure fills this crucial void in probit model inference.     

ACADEA—a decision support system for faculty performance reviews

ACADEA, a multi‐criteria decision support system for the performance review of individual faculty, is presented. Developed from the point of view of a department that is facing exogenously as well as self imposed objectives, the support system looks upon the aggregate performance of an academic department as the result of individual faculty member's multi‐criteria evaluations. Five objectives, research output, teaching output, external service, internal service and cost, are operationalized into criteria. The system is applied to a university department with 30 faculty members evaluated over a 3‐year period. The results identify promotional candidates and reveal underlying problems in managerial consistency, departmental sub‐groupings and the incentive structure. The outcomes of the support system are consistent with the position that equity in faculty governance does not necessarily imply equal loads on all tasks. Copyright © 2000 John Wiley & Sons, Ltd.     

Friend or foe? Postdivorce hostility among recently divorced individuals

High levels of hostility often occur during and postdivorce and may significantly affect the quality of life, parent–child relationships, and social functioning of divorcees. Moreover, hostility may predict aggressive and violent behavior. This study sought to (a) compare average general hostility levels of a large sample of Danish divorcees to the norms of the general adult Danish population, (b) compare general hostility levels between male and female divorcees, and (c) investigate the explanatory value of various sociodemographic and divorce-related factors on postdivorce general hostility and whether these factors differ across gender. Cross-sectional baseline data (N = 1,856) from a larger randomized controlled trial study was used in this study. Normative data from a general sample of Danish adults (N = 2,040) was used for comparisons of hostility levels between our study sample and the Danish background population. This study found that male and female divorcees did not report significantly different hostility levels. However, participants reported significantly higher hostility levels postdivorce than the comparative Danish norm sample. Significant predictors of postdivorce hostility were lower age, lower educational level, infidelity as a reason for divorce, higher degree of postdivorce conflict, worse communication with the former spouse, the former spouse as the initiator of the divorce, and new partner status with neither divorcees having a new partner, or only the former spouse having a new partner. The predictive strength of the factors did not differ across gender. The findings may be especially relevant for interventions targeting problematic outcomes postdivorce (e.g., preventing aggressive behavior).     

Comparison of Common Amplitude Metrics in Event-Related Potential Analysis

Abstract

Waveform data resulting from time-intensive longitudinal designs require careful treatment. In particular, the statistical properties of summary metrics in this area are crucial. We draw on event-related potential (ERP) studies, a field with a relatively long history of collecting and analyzing such data, to illustrate our points. In particular, three summary measures for a component in the average ERP waveform feature prominently in the literature: the maximum (or peak amplitude), the average (or mean amplitude) and a combination (or adaptive mean). We discuss the methodological divide associated with these summary measures. Through both analytic work and simulation study, we explore the properties (e.g., Type I and Type II errors) of these competing metrics for assessing the amplitude of an ERP component across experimental conditions. The theoretical and simulation-based arguments in this article illustrate how design (e.g., number of trials per condition) and analytic (e.g., window location) choices affect the behavior of these amplitude summary measures in statistical tests and highlight the need for transparency in reporting the analytic steps taken. There is an increased need for analytic tools for waveform data. As new analytic methods are developed to address these time-intensive longitudinal data, careful treatment of the statistical properties of summary metrics used for null hypothesis testing is crucial.     

Analysis of Interactions and Nonlinear Effects with Missing Data: A Factored Regression Modeling Approach Using Maximum Likelihood Estimation

Abstract

When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., x²) or are included in interaction terms (e.g., x·z). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.     

Attachment to parents and to God: a panel-data approach

ABSTRACT

Research at the nexus of attachment theory and religion has generally been constrained both by data limitations and by a view of attachment style as fixed early in life. I use three waves of data to test key hypotheses from this literature in new ways. Closeness to mother and closeness to father serve as proxies for attachment to parents and closeness to God serves as a proxy for attachment to God. The correspondence hypothesis predicts that people who feel closer to their parents feel closer to God, the compensation hypothesis predicts that people lacking a parent feel closer to God, and the socialized correspondence hypothesis predicts that people with nonreligious parents will feel less close to God if they feel closer to their parents. I find strong evidence in favor of the correspondence hypothesis, but I find no evidence in favor of the compensation hypothesis or the socialized correspondence hypothesis.     

Early communication in dyads with visual impairment

The ability of dyads with restricted access to the visual channel of communication to establish a reliable pre‐linguistic communicative signalling system has traditionally been viewed as problematic. Such a conclusion is due in part to the emphasis that has been placed on vision as central to communication by traditional theory. The data presented in this paper question these assertions. The results of a longitudinal study exploring the nature of early dyadic interactions in dyads with visual impairment are presented. The dyads' use of three types of non‐visual behaviour—touch, vocalizations and facial orientation—were investigated in terms of their potential as alternatives to visual communication. It is argued that the results are evidence that visually impaired dyads engage in sophisticated communicative exchanges prior to infants' acquisition of language. Copyright © 2005 John Wiley & Sons, Ltd.     

Measuring illness perceptions in the family context: psychometric properties of the IPQ-R adapted for adolescent–caregiver dyads

Objectives: Given the lack of validated measures assessing illness perceptions in families, the aim of our study was the development and psychometric testing of an adapted version of the Illness Perceptions Questionnaire-Revised (IPQ-R) allowing for Common Sense Model-based dyadic assessment of adolescents’ and caregivers’ perceptions of a chronic illness in adolescence.

Methods: Using a cross-sectional survey design, factor structure, reliability and validity of the adapted measure You-IPQ-R were tested in a sample of adolescents with asthma (N?=?155) and their primary caregivers (N?=?132). Analysis included a dyadic methodology (dyadic confirmatory factor analyses) and examination of the suitability of the measure for different age groups.

Results: Both the adolescent and the caregiver versions of the You-IPQ-R revealed good overall validity and reliability. For all Common Sense Model dimensions except for timeline cyclical in the caregiver version, unidimensional scales aligning with the original IPQ-R structure could be confirmed. Age-specific analyses revealed good to excellent measurement properties in adolescents aged 14 years or older, but considerably poorer indices in younger adolescents.

Conclusion: The dyadically validated You-IPQ-R will enable researchers and clinicians to compare illness perceptions in adolescent–caregiver dyads and to assess the effects of family illness perceptions’ congruence upon medical, psychosocial and behavioural outcomes.