Gleaning Information for Cognitive Operations from Don’t Know Responses in Cognitive and Noncognitive Assessments

The Don’t Know (DK) response – taking the form of an omitted response or not-reached at the end of a cognitive test, or explicitly presented as a response option in a social survey – contains important information that is often overlooked. Direct psychometric modeling efforts for DK responses are few and far between. In this article, the linear logistic test model (LLTM) is proposed for delineating the impacts of cognitive operations for a test that contains DK responses. We assume that the DK response is a valid response. The assumption is reasonable for many situations, including low-stakes cognitive tests and attitudinal assessments. By extracting information embedded in the DK response, the method shows how DK can inform the latent construct of interest and the cognitive operations underlying the response to stimuli. Using a proven recoding scheme, the LLTM could be implemented through commonly used programs such as PROC GLIMMIX. Two simulation experiments to evaluate how well the parameters can be recovered were conducted. In addition, two real data examples, from a noncognitive test of health belief assessment and a cognitive test of knowledge in diabetes, are also presented as case studies to illustrate the LLTM for DK response.     

Generalized constrained multiple correspondence analysis

A comprehensive approach for imposing both row and column constraints on multivariate discrete data is proposed that may be called generalized constrained multiple correspondence analysis (GCMCA). In this method each set of discrete data is first decomposed into several submatrices according to its row and column constraints, and then multiple correspondence analysis (MCA) is applied to the decomposed submatrices to explore relationships among them. This method subsumes existing constrained and unconstrained MCA methods as special cases and also generalizes various kinds of linearly constrained correspondence analysis methods. An example is given to illustrate the proposed method.Heungsun Hwang is now at Claes Fornell International Group. The work reported in this paper was supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the second author.     

Falsification of matching theory's account of single-alternative responding: Herrnstein's k varies with sucrose concentration

Eight rats pressed levers for varying concentrations of sucrose in water under eight variable-interval schedules that specified a wide range of reinforcement rate. Herrnstein's (1970) hyperbolic equation described the relation between reinforcement and responding well. Although the y asymptote, k, of the hyperbola appeared roughly constant over conditions that approximated conditions used by Heyman and Monaghan (1994), k varied when lower concentration solutions were included. Advances in matching theory that reflect asymmetries between response alternatives and insensitive responding were incorporated into Herrnstein's equation. After fitting the modified equation to the data, Herrnstein's k also increased. The results suggest that variation in k can be detected under a sufficiently wide range of reinforcer magnitudes, and they also suggest that matching theory's account of response strength is false. The results support qualitative predictions made by linear system theory.     

Bounds on variances of estimators for multinomial processing tree models

When there are order constraints among the parameters of a binary, multinomial processing tree (MPT) model, methods have been developed for reparameterizing the constrained MPT into an equivalent unconstrained MPT. This note provides a theorem that is useful in computing bounds on the estimator variances for the parameters of the constrained model in terms of estimator variances of the parameters of the unconstrained model. In particular, we show that if X and Y are random variables taking values in [0,1], then Var[XY]?2(Var[X]+Var[Y]).     

More evidence on size modification in spatial axes systems of varying complexity

Pictorial space can be conceptualized as aggregate space (where figures compete for limited available space) or as axial space (where space is infinite and exists independently of figures). That these two kinds of space concepts follow a developmental sequence was tested by investigating size regulation mechanisms in 7- to 12-year-old children's figure drawings. An earlier longitudinal study had shown that the more figures were drawn and the more complex the spatial axes system, the smaller the figures. Two studies confirmed that object-driven size reduction was the size regulation mechanism in younger children, whereas axes-driven size reduction was the only factor regulating figure size in 12-year-old children. Size reduction occurred in a gradual fashion in younger children, whereas size reduction was more pronounced in crossed axes systems in older children. In addition, 7-year-old children showed a dynamic and fluid interaction between internal and external task demands for size regulation.     

When is search for meaning in life beneficial for well-being? A cross-national study

Previous research has found cross-national variations in the association between search for meaning in life (SMIL) and well-being (i.e. SMIL–WB link). This study extended and tested a “self-improvement hypothesis” that accounts for such cross-national variations based on an international database—the sixth wave of World Values Survey. SMIL represents a self-improvement effort which is more demanded in contexts with stronger external constraints. Thus, we expected a stronger positive SMIL–WB link in such contexts. A series of multilevel analyses was used to verify this hypothesis. The results showed that the SMIL–WB link varied across different societies, with well-being indexed by happiness, life satisfaction and subjective health. Moreover, external constraints from cultural, social-institutional, economic and ecological contexts (collectivism, peace threats, economic scarcity and environmental threats) moderated the SMIL–WB links. We thus call for advancing SMIL theory by considering person–context interaction.     

Concurrent schedules: How responses per reinforcer affects estimates of sensitivity to reinforcement

Conventionally, when choice is measured under concurrent schedules, all responses are included. However, the class of all responses consists of 2 sub-classes which are discriminable by their properties: Reinforced responses always equal obtained reinforcers, while unreinforced responses are free to vary. As a result, the inclusion of reinforced responses in choice measures results in sensitivity values in generalized matching that are biased toward larger values, and this bias becomes extreme in some combinations of overall response and reinforcer rates. Different ways of varying concurrent-schedule values also affect estimated sensitivity and the linearity between choice based on all responses and reinforcer ratios. To avoid spurious results and comparisons, and as a matter of good practice, generalized-matching fits and measures should be done using only unreinforced responses.