Model Fit and Item Factor Analysis: Overfactoring,Underfactoring, and a Program to Guide Interpretation

In exploratory item factor analysis (IFA), researchers may use model fit statistics and commonly invoked fit thresholds to help determine the dimensionality of an assessment. However, these indices and thresholds may mislead as they were developed in a confirmatory framework for models with continuous, not categorical, indicators. The present study used Monte Carlo simulation methods to investigate the ability of popular model fit statistics (chi-square, root mean square error of approximation, the comparative fit index, and the Tucker–Lewis index) and their standard cutoff values to detect the optimal number of latent dimensions underlying sets of dichotomous items. Models were fit to data generated from three-factor population structures that varied in factor loading magnitude, factor intercorrelation magnitude, number of indicators, and whether cross loadings or minor factors were included. The effectiveness of the thresholds varied across fit statistics, and was conditional on many features of the underlying model. Together, results suggest that conventional fit thresholds offer questionable utility in the context of IFA.     

The contribution of executive function and social understanding to preschoolers’ letter and math skills

The influence of executive function and social understanding on letter and math skills was examined in 129 3–5-year-olds. Tasks were administered to measure working memory, inhibition, social understanding, letter and math skills, and vocabulary. Using latent variable analyses, multiple models were compared in order to examine the influence of executive function and social understanding on participants’ emerging academic skills. In the best