Alpha-maximized factor analysis (alphamax): Its relation to alpha and canonical factor analysis

An alpha-O coefficient of internal consistency is defined for an observed score composite. Maximizing alpha-O leads to a system of psychometric (vs. statistical) factor analysis in which successive factors describe dimensions of successively less internal-consistency. Factoring stops when alpha-O is zero or less. In contrast to Kaiser-Caffrey's alpha-C analysis, when the factored matrix is rank 1, alpha-O does not reach unity; it can approach unity only as the number of variables reach infinity. The relative usefulness and domains of generalization of alpha-C and alpha-O are compared. Basically, alpha-C analysis is concerned with the representativeness of factors while alpha-O analysis is concerned with the assessibility of factors. Consequently, either system of factoring can and should be summarized by both the alpha-C and alpha-O coefficients. Not surprisingly, alpha-O analysis is computationally analogous to Rao's canonical factor analysis.     

The relation between factor loadings and biserial correlations in item analysis

The first centroid factor loadings obtained from various interitem relations are compared with item discrimination indices commonly used in item analysis. Depending upon what type of matrix is factored, the factor loadings are shown to be related to point biserial and biserial correlations.     

Classroom application of a trial-based functional analysis

We evaluated a trial-based approach to conducting functional analyses in classroom settings. Ten students referred for problem behavior were exposed to a series of assessment trials, which were interspersed among classroom activities throughout the day. Results of these trial-based functional analyses were compared to those of more traditional functional analyses. Outcomes of both assessments showed correspondence in 6 of the 10 cases and partial correspondence in a 7th case. Results of the standard functional analysis suggested reasons for obtained differences in 2 cases of noncorrespondence, which were verified when portions of the trial-based functional analyses were modified and repeated. These results indicate that a trial-based functional analysis may be a viable assessment method when resources needed to conduct a standard functional analysis are unavailable. Implications for classroom-based assessment methodologies and future directions for research are discussed.     

Asymptotic sampling variances for factor analytic models identified by specified zero parameters

Formulas are derived for the asymptotic variances and covariances of the maximum likelihood estimators for oblique simple structure models which are identified by prior specification of zero elements in the factor loading matrix. The formulas are expressed in terms of the various submatrices of the inverse of the required variance-covariance matrix. A numerical example using artificial data is given and problems in the application of the formulas discussed.Now at The Pennsylvania State University.     

The relation between results obtainable with raw and corrected correlation coefficients in multiple factor analysis

This paper presents three theorems concerning the relation between results with obtained and corrected correlation coefficients in the Thurstone method of multiple factor analysis. (1) The rank of the correlational matrix, and thus the number of factors involved, is unaffected by correcting the obtained coefficients for attenuation. (2) The communality of a variable when the obtained coefficients have been corrected for attenuation is equal to the communality with obtained coefficients divided by the reliability coefficient of the variable. (3) The relationship is shown between the factorial matrix of a correlational matrix of raw correlation coefficients and the factorial matrix of a correlational matrix of corrected correlation coefficients, and a method of obtaining either of these factorial matrices from the other is indicated.     

The Hopelessness Scale: a factor analysis

A confirmatory factor analysis of the Beck Hopelessness Scale in a sample of 340 Italian students did not support the 3-factor model reported for previous samples of psychiatric patients. A follow-up principal axis factor analysis yielded two interpretable correlated factors, suggesting that the structure of the scale may differ across clinical and nonclinical groups and as a function of nationality.     

Statistical aspects of a three-mode factor analysis model

A special case of Bloxom's version of Tucker's three-mode model is developed statistically. A distinction is made between modes in terms of whether they are fixed or random. Parameter matrices are associated with the fixed modes, while no parameters are associated with the mode representing random observation vectors. The identification problem is discussed, and unknown parameters of the model are estimated by a weighted least squares method based upon a Gauss-Newton algorithm. A goodness-of-fit statistic is presented. An example based upon self-report and peer-report measures of personality shows that the model is applicable to real data. The model represents a generalization of Thurstonian factor analysis; weighted least squares estimators and maximum likelihood estimators of the factor model can be obtained using the proposed theory.This investigation was supported in part by a Research Scientist Development Award (K02-DA00017) and a research grant (DA01070) from the U. S. Public Health Service. The very helpful comments of several anonymous reviewers are gratefully acknowledged.     

Problem behavior maintained by a precurrent relation

Differential reinforcement of alternative behavior is a well-established treatment for problem behavior in which the functional reinforcer is delivered after the occurrence of a replacement behavior and withheld after the occurrence of problem behavior. However, sometimes problem behavior continues to occur under these conditions, raising a question as to why problem behavior might maintain when its reinforcer is withheld. This study examined the possibility that problem behavior could be maintained indirectly in a precurrent relation. A functional analysis was conducted to identify a response-response relation between self-injurious behavior (SIB) and an alternative response. The results suggest that SIB was maintained by its relation with the alternative response.     

