Functional Analysis Literature Research Articles

Latency measurement in functional analysis and treatment of behaviors targeted for reduction

AbstractResearch has demonstrated that latency is a reasonable index of response strength in the functional analysis and treatment of behaviors targeted for reduction. The literature contains numerous examples of functional analyses emphasizing latency informing effective treatment for problem behavior in various scenarios. Latency measurement can improve the versatility of functional analyses by allowing researchers and practitioners to examine behaviors that are not amenable to a traditional functional analysis arrangement and conduct assessments in challenging environments. Although there have been several reviews of the functional analysis literature, to date none have specifically addressed functional analyses emphasizing latency measurement. Given the unique advantages of latency‐based functional analyses, a systematic review could be beneficial to researchers and practitioners in behavior analysis. Therefore, we conducted a systematic literature review of research on functional analyses using latency to measure target behaviors. Our review included 79 cases across 27 empirical research articles. We present a summary of the extant literature, highlight strengths and limitations of the empirical foundations, provide clinical implications, and discuss future directions for research.

A Concise Tutorial on Functional Analysis for Applications to Signal Processing

Functional analysis is a well-developed field in the discipline of Mathematics, which provides unifying frameworks for solving many problems in applied sciences and engineering. In particular, several important topics (e.g., spectrum estimation, linear prediction, and wavelet analysis) in signal processing had been initiated and developed through collaborative efforts of engineers and mathematicians who used results from Hilbert spaces, Hardy spaces, weak topology, and other topics of functional analysis to establish essential analytical structures for many subfields in signal processing. This paper presents a concise tutorial for understanding the theoretical concepts of the essential elements in functional analysis, which form a mathematical framework and backbone for central topics in signal processing, specifically statistical and adaptive signal processing. The applications of these concepts for formulating and analyzing signal processing problems may often be difficult for researchers in applied sciences and engineering, who are not adequately familiar with the terminology and concepts of functional analysis. Moreover, these concepts are not often explained in sufficient details in the signal processing literature; on the other hand, they are well-studied in textbooks on functional analysis, yet without emphasizing the perspectives of signal processing applications. Therefore, the process of assimilating the ensemble of pertinent information on functional analysis and explaining their relevance to signal processing applications should have significant importance and utility to the professional communities of applied sciences and engineering. The information, presented in this paper, is intended to provide an adequate mathematical background with a unifying concept for apparently diverse topics in signal processing. The main objectives of this paper from the above perspectives are summarized below: (1) Assimilation of the essential information from different sources of functional analysis literature, which are relevant to developing the theory and applications of signal processing. (2) Description of the underlying concepts in a way that is accessible to non-specialists in functional analysis (e.g., those with bachelor-level or first-year graduate-level training in signal processing and mathematics). (3) Signal-processing-based interpretation of functional-analytic concepts and their concise presentation in a tutorial format.

Probability inequalities and tail estimates for metric semigroups

We study probability inequalities leading to tail estimates in a general semigroup $\mathscr{G}$ with a translation-invariant metric $d_{\mathscr{G}}$. (An important and central example of this in the functional analysis literature is that of $\mathscr{G}$ a Banach space.) Using our prior work [Ann. Prob. 2017] that extends the Hoffmann-Jorgensen inequality to all metric semigroups, we obtain tail estimates and approximate bounds for sums of independent semigroup-valued random variables, their moments, and decreasing rearrangements. In particular, we obtain the "correct" universal constants in several cases, extending results in the Banach space literature by Johnson-Schechtman-Zinn [Ann. Prob. 1985], Hitczenko [Ann. Prob. 1994], and Hitczenko and Montgomery-Smith [Ann. Prob. 2001]. Our results also hold more generally, in a very primitive mathematical framework required to state them: metric semigroups $\mathscr{G}$. This includes all compact, discrete, or (connected) abelian Lie groups.

On the Standardization of the Functional Analysis.

The functional analysis procedures described in the seminal Iwata et al. (1982/1994) study are prominent in the applied behavior analytic literature, having been replicated hundreds of times over the past 30years (Beavers, Iwata, & Lerman, 2013; Hanley, McCord, Iwata, 2003). However, the extent to which particular components of this functional analysis model have become more or less prominent over time is not clear from these literature reviews. We therefore conducted a review of the functional analysis literature between the years of 1965 and 2016 to determine the trends in the usage of particular components over time and to determine if the published literature reflects a standardization of the manner in which functional analyses of problem behavior are conducted. Furthermore, we discuss whether or not this standardization of a functional analysis model is currently necessary.

Response latency as a measure of behavior in the assessment of elopement.

Elopement is a common form of problem behavior but is relatively underrepresented in the functional analysis literature. One barrier to assessing elopement experimentally is the need to retrieve the subject following an instance of elopement. This retrieval confounds programmed session contingencies when the goal is to obtain repeated measurement of free-operant behavior. The current study evaluated latency to elopement as an alternative to free-operant measurement. We first compared response latency to allocation in 5-min sessions and then measured latency alone in a trial-based format. The identified reinforcers matched across both data analysis modalities in the session-based assessments, and the trial-based functional analysis showed a significant time savings in identifying the function of behavior over a session-based assessment. Results indicated that elopement serves idiosyncratic social functions in young children with intellectual and developmental disabilities, and that a latency-based assessment saves time while yielding equally clear results.

