An overview of applied robust methods

Data in social sciences are typically non-normally distributed and characterized by heavy tails. However, most widely used methods in social sciences are still based on the analyses of sample means and sample covariances. While these conventional methods continue to be used to address new substantive issues, conclusions reached can be inaccurate or misleading. Although there is no ‘best method’ in practice, robust methods that consider the distribution of the data can perform substantially better than the conventional methods. This article gives an overview of robust procedures, emphasizing a few that have been repeatedly shown to work well for models that are widely used in social and behavioural sciences. Real data examples show how to use the robust methods for latent variable models and for moderated mediation analysis when a regression model contains categorical covariates and product terms. Results and logical analyses indicate that robust methods yield more efficient parameter estimates, more reliable model evaluation, more reliable model/data diagnostics, and more trustworthy conclusions when conducting replication studies. R and SAS programs are provided for routine applications of the recommended robust method.     

Decomposing the social gradient in children’s vocabulary skills at 3 years of age: A mediation analysis using data from a large representative cohort study

Disparities in children’s expressive language by socio-economic status are evident early in childhood and impact children’s development and educational attainment. This study investigated the processes by which maternal education, as a powerful indicator for socio-economic status, affects early expressive language. A nationally representative cohort study of 8,062 children resident in the Republic of Ireland were assessed on the British Ability Scales (BAS) Naming Vocabulary Test at 36 months. A significant difference of almost six points was found between the mean vocabulary test scores of children whose mothers had completed the minimum level of educational attainment compared with children whose mothers had a degree-level qualification. Mediation analysis revealed that 78% of the difference was explained by mediating variables, with differences in household income, parental practice, and material resources accounting for most of the variation. The findings support interventions which redress gaps in maternal education, income, and caregiving.     

Further extensions of precision medicine to behavior analysis: A demonstration using functional communication training

The potential applicability of concepts and methods of the paradigm of precision medicine to the field of applied behavior analysis is only beginning to be explored. Both precision medicine and applied behavior analysis seek to understand and classify clinical problems through identification of their causal pathways. Both aim to develop treatments directly targeting those causal pathways, which also requires an understanding of the mechanisms by which treatments produce change (treatment-action pathways). In the current study, we extend the data-analytic methods and concepts described by Hagopian et al. (2018) toward the identification of variables that predict response to functional communication training (FCT). We discuss emerging conceptual issues, including the importance of distinguishing predictive behavioral markers from predictor variables based on their purported involvement in the causal or treatment-action pathways. Making these discriminations is a complex undertaking that requires knowledge of these mechanisms and how they interact.     

Transformation to achieve a longitudinally stationary factor pattern matrix

Meredith's method of extracting a factorially invariant solution is adapted to longitudinal settings. An explorational estimation procedure is presented which attempts to identify the longitudinal factor components of an across occasion variance-covariance matrix. This is effected by transforming an initial factor pattern matrix to stationarity. The estimation is performed in two parts, the first employing a stepwise algorithm to ascertain the dimensionality and existence of the longitudinal components and the second being the direct estimation of the existing factor pattern.     

Bayes modal estimation in item response models

This article describes a Bayesian framework for estimation in item response models, with two-stage prior distributions on both item and examinee populations. Strategies for point and interval estimation are discussed, and a general procedure based on the EM algorithm is presented. Details are given for implementation under one-, two-, and three-parameter binary logistic IRT models. Novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest. Improved estimation in a moderately small sample is demonstrated with simulated data.This research was supported by a grant from the Spencer Foundation, Chicago, IL. Comments and suggestions on earlier drafts by Charles Lewis, Frederic Lord, Rosenbaum, James Ramsey, Hiroshi Watanabe, the editor, and two anonymous referees are gratefully acknowledged.     

A note on structural models for the circumplex

Jöreskog (1974) developed a latent variable model for the covariance structure of the circumplex which, under certain conditions, includes a model for a patterned correlation matrix (Browne, 1977). This model is of limited usefulness, however, in that it employs a known matrix that is rank deficient for many problems. Furthermore, the model is inappropriate for the circumplex which contains negative covariances. This paper presents alternative models for the perfect circumplex and quasi-circumplex that avoids these difficulties, and that includes the important model for a patterned correlation circumplex matrix. Two numerical examples are provided.This research was supported in part by a grant from the Graduate School of the University of Minnesota. I wish to thank M. W. Browne for suggesting the final model presented in this paper. James Steiger and the Editor also made several valuable suggestions.     

A BEHAVIORAL SYSTEM FOR ASSESSING AND TRAINING CARDIOPULMONARY RESUSCITATION SKILLS AMONG EMERGENCY MEDICAL TECHNICIANS

Many deaths from cardiopulmonary arrest can be prevented by the prompt and effective administration of cardiopulmonary resuscitation (CPR). In this study, we examined the standard training program for teaching CPR to emergency medical technicians (EMTs). We developed an alternative experimental program whereby the behaviors involved in CPR were assessed easily and in greater detail. This assessment provided the basis for a system in which effective CPR skills were reinforced and problems were corrected. Subjects who were trained in CPR according to this experimental program performed more effectively than subjects in the standard program. In addition, retention (maintenance) measures indicated that experimental subjects continued to perform well, often more effectively than professionally employed EMTs.     

ON THE RELATIONSHIP BETWEEN SELF-INJURIOUS BEHAVIOR AND SELF-RESTRAINT

Many individuals who exhibit self-injurious behavior (SIB) also exhibit self-restraint. Three hypotheses about the determinants of self-restraint have been suggested: (a) Self-restraint is maintained by escape from or avoidance of aversive aspects of SIB, (b) self-restraint and SIB are members of the same functional class, and (c) self-restraint and SIB are functionally independent. This study examined a method by which the relationship between self-restraint and SIB may be investigated using functional analysis. Data were collected on the self-restraint and SIB exhibited by 5 mentally retarded males, while conditions suspected to maintain SIB were manipulated. Results suggested that self-restraint, like SIB, may be maintained by idiosyncratic contingencies. Implications of an understanding of self-restraint for the analysis and treatment of SIB are discussed, as are some general possibilities for future research.     

ANALYSIS OF THE EFFECTS OF TASK PREFERENCES,TASK DEMANDS,AND ADULT ATTENTION ON CHILD BEHAVIOR IN OUTPATIENT AND CLASSROOM SETTINGS

Two studies were conducted with children who displayed behavior problems to evaluate the effects of task preference, task demands, and adult attention on child behavior. In Study 1, we conducted brief functional analyses in an outpatient clinic to identify variables that facilitated appropriate behavior. For 8 of 10 children, distinct patterns of performance occurred; 3 children displayed improved behavior with changes in task demands, 1 child displayed improved behavior with a preferred task, and 4 children displayed improved behavior with changes in adult attention. In most cases, the children's parents carried out the assessments with adequate procedural integrity. In Study 2, we applied similar assessment methods to a classroom setting over an extended period of time. We identified independent variables controlling appropriate, on-task, and academic behavior for 2 children on two tasks, with slightly different treatment procedures across tasks for both children. In addition, the results of brief functional analyses for both children corresponded to the extended classroom assessments.