From Knowledge-based Programs to Graded Belief-based Programs,Part I: On-line Reasoning<Superscript>*</Superscript>

Knowledge-based programs (KBPs) are a powerful notion for expressing action policies in which branching conditions refer to implicit knowledge and call for a deliberation task at execution time. However, branching conditions in KBPs cannot refer to possibly erroneous beliefs or to graded belief, such as “if my belief that φ holds is high then do some action α else perform some sensing action β”. The purpose of this paper is to build a framework where such programs can be expressed. In this paper we focus on the execution of such a program (a companion paper investigates issues relevant to the off-line evaluation and construction of such programs). We define a simple graded version of doxastic logic KD45 as the basis for the definition of belief-based programs. Then we study the way the agent’s belief state is maintained when executing such programs, which calls for revising belief states by observations (possibly unreliable or imprecise) and progressing belief states by physical actions (which may have normal as well as exceptional effects). ^* A premliminary and shorter version of this paper in the Proceedings of the 16th European Conference on Artificial Intelligence (ECAI-04), pp. 368–372 (Laverny and Lang 2004).     

Statistical guidelines for studies of the theory of reasoned action and the theory of planned behaviour

Abstract

We identify potential problems in the statistical analysis of social cognition model data, with special emphasis on the theories of reasoned action (TRA) and planned behaviour (TPB). Some statistical guidelines are presented for empirical studies of the TRA and the TPB based upon multiple linear regression and structural equation modelling (SEM). If the model is tested using multiple regression, the assumptions of this technique must be considered and variables transformed if necessary. Adjusted R² (not R²) should be used as a measure of explained variance and semipartial correlations are useful in assessing each component's unique contribution to explained variance. R² is not an indicator of model adequacy and residuals should be examined. Expectancy-value variables that are the product of expectancy and value measures represent the interaction term in a multiple regression and should not be used. SEM approaches make explicit the assumptions of unidimensionality of constructs in the TRA/TPB, assumptions that might usefully be challenged by competing models with multidimensional constructs. Finally, statistical power and sample size should be considered for both approaches. Inattention to any of these aspects of analysis threatens the validity of TRA/TPB research.     

A COMMENT ON RCC: FROM RCC TO RCC<Superscript>++</Superscript>

The Region Connection Calculus (RCC theory) is a well-known spatial representation of topological relations between regions. It claims that the connection relation is primitive in the spatial domain. We argue that the connection relation is indeed primitive to the spatial relations, although in RCC theory there is no room for distance relations. We first analyze some aspects of the RCC theory, e.g. the two axioms in the RCC theory are not strong enough to govern the connection relation, regions in the RCC theory cannot be points, the uniqueness of the operation in the theory is not guaranteed, etc. To solve some of the problems, we propose an extension to the RCC theory by introducing the notion of region category and adding a new axiom which governs the characteristic property of the connection relation. The extended theory is named as RCC⁺⁺. We support the claim that the connection relation is primitive to spatial domain by showing how distance relations, size relations are developed in RCC⁺⁺. At last we revisit a sub-family of un-intended models in RCC theory, argue that RCC⁺⁺ is more suitable than RCC with regards to its original intended model, and discuss the representation limitation of the RCC, as well as RCC⁺⁺.     

A General Family of Limited Information Goodness-of-Fit Statistics for Multinomial Data

Maydeu-Olivares and Joe (J. Am. Stat. Assoc. 100:1009–1020, 2005; Psychometrika 71:713–732, 2006) introduced classes of chi-square tests for (sparse) multidimensional multinomial data based on low-order marginal proportions. Our extension provides general conditions under which quadratic forms in linear functions of cell residuals are asymptotically chi-square. The new statistics need not be based on margins, and can be used for one-dimensional multinomials. We also provide theory that explains why limited information statistics have good power, regardless of sparseness. We show how quadratic-form statistics can be constructed that are more powerful than X ² and yet, have approximate chi-square null distribution in finite samples with large models. Examples with models for truncated count data and binary item response data are used to illustrate the theory.     

