Three-mode orthomax rotation

Factor analysis and principal components analysis (PCA) are often followed by an orthomax rotation to rotate a loading matrix to simple structure. The simple structure is usually defined in terms of the simplicity of the columns of the loading matrix. In Three-mode PCA, rotational freedom of the so called core (a three-way array relating components for the three different modes) can be used similarly to find a simple structure of the core. Simple structure of the core can be defined with respect to all three modes simultaneously, possibly with different emphases on the different modes. The present paper provides a fully flexible approach for orthomax rotation of the core to simple structure with respect to three modes simultaneously. Computationally, this approach relies on repeated (two-way) orthomax applied to supermatrices containing the frontal, lateral or horizontal slabs, respectively. The procedure is illustrated by means of a number of exemplary analyses. As a by-product, application of the Three-mode Orthomax procedures to two-way arrays is shown to reveal interesting relations with and interpretations of existing two-way simple structure rotation techniques.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 and two anonymous reviewers for useful comments on an earlier version of this paper.     

A bayesian estimation of factor score in confirmatory factor model with polytomous, censored or truncated data

The posterior analysis in estimating factor score in a confirmatory factor analysis model with polytomous, censored or truncated data is investigated in this paper. For the above three types of data, posterior distributions of the factor score are studied, and the estimators of the factor score are obtained to be the location parameters of the posterior distributions. The accuracy of Bayesian estimates is studied via simulation studies.This research was supported by a Hong Kong UGC grant.     

Norms for Parental Ratings on Conners' Abbreviated Parent-Teacher Questionnaire: Implications for the Design of Behavioral Rating Inventories and Analyses of Data Derived from Them

Despite the wide usage of Conners' 10-item Abbreviated Parent-Teacher Questionnaire (APTQ), normative data for parental ratings on the APTQ are rare. Moreover, its psychometric properties as a stand alone behavioral rating instrument have yet to be examined in detail. Using data from parental ratings for 6,841 children aged 5 to 14 years, this paper reports the psychometric properties of the APTQ and provides normative and prevalence estimates for four age cohorts (5 to 6, 7 to 8, 9 to 11, and 12 to 14 years) by gender. In presenting the findings, the paper highlights key methodological issues endemic to the design of behavioral rating inventories like the APTQ and the analysis of data derived from them. These issues are illustrated and discussed in terms of their implications for the measurement and determination of prevalence estimates of problem behaviors in child psychology and child psychiatry. The need to revise the design, content, and response formats of child behavior rating inventories is stressed.     

The Effect of a Neutralizing Routine on Problem Behavior Performance

A functional analysis of noncompliance, aggression, and disruptive behavior during instruction was conducted with a 10-year-old boy with severe disabilities. We studied the relation between participant responsiveness and the rate and function of problem behavior. Results showed that unresponsiveness before difficult instruction was associated with higher rates of problem behavior negatively reinforced by termination of that instruction. A neutralizing routine, called precorrection, was then applied before difficult instruction when the participant was rated as not responsive. Results showed that the neutralizing event increased responsiveness and reduced problem behavior during difficult instruction. The study demonstrates a promising assessment and treatment method for problematic behavior that begins prior to instruction.     

Conjoint schedules of timeout deletion in pigeons.

This experiment attempted to bring behavior under joint control of two distinct contingencies, one that provided food and a second that extended the periods during which that food was available. Pigeons' responses on each of two keys were reinforced according to a single random-interval schedule of food presentation except during signaled timeout periods during which the schedule was temporarily disabled. By means of a conjoint schedule, responses on the initially less preferred key not only produced food but also canceled impending timeouts. When behavior came to predominate on this conjoint alternative, the consequences of responding on the two keys were reversed. Responding in 3 of 4 pigeons proved sensitive to the conjoint scheduled consequences, as evidenced by systematic shifts in response rates favoring the conjoint key. In 2 of these 3 pigeons, sensitivity to the conjoint contingency was evident under time-in:timeout ratios of 2:1 (time-in = 120 s, timeout = 60 s) and 1:5 (time-in = 30 s, timeout = 150 s), whereas for the other pigeon preference for the conjoint key was observed only under the latter sequence of conditions. There was only weak evidence of control by the conjoint scheduled consequences in the 4th subject, despite extended training and forced exposure to the conjoint alternative. The overall pattern of results is consistent with studies of timeout avoidance but also shares features in common with positively reinforced behavior.     

Effect analysis and causation in linear structural equation models

This paper considers total and direct effects in linear structural equation models. Adopting a causal perspective that is implicit in much of the literature on the subject, the paper concludes that in many instances the effects do not admit the interpretations imparted in the literature. Drawing a distinction between concomitants and factors, the paper concludes that a concomitant has neither total nor direct effects on other variables. When a variable is a factor and one or more intervening variables are concomitants, the notion of a direct effect is not causally meaningful. Even when the notion of a direct effect is meaningful, the usual estimate of this quantity may be inappropriate. The total effect is usually interpreted as an equilibrium multiplier. In the case where there are simultaneity relations among the dependent variables in tghe model, the results in the literature for the total effects of dependent variables on other dependent variables are not equilibrium multipliers, and thus, the usual interpretation is incorrect. To remedy some of these deficiencies, a new effect, the total effect of a factorX on an outcomeY, holding a set of variablesF constant, is defined. When defined, the total and direct effects are a special case of this new effect, and the total effect of a dependent variable on a dependent variable is an equilibrium multiplier.For helpful comments, I am grateful to G. Arminger, K. Bollen, W. Faris, R. m. Hauser, T. Petersen, three anonymous Psychometrikas reviewers, and the Editor. For computational assistance, I am grateful to B. D. Kim.     

A latent-trait based reliability estimate and upper bound

An estimate and an upper-bound estimate for the reliability of a test composed of binary items is derived from the multidimensional latent trait theory proposed by Bock and Aitkin (1981). The estimate derived here is similar to internal consistency estimates (such as coefficient alpha) in that it is a function of the correlations among test items; however, it is not a lowerbound estimate as are all other similar methods.An upper bound to reliability that is less than unity does not exist in the context of classical test theory. The richer theoretical background provided by Bock and Aitkin's latent trait model has allowed the development of an index (called here) that is always greater-than or equal-to the reliability coefficient for a test (and is less-than or equal-to one). The upper bound estimate of reliability has practical uses—one of which makes use of the greatest lower bound.     

The Problem of local optimality with OSMOD

The possibility of obtaining locally optimal solutions with categorical data is pointed out for the original version of OSMOD development by Saito and Otsu. A revision of the initialization strategy in OSMOD is suggested, and its effectiveness in diminishing this possibility is demonstrated.