Evaluating Factorial Invariance: An Interval Estimation Approach Using Bayesian Structural Equation Modeling

In this study, we introduce an interval estimation approach based on Bayesian structural equation modeling to evaluate factorial invariance. For each tested parameter, the size of noninvariance with an uncertainty interval (i.e. highest density interval [HDI]) is assessed via Bayesian parameter estimation. By comparing the most credible values (i.e. 95% HDI) with a region of practical equivalence (ROPE), the Bayesian approach allows researchers to (1) support the null hypothesis of practical invariance, and (2) examine the practical importance of the noninvariant parameter. Compared to the traditional likelihood ratio test, simulation results suggested that the proposed Bayesian approach could offer additional insight into evaluating factorial invariance, thus, leading to more informative conclusions. We provide an empirical example to demonstrate the procedures necessary to implement the proposed method in applied research. The importance of and influences on the choice of an appropriate ROPE are discussed.     

Assessing human reorientation ability inside virtual reality environments: the effects of retention interval and landmark characteristics

The purpose of the present study was to assess the navigational behaviour of adult humans following a disorientation procedure that perturbed their egocentric frame of reference. The assessment was carried out in a virtual reality (VR) environment by manipulating the disorientation procedure, the retention interval, the relative positions of target and landmark. The results of experiment I demonstrated that adding a physical rotation to a virtual disorientation procedure did not yield an additional decrease in searching performance. The results of experiment II showed that shortening the delay between study and test phase decreased the errors more markedly for geometric than landmark ones. An orientation specificity effect due to the manipulation of the relative position between target and landmark was discussed across the experiments. In conclusion, VR seemed to be a valuable method for studying human reorientation. Moreover, the virtual experimental setting involved here promoted knowledge of the relationship between working memory and spatial reorientation paradigm.     

Optimal behavior and concurrent variable interval schedules

Behavior maintained with 2-component concurrent variable interval schedules of reinforcement (CONC VIVI) is described well by the matching law. Deviations from matching behavior have been handled by adding free parameters to the matching law equation. With CONC VIVI schedules there are infinitely many solutions to the matching law equation at each value of the procedural parameters. However, at each value of the procedural parameters, only one combination of durations of intervals spent in each VI component (dwell times) yields the combined maximum reinforcement rate. The equations that yield the optimal dwell times solution for CONC VIVI schedules are mathematically incompatible with the matching law. Optimal performance and matching coincide only when the parameter values of the two VI components are equal. It seems reasonable to use optimal behavior to assess performance in these schedules. Researchers have not compared optimal and empirical performances in CONC VIVI possibly because the equations for optimal dwell times (ODT) can be solved only numerically. We present a table of ODT for a wide range of VIs and changeover delays. We also derive a function m that can be used to compare matching data and the matching behavior predictions of optimization. We prove that 0.5<m<1.003502, and we describe some of the more nteresting properties of the function.     

Do local properties function as cues for musical key perception?1

Abstract: A global property (i.e., pitch set) of a melody appears to serve as a primary cue for key identification. Previous studies have proposed specific local properties in a melody (e.g., the augmented fourth, the perfect fifth, etc.) that may function as further cues. However, the role of the latter in key identification is controversial. The present study was designed to investigate what kinds of local properties, if any, function as reliable cues for key identification. Listeners were asked to identify keys for 450 melodies that consisted of the same pitch set, but which differed in sequential constraints. Using multiple discriminant analyses, we evaluated relative contributions of as many kinds of local properties as possible (e.g., single intervals, single pitch classes in each sequential position, etc.). The results showed that, except for the pitch class of the final tone, for which interpretation should be taken cautiously, none of the specific local properties examined contributed significantly to key identification. This finding suggests that, contrary to prior findings, key identification is derived from unidentified properties other than the specific local properties.     

Reward value effects on timing in the peak procedure

Three experiments examined the effect of motivational variables on timing in the peak procedure. In Experiment 1, rats received a 60-s peak procedure that was coupled with long-term, between-phase changes in reinforcer magnitude. Increases in reinforcer magnitude produced a leftward shift in the peak that persisted for 20 sessions of training. In a final phase, the rats received lithium chloride-induced aversion prior to testing and a rightward shift in the peak was observed. Experiment 2 confirmed the rightward shift in the peak under lithium chloride devaluation and induced a comparable shift with satiety devaluation. The degree of rightward shift was neither additive nor multiplicative, suggesting that two processes may have contributed. Experiment 3 examined the effect of extinction on peak responding, revealing a decrease in response rate, but no evidence of any change in the timing of responding. The implications of the results for contemporary timing theories are discussed.     