ATC-lab<Superscript>Advanced</Superscript>: An air traffic control simulator with realism and control

ATC-lab^Advanced is a new, publicly available air traffic control (ATC) simulation package that provides both realism and experimental control. ATC-lab^Advanced simulations are realistic to the extent that the display features (including aircraft performance) and the manner in which participants interact with the system are similar to those used in an operational environment. Experimental control allows researchers to standardize air traffic scenarios, control levels of realism, and isolate specific ATC tasks. Importantly, ATC-lab^Advanced also provides the programming control required to cost effectively adapt simulations to serve different research purposes without the need for technical support. In addition, ATC-lab^Advanced includes a package for training participants and mathematical spreadsheets for designing air traffic events. Preliminary studies have demonstrated that ATC-lab^Advanced is a flexible tool for applied and basic research.     

Sensitivity of MRQAP Tests to Collinearity and Autocorrelation Conditions

Multiple regression quadratic assignment procedures (MRQAP) tests are permutation tests for multiple linear regression model coefficients for data organized in square matrices of relatedness among n objects. Such a data structure is typical in social network studies, where variables indicate some type of relation between a given set of actors. We present a new permutation method (called “double semi-partialing”, or DSP) that complements the family of extant approaches to MRQAP tests. We assess the statistical bias (type I error rate) and statistical power of the set of five methods, including DSP, across a variety of conditions of network autocorrelation, of spuriousness (size of confounder effect), and of skewness in the data. These conditions are explored across three assumed data distributions: normal, gamma, and negative binomial. We find that the Freedman–Lane method and the DSP method are the most robust against a wide array of these conditions. We also find that all five methods perform better if the test statistic is pivotal. Finally, we find limitations of usefulness for MRQAP tests: All tests degrade under simultaneous conditions of extreme skewness and high spuriousness for gamma and negative binomial distributions. Special thanks go to Cajo Ter Braak, Philip Hans Franses, Patrick Houweling, Pierre Legendre, three anonymous reviewers, the associate editor, and the editor for comments.     

Linearity of Personality–Performance Relationships: A large‐scale examination

This paper reviews theory and past research concerning nonlinear relationships between personality tests and job performance. We compare linear and nonlinear regression models for each of the 32 Occupational Personality Questionnaire (OPQ32i) scales using job performance as the criterion variable. We evaluate linear, quadratic, and cubic relationships between personality and job performance by calculating changes in R (ΔR) between the linear and nonlinear models. We use 3 decision rules of varying levels for ΔR and divide a large sample randomly into 2 samples to cross‐validate any nonlinear effects found. Few scales exhibited nonlinearity and the magnitude of the departures from linearity were small.     

Multiple rectilinear prediction and the resolution into components: II

Given a battery ofn tests that has already been resolved intor orthogonal common factors andn unique factors, procedures are outlined for computing the following types of linear multiple regressions directly from the factor loadings: (i) the regression of any one test on then?1 remaining tests; (ii) all then different regressions of ordern?1 for then tests, computed simultaneously; (iii) the regression of any common factor on then tests; (iv) the regressions of all the common factors on then tests computed simultaneously; (v) the regression of any unique factor on then tests; (vi) the regressions of all the unique factors on then tests, computed simultaneously. Multiple and partial correlations are then determined by ordinary formulas from the regression coefficients. A worksheet with explicit instructions is provided, with a completely worked out example. Computing these regressions directly from the factor loadings is a labor-saving device, the efficiency of which increases as the number of tests increases. The amount of labor depends essentially on the number of common factors. This is in contrast to computations based on the original test intercorrelations, where the amount of labor increases more than proportionately as the number of tests increases. The procedures evaluate formulas developed in a previous paper (2). They are based essentially on a shortened way of computing the inverse of the test intercorrelation matrix by use of the factor loadings.     

Equivalence tests for comparing correlation and regression coefficients

Equivalence tests are an alternative to traditional difference‐based tests for demonstrating a lack of association between two variables. While there are several recent studies investigating equivalence tests for comparing means, little research has been conducted on equivalence methods for evaluating the equivalence or similarity of two correlation coefficients or two regression coefficients. The current project proposes novel tests for evaluating the equivalence of two regression or correlation coefficients derived from the two one‐sided tests (TOST) method (Schuirmann, 1987, J. Pharmacokinet. Biopharm, 15, 657) and an equivalence test by Anderson and Hauck (1983, Stat. Commun., 12, 2663). A simulation study was used to evaluate the performance of these tests and compare them with the common, yet inappropriate, method of assessing equivalence using non‐rejection of the null hypothesis in difference‐based tests. Results demonstrate that equivalence tests have more accurate probabilities of declaring equivalence than difference‐based tests. However, equivalence tests require large sample sizes to ensure adequate power. We recommend the Anderson–Hauck equivalence test over the TOST method for comparing correlation or regression coefficients.     

