Interpolation and Definability in Guarded Fragments

The guarded fragment (GF) was introduced by Andréka, van Benthem and Németi as a fragment of first order logic which combines a great expressive power with nice, modal behavior. It consists of relational first order formulas whose quantifiers are relativized by atoms in a certain way. Slightly generalizing the admissible relativizations yields the packed fragment (PF). In this paper we investigate interpolation and definability in these fragments. We first show that the interpolation property of first order logic fails in restriction to GF and PF. However, each of these fragments turns out to have an alternative interpolation property that closely resembles the interpolation property usually studied in modal logic. These results are strong enough to entail the Beth definability property for GF and PF. Even better, every guarded or packed finite variable fragment has the Beth property. For interpolation, we characterize exactly which finite variable fragments of GF and PF enjoy this property.     

Studies of wheel-running reinforcement: parameters of Herrnstein's (1970) response-strength equation vary with schedule order

Six male Wistar rats were exposed to different orders of reinforcement schedules to investigate if estimates from Herrnstein's (1970) single-operant matching law equation would vary systematically with schedule order. Reinforcement schedules were arranged in orders of increasing and decreasing reinforcement rate. Subsequently, all rats were exposed to a single reinforcement schedule within a session to determine within-session changes in responding. For each condition, the operant was lever pressing and the reinforcing consequence was the opportunity to run for 15 s. Estimates of k and R(O) were higher when reinforcement schedules were arranged in order of increasing reinforcement rate. Within a session on a single reinforcement schedule, response rates increased between the beginning and the end of a session. A positive correlation between the difference in parameters between schedule orders and the difference in response rates within a session suggests that the within-session change in response rates may be related to the difference in the asymptotes. These results call into question the validity of parameter estimates from Herrnstein's (1970) equation when reinforcer efficacy changes within a session.     

Prediction and classification in nonlinear data analysis: Something old,something new,something borrowed,something blue

Prediction and classification are two very active areas in modern data analysis. In this paper, prediction with nonlinear optimal scaling transformations of the variables is reviewed, and extended to the use of multiple additive components, much in the spirit of statistical learning techniques that are currently popular, among other areas, in data mining. Also, a classification/clustering method is described that is particularly suitable for analyzing attribute-value data from systems biology (genomics, proteomics, and metabolomics), and which is able to detect groups of objects that have similar values on small subsets of the attributes.This article is based on the Presidential Address Jacqueline Meulman gave on July 9, 2003 at the 68th Annual Meeting of the Psychometric Society held near Cagliari, Italy on the island of Sardinia.—Editor     

Response-independent milk delivery enhances persistence of pellet-reinforced lever pressing by rats

If, during training, one stimulus is correlated with a higher rate of reinforcement than another, responding will be more resistant to extinction in the presence of that higher rate signal, even if many of the reinforcers have been presented independently of responding. For the present study we asked if the response-independent reinforcers must be the same as the response-dependent reinforcers to enhance the response's persistence. Twelve Long-Evans hooded rats obtained 45-mg food pellets by lever pressing (variable-interval 100-s schedules) in the presence of two discriminative stimuli (blinking vs. steady lights) that alternated every minute during daily sessions. Also, in the presence of one of the stimuli (counterbalanced across rats), the rats received additional response-independent deliveries of sweetened condensed milk (a variable-time schedule). Extinction sessions were exactly like training sessions except that neither pellets nor milk were presented. Lever pressing was more resistant to extinction in the presence of the milk-correlated stimulus when (a) the size of the milk deliveries during training (under a variable-time 30 s schedule) was 0.04 ml (vs. 0.01 ml) and (b) 120-s or 240-s blackouts separated components. Response-independent reinforcers do not have to be the same as the response-dependent reinforcers to enhance persistence.     