Validating trial-based functional analyses in mainstream primary school classrooms.

There is growing evidence to support the use of trial-based functional analyses, particularly in classroom settings. However, there currently are no evaluations of this procedure with typically developing children. Furthermore, it is possible that refinements may be needed to adapt trial-based analyses to mainstream classrooms. This study was designed to expand the trial-based functional analysis literature by implementing the procedure in 2 mainstream primary school classrooms and validating the analysis through comparison of multiple treatment options, including some that were not indicated by the functional analysis. We also extended the procedure by including a peer-attention condition and obtaining data from teachers regarding the feasibility of the procedures. For all participants, functional analysis results helped to identify effective treatments. Furthermore, relative effects among treatments were accurately predicted by the functional analysis outcomes. Teachers reported that they understood the logic of functional analysis and found both analysis and treatment procedures to be easy and effective.

Inappropriate mealtime behavior: the effects of noncontingent access to preferred tangibles on responding in functional analyses.

An understanding of the functional variables associated with inappropriate mealtime behavior (IMB) is critical to developing an effective and efficient treatment for food refusal. To this aim, functional analysis methodology has been modified for the meal context, and previous research has shown that multiple sources of reinforcement maintain IMB. Functional analysis literature, related to severe problem behavior, suggests that access to preferred stimuli may abolish or compete with social reinforcers in some cases. The role of noncontingent access to preferred stimuli during the assessment of IMB has not been evaluated. The purpose of the current study was to examine the effects noncontingent access to preferred toys/activities on IMB in the presence and absence of social consequences. The specific aims were to evaluate: (1) levels of IMB when the spoon is held stationary at the child's lips when preferred tangible stimuli are present noncontingently vs. absent; (2) levels of IMB when social consequences were provided contingent upon IMB when preferred tangible stimuli are present noncontingently vs. absent. For many participants, levels of IMB were reduced with the inclusion of preferred toys/activities; while for one, levels of IMB increased. Possible implications of these findings on functional analyses of IMB will be discussed.

IDIOSYNCRATIC VARIABLES THAT AFFECT FUNCTIONAL ANALYSIS OUTCOMES: A REVIEW (2001–2010)

Although typical functional analyses often produce clear outcomes, some studies have reported ambiguous results that cannot be interpreted. Such undifferentiated outcomes may occur if test conditions do not include relevant antecedent or consequent events. Clinicians then may try to modify the functional analysis conditions to include those events. Hanley, Iwata, and McCord (2003) reviewed the functional analysis literature through 2000 and described idiosyncratic variables included in modified functional analyses. The objective of the present review was to present a quantitative analysis of idiosyncratic antecedents and consequences in modified functional analyses during the past decade (2001 to 2010). We discuss the range of stimulus parameters tested and the assessment strategies used for informing the modified analysis conditions.

Teacher and Peer Participation in Functional Analysis and Intervention for a First Grade Student with Attention Deficit Hyperactivity Disorder

This study evaluated the current trend in functional analysis literature toward conducting the analysis in the classroom with teachers and peers. Procedures included a functional behavioral interview with the teacher, a descriptive observation, teacher training on the functional analysis procedures, a functional analysis, and implementing a socially valid and function-based classroom intervention. Functional analysis measures included the percentage of partial intervals in which the target behaviors (inappropriate vocalizations and disruptions) occurred as well as condition integrity for both the teacher and the peers. Classroom intervention measures included the rate of target behaviors and three descriptive variables: teacher and peer contingent attention to target behaviors and teacher praise. The results showed the function-based intervention effectively reduced the rate of target behaviors from baseline. The results also suggested general education teachers and peers are capable of participating in the functional analysis within the natural schedule of the classroom.

Curriculum-Based Assessment Procedures Embedded within Functional Behavioral Assessments: Identifying Escape-Motivated Behaviors in a General Education Classroom

The purpose of this study was to examine whether curriculum-based assessment (CBA) procedures could be incorporated into a functional behavioral assessment (FBA) to identify antecedent events that occasion off-task classroom behaviors of students in a general education classroom. A multi-element design was used to conduct a two-phase FBA and monitor changes in off-task behavior of 3 male students in the classroom. Phase 1 consisted of a teacher interview, an academic assessment, and a descriptive analysis. Phase 2 consisted of an antecedent manipulation phase in which the difficulty level of academic activities was systematically manipulated to determine events that may elicit the off-task classroom behaviors for each student. The present study builds upon the FBA and functional analysis literature in two ways. First, this study examined the use of CBA procedures to identify antecedent events related to off-task classroom behaviors, given the assumption that these behaviors were motivated by escape from academic activities that were too difficult relative to students' skill levels. Second, this study examined the use of FBA in a general education classroom rather than analogue or clinic-based school settings in which these procedures frequently have been employed. Third, their use was examined with general education students who were experiencing problem behaviors rather than with special education students for whom FBA procedures are often implemented.