Limited‐information goodness‐of‐fit testing of hierarchical item factor models

In applications of item response theory, assessment of model fit is a critical issue. Recently, limited‐information goodness‐of‐fit testing has received increased attention in the psychometrics literature. In contrast to full‐information test statistics such as Pearson’s X² or the likelihood ratio G², these limited‐information tests utilize lower‐order marginal tables rather than the full contingency table. A notable example is Maydeu‐Olivares and colleagues’M₂ family of statistics based on univariate and bivariate margins. When the contingency table is sparse, tests based on M₂ retain better Type I error rate control than the full‐information tests and can be more powerful. While in principle the M₂ statistic can be extended to test hierarchical multidimensional item factor models (e.g., bifactor and testlet models), the computation is non‐trivial. To obtain M₂, a researcher often has to obtain (many thousands of) marginal probabilities, derivatives, and weights. Each of these must be approximated with high‐dimensional numerical integration. We propose a dimension reduction method that can take advantage of the hierarchical factor structure so that the integrals can be approximated far more efficiently. We also propose a new test statistic that can be substantially better calibrated and more powerful than the original M₂ statistic when the test is long and the items are polytomous. We use simulations to demonstrate the performance of our new methods and illustrate their effectiveness with applications to real data.     

Causal modeling with the TETRAD program

Drawing substantive conclusions from linear causal models that perform acceptably on statistical tests is unreasonable if it is not known how alternatives fare on these same tests. We describe a computer program, TETRAD, that helps to search rapidly for plausible alternatives to a given causal structure. The program is based on principles from statistics, graph theory, philosophy of science, and artificial intelligence. We describe these principles, discuss how TETRAD employs them, and argue that these principles make TETRAD an effective tool. Finally, we illustrate TETRAD's effectiveness by applying it to a multiple indicator model of Political and Industrial development. A pilot version of the TETRAD program is described in this paper. The current version is described in our forthcoming Discovering Causal Structure: Artificial Intelligence for Statistical Modeling.     

Maximal reliability and power in covariance structure models

In covariance structure modelling, the non‐centrality parameter of the asymptotic chi‐squared distribution is typically used as an indicator of asymptotic power for hypothesis tests. When a latent linear regression is of interest, the contribution to power by the maximal reliability coefficient, which is associated with used latent variable indicators, is examined and this relationship is further explicated in the case of congeneric measures. It is also shown that item parcelling may reduce power of tests of latent regression parameters. Recommendations on weights for parcelling to avoid power loss are provided, which are found to be those of optimal linear composites with maximal reliability.     

Sequential Down Syndrome Screening: The Importance of First and Second Trimester Test Correlations when Calculating Risk

Down syndrome screening can be particularly effective when both first and second trimester tests are performed. However, the counseling of women who have received sequential first and second trimester screening can be problematic. We evaluated an approximation where the post-test risk from the first trimester screening is used as the new a priori risk for the second trimester screening. The approximation disregards between-trimester test correlations. The Down syndrome detection rate based on the approximation (90.2%) would be close to that obtained when all correlations were considered (90.8%) but the false positive rate would be 26% higher (3.9% versus 3.1%, respectively). For any particular woman, the use of the approximation could result in highly inaccurate risks. We conclude that the correlations that exist between first and second trimester screening tests preclude the use of second trimester risks derived from the direct product of separate first and second trimester screening. Counseling issues in the delivery of sequential screening are discussed.     

A Bayesian Semiparametric Latent Variable Model for Mixed Responses

In this paper we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric Gaussian regression model. We extend existing LVMs with the usual linear covariate effects by including nonparametric components for nonlinear effects of continuous covariates and interactions with other covariates as well as spatial effects. Full Bayesian modelling is based on penalized spline and Markov random field priors and is performed by computationally efficient Markov chain Monte Carlo (MCMC) methods. We apply our approach to a German social science survey which motivated our methodological development. We thank the editor and the referees for their constructive and helpful comments, leading to substantial improvements of a first version, and Sven Steinert for computational assistance. Partial financial support from the SFB 386 “Statistical Analysis of Discrete Structures” is also acknowledged.     

On the Use of Nonparametric Regression in Assessing Parametric Regression Models

We develop a new method for assessing the adequacy of a smooth regression function based on nonparametric regression and the bootstrap. Our methodology allows users to detect systematic misfit and to test hypotheses of the form “the proposed smooth regression model is not significantly different from the smooth regression model that generated these data.” We also provide confidence bands on the location of nonparametric regression estimates assuming that the proposed regression function is true, allowing users to pinpoint regions of misfit. We illustrate the application of the new method, using local linear nonparametric regression, both where an error model is assumed and where the error model is an unknown non-stationary function of the predictor.     

Predicting Individuals’ Experienced Fear From Multimodal Physiological Responses to a Fear-Inducing Stimulus

Emotions are experienced differently by individuals, and thus, it is important to account for individuals’ experienced emotions to understand their physiological responses to emotional stimuli. The present study investigated the physiological responses to a fear-inducing stimulus and examined whether these responses can predict experienced fear. A total of 230 participants were presented with neutral and fear-inducing film clips, after which they self-rated their experienced emotions. Physiological measures (skin conductance level and response: SCL, SCR, heart rate: HR, pulse transit time: PTT, fingertip temperature: FT, and respiratory rate: RR) were recorded during the stimuli presentation. We examined the correlations between the physiological measures and the participants’ experienced emotional intensity, and performed a multiple linear regression to predict fear intensity based on the physiological responses. Of the participants, 92.5% experienced the fear emotion, and the average intensity was 5.95 on a 7-point Likert scale. Compared to the neutral condition, the SCL, SCR, HR, and RR increased significantly during the fear-inducing stimulus presentation whereas FT and PTT decreased significantly. Fear intensity correlated positively with SCR and HR and negatively with SCL, FT, PTT, and RR. The multiple linear regression demonstrated that fear intensity was predicted by a combination of SCL, SCR, HR, FT, and RR. Our findings indicate that the physiological responses to experiencing fear are associated with cholinergic, sympathetic, and α-adrenergic vascular activation as well as myocardial β-sympathetic excitation, and support the use of multimodal physiological signals for quantifying emotions.     

Perceived organizational support‐burnout‐satisfaction relationship in workers with disabilities: The moderation of family support

Our study tests the perceived organizational support‐burnout‐satisfaction relationship based on stressor–strain–outcome model of stress (Koeske & Koeske, 1993 ) and on the conservation of resources theory (Hobfoll, 1989 ) in workers with disabilities employed in ordinary or competitive jobs (open labor market), analyzing the relationship between perceived organizational support, family support, job satisfaction and burnout. We use a sample of 246 workers with physical, motor, sensory and psychological disabilities working in ordinary jobs. To test our proposed model we used a regression‐based path analysis using PROCESS software, which is a computational tool for estimating and probing interactions and the conditional indirect effects of moderated mediation models. We find that the positive relationship between organizational support and job satisfaction was partially mediated by the levels of cynicism and the relationship between burnout and job satisfaction was moderated by family support. Employees with low support from family had identical job satisfaction with high burnout or low burnout, but employees with high support from family when they had high burnout had lower job satisfaction than when they had low burnout, indicating that the support outside work could have a negative effect in workers’ life. Practical implications and future research are discussed and proposed. 1 1 A previous version of the abstract has been published in the European Congress of Psychology‐2015‐Abstract Book.
     

Some Comments on Pareto Thinking,Test Validity,and Adverse Impact: When ‘and’ is optimal and ‘or’ is a trade‐off

De Corte, Lievens, and Sackett add to the literature on selection test validity and adverse impact (AI). Their Pareto‐based weighting scheme essentially asks organizations if they are willing to give up some validity to hopefully achieve some reduction in AI. We considered their approach and conclusions in relation to the regression weighting method we used, and we offer five points that reflect our observations as well as our shared goals. We hope our comments, like their work in this field, will invigorate the pursuit of new ways of examining, and one day resolving, the persistent concern regarding the AI associated with valid selection tests.     

Developmental trajectory in the relationship between calculation skill and finger dexterity: A longitudinal study

A 2‐year longitudinal study of 33 children aged 4–6 years was conducted to clarify the developmental relationship between calculation skill and finger dexterity, as well as the selectivity of the predictive power of finger dexterity on later calculation skill. We examined individual developmental change in the relationship between addition performance and finger dexterity and observed whether children fit a linear developmental pattern. Multiple regression analysis showed that participants' performance on addition tests was strongly predicted by their finger dexterity. However, their performance on vocabulary tests was not strongly influenced by finger dexterity. These findings suggest that calculation skill in children aged 4–6 years is strongly related to finger dexterity.