Toward a functional analysis of delusional speech and hallucinatory behavior

An approach to a functional analysis of delusional speech and hallucinatory behavior is described and discussed using concepts found in Goldiamond's (1975a and 1984) nonlinear contingency analysis and Skinner's Verbal Behavior (1957). This synthesis draws upon and concords with research from the animal laboratory, with the extensive experimental literatures on stimulus control and signal detection theory, and with our own clinical experiences.In this formulation, delusional speech and hallucinatory behavior are viewed as successful operants. Accordingly, we argue that such behaviors can be considered adaptive and rational, rather than maladaptive and irrational, when analyzed within a model of consequential governance that includes alternative sets of contingencies. Several clinical examples are offered to illustrate both analytic procedures and the design of systemic treatment programs based upon a behavioral contingency analysis derived from a natural science of behavior. Throughout, we emphasize the consequential governance of these clinically important classes of behavior, in contrast to other approaches which suggest formal similarities to operant verbal behavior but largely ignore the role of consequential contingencies.     

An evaluation of a brief functional analysis format within a vocational setting

We conducted and compared both brief and extended functional analyses of disruptive behaviors for 3 individuals with developmental disabilities who attended a vocational training program. Results demonstrated that the brief assessment identified the function of 2 of the 3 participants' disruptive behavior compared to the extended assessment.     

Embedding a functional analysis of compliance in small group instruction

Research on adaptations to standard functional analyses for use in classroom settings has increased in recent years. However, few studies have focused on procedural variations specific to assessing noncompliance in the context of academic instruction. In the current study, we trained a special education teacher to embed a functional analysis of compliance in small group instruction. The goal of the functional analysis was to identify an effective reinforcement contingency for compliance for a second grade student with an intellectual disability. Results suggested a combined escape + tangible contingency increased compliance to instructional prompts relative to other conditions. The functional analysis of compliance represents a variation on previous functional analyses of noncompliance with potential to increase ecological and social validity of assessment procedures for classroom settings.     

Testing a simple structure hypothesis in factor analysis

It is assumed that the investigator has set up a simple structure hypothesis in the sense that he has specified the zero loadings of the factor matrix. The maximum-likelihood method is used to estimate the factor matrix and the factor correlation matrix directly without the use of rotation methods, and the likelihood-ratio technique is used to test the simple structure hypothesis. Numerical examples are presented.The work was supported by a grant (NSF-GB 1985) from the National Science Foundation to Educational Testing Service. Reproduction in whole or in part for any purpose of the United States Government is permitted.The work was carried out when the author was Visiting Research Statistician at Educational Testing Service. The author wishes to thank Dr. Frederic M. Lord for many helpful suggestions throughout the course of this study.     

Separation of data as a principle in factor analysis

Two systems of factor analysis—factoring correlations with units in the diagonal cells and factoring correlations with communalities in the diagonal cells—are considered in relation to the commonly used statistical procedure of separating a set of data (scores) into two or more parts. It is shown that both systems of factor analysis imply the separation of the observed data into two orthogonal parts. The matrices used to achieve the separation differ for the two systems of factor analysis.     

Twinning behaviour of TWIP steel studied by Taylor factor analysis

The twinning behaviour of Twinning-induced plasticity (TWIP) steel has been studied by analysing the grain orientation and the Taylor factor, based on microstructural and electron backscatter diffraction device observations. It is demonstrated that the Taylor factor can give an important guideline for determining the deformation mode of TWIP steel. The higher the Taylor factor, the easier the formation of twins and thus a tendency for the deformation mode to be mechanical twinning, while a low Taylor factor corresponds to a slip deformation mode. When the loading temperature is relatively low, the high Taylor factor regions increase and thus deformation twinning becomes easier while slip becomes more difficult, leading to increased tensile stress and decreased elongation.     

Tableau algorithms for factor analysis by instrumental variable methods

Simple tableau algorithms are given for the noniterative instrumental variable (FABIN 2) and two stage regression (FABIN 3) factor loading estimates of Hägglund. Corresponding generalized least squares estimates of factor covariances and unique variances are introduced. An example is given for the purpose of illustration and comparison.This research was supported by NSF Grant MCS-8301587.     

Locus of control as a contributing factor in the relation between self-perception and adolescent aggression

Researchers continue to debate the role of self-esteem in aggression, but research has shown a consistent association between narcissism and aggression in adults and adolescents [e.g., Barry et al., 2007; Bushman and Baumeister, 1998; Stucke, 2007]. The primary aim of the current study was to examine whether locus of control (LOC) moderated the relation between self-perception variables (i.e., self-esteem and narcissism) and aggression in adolescents. Participants were 174 youth (145 males, 26 females) between the ages of 16 and 19 who were enrolled in a voluntary residential program for youth who have dropped out of school. The results showed that LOC moderated the association between self-esteem and aggression such that low self-esteem was associated with higher levels of aggression for individuals with an external LOC. Contrary to expectations, LOC failed to moderate the narcissism-aggression relation. The implications of this study for understanding how self-perception is related to adolescent aggression are discussed.