CHANGES IN BLOOD PRESSURE AND HEART RATE DURING FIXED‐INTERVAL RESPONDING IN SQUIRREL MONKEYS

Episodic and sustained increases in heart rate and mean arterial blood pressure can occur with recurring patterns of schedule‐controlled behavior. Most previous studies were conducted under fixed‐ratio schedules, which maintained a consistent high rate of responding that alternated with periods of no responding during times when the schedule was not in operation. The present study examined changes in heart rate and blood pressure under fixed‐interval schedules which maintained a range of rates that varied from little or no responding at the beginning of the fixed interval to high rates at the end of the interval. The relations of cardiovascular function to rate of responding were examined. Squirrel monkeys prepared with arterial catheters were trained to respond under fixed‐interval schedules of electric‐shock presentation. The duration of the interval was varied across sessions and cardiovascular parameters were examined. Local rates of responding were typically near zero during timeout periods, low at the beginning of each fixed‐interval cycle, and then increased as the fixed interval progressed. At most schedule durations, arterial blood pressure and heart rate levels were lowest at the beginning of the interval cycles, increased as the rate of responding increased, and then decreased during the timeout periods. At all parameters studied, there was a direct relationship between changes in response rate within fixed‐interval cycles and changes in heart rate and blood pressure. The results suggest that a much closer concordance of these cardiovascular parameters and schedule‐controlled responding is obtained by examining ongoing behavior as it occurs within the contingencies by which it is maintained.     

An eight-alternative concurrent schedule: foraging in a radial maze.

In two experiments conducted in an eight-arm radial maze, food pellets were delivered when a photocell beam was broken at the end of each arm via a nose poke, according to either fixed-interval or random-interval schedules of reinforcement, with each arm providing a different frequency of reinforcement. The behavior of rats exposed to these procedures was well described by the generalized matching law; that is, the relationships between log behavior ratios and log pellet ratios were approximated by linear functions. The slopes of these log-log functions, an index of sensitivity to reinforcement frequency, were greatest for nose pokes, intermediate for time spent in an arm, and least for arm entries. Similar results were obtained with both fixed-interval and random-interval schedules. Addition of a 10-s changeover delay in both experiments eliminated the slope differentials between nose pokes and time spent in an arm by reducing the slopes of the nose-poke functions. These results suggest that different aspects of foraging may be differentially sensitive to reinforcement frequency. With concurrent fixed-interval schedules, the degree of temporal control exerted by individual fixed-interval schedules was directly related to reinforcement frequency.     

Matching, maximizing, and hill-climbing

In simple situations, animals consistently choose the better of two alternatives. On concurrent variable-interval variable-interval and variable-interval variable-ratio schedules, they approximately match aggregate choice and reinforcement ratios. The matching law attempts to explain the latter result but does not address the former. Hill-climbing rules such as momentary maximizing can account for both. We show that momentary maximizing constrains molar choice to approximate matching; that molar choice covaries with pigeons' momentary-maximizing estimate; and that the “generalized matching law” follows from almost any hill-climbing rule.     

Uninstructed human responding: Sensitivity of low-rate performance to schedule contingencies

College students' presses on a telegraph key occasionally turned on a light in the presence of which button presses produced points later exchangeable for money. Initially, responding was maintained by low-rate contingencies superimposed on either random-interval or random-ratio schedules. Later, the low-rate contingencies were relaxed. Low-rate key pressing had been established for some students by shaping and for others by demonstration and written instructions. After the low-rate contingencies were relaxed, higher response rates generally did not increase point earnings with random-interval scheduling, but did so with random-ratio scheduling. In both cases, shaped responding usually increased, and instructed responding usually continued at an unchanged low rate. The insensitivity of instructed responding typically occurred despite contact with the contingencies. The differential sensitivity to schedule contingencies of shaped responding relative to instructed responding is consistent with the different properties of contingency-governed and rule-governed behavior and is not rate-dependent.     

Time, trace, memory

Objections to a trace hypothesis for interval timing do not apply to the multiple-time-scale (MTS) theory, which incorporates a dynamic trace tuned by the system history and can easily accommodate interval timing over a 1,000:1 range. The MTS model can also account for Weber's law as well as systematic deviations from it. Contrary to our critics, we contend that patterns of variance in interval timing experiments are not fully described by scalar expectancy theory, and that attempting to understand timing by assigning variance to different elements of a flexible model that lacks inductive support is a flawed strategy, because the attempt may be successful even if the model is wrong. We further argue that biological plausibility is an unreliable guide to the development of behavioral theory, that prediction is not the same as test, that induction should precede deduction, and that a rat is not a clock.