Colour-cueing in visual search

Several studies have shown that people can selectively attend to stimulus colour, e.g., in visual search, and that preknowledge of a target colour can improve response speed/accuracy. The purpose was to use a form-identification task to determine whether valid colour precues can produce benefits and invalid cues costs. The subject had to identify the orientation of a "T"-shaped element in a ring of randomly-oriented "L"s when either two or four of the elements were differently coloured. Contrary to Moore and Egeth's (1998) recent findings, colour-based attention did affect performance under data-limited conditions: Colour cues produced benefits when processing load was high; when the load was reduced, they incurred only costs. Surprisingly, a valid colour cue succeeded in improving performance in the high-load condition even when its validity was reduced to the chance level. Overall, the results suggest that knowledge of a target colour does not facilitate the processing of the target, but makes it possible to prioritize it.     

Factor copula models for mixed data

We develop factor copula models to analyse the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and nonlinear dependence. They can be explained as conditional independence models with latent variables that do not necessarily have an additive latent structure. We focus on important issues of interest to the social data analyst, such as model selection and goodness of fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by reanalysing three mixed response data sets. Our studies suggest that there can be a substantial improvement over the standard factor model for mixed data and make the argument for moving to factor copula models.     

Some Behaviorial Science Measurement Concerns and Proposals

Primarily from a measurement standpoint, we question some basic beliefs and procedures characterizing the scientific study of human behavior. The relations between observed and unobserved variables are key to an empirical approach to building explanatory theories and we are especially concerned about how the former are used as proxies for the latter. We believe that behavioral science can profitably reconsider the prevailing version of this arrangement because of its vulnerability to limiting idiosyncratic aspects of observed/unobserved variable relations. We describe a general measurement approach that takes into account idiosyncrasies that should be irrelevant to the measurement process but can intrude and may invalidate it in ways that distort and weaken relations among theoretically important variables. To clarify further our major concerns, we briefly describe one version of the measurement approach that fundamentally supports the individual as the primary unit of analysis orientation that we believe should be preeminent in the scientific study of human behavior.     

Cooperative responding in rats maintained by fixed‐ and variable‐ratio schedules

The present study investigated the effects of fixed‐ratio (FR) and variable‐ratio (VR) reinforcement schedules on patterns of cooperative responding in pairs of rats. Experiment 1 arranged FR 1, FR 10, and VR 10 schedules to establish cooperative responding (water delivery depended on the joint responding of two rats). Cooperative response rates and proportions were higher under intermittent schedules than under continuous reinforcement. The FR 10 schedule generated a break‐and‐run pattern, whereas the VR 10 schedule generated a relatively high and constant rate pattern. Experiment 2 evaluated the effects of parametric manipulations of FR and VR schedules on cooperative responding. Rates and proportions of cooperative responding generally increased between ratio sizes of 1 and 5 but showed no consistent trend as the ratio increased from 5 to 10. Experiment 3 contrasted cooperative responding between an FR6 schedule and a yoked control schedule. Coordinated behavior occurred at a higher rate under the former schedule. The present study showed that external consequences and the schedules under which the delivery of these consequences are based, select patterns of coordinated behavior.     

A new variable interval schedule with constant hazard rate and finite time range

We propose a new variable interval (VI) schedule that achieves constant probability of reinforcement in time while using a bounded range of intervals. By sampling each trial duration from a uniform distribution ranging from 0 to 2 T seconds, and then applying a reinforcement rule that depends linearly on trial duration, the schedule alternates reinforced and unreinforced trials, each less than 2 T seconds, while preserving a constant hazard function.     

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

In recent years, network models have been proposed as an alternative representation of psychometric constructs such as depression. In such models, the covariance between observables (e.g., symptoms like depressed mood, feelings of worthlessness, and guilt) is explained in terms of a pattern of causal interactions between these observables, which contrasts with classical interpretations in which the observables are conceptualized as the effects of a reflective latent variable. However, few investigations have been directed at the question how these different models relate to each other. To shed light on this issue, the current paper explores the relation between one of the most important network models—the Ising model from physics—and one of the most important latent variable models—the Item Response Theory (IRT) model from psychometrics. The Ising model describes the interaction between states of particles that are connected in a network, whereas the IRT model describes the probability distribution associated with item responses in a psychometric test as a function of a latent variable. Despite the divergent backgrounds of the models, we show a broad equivalence between them and also illustrate several opportunities that arise from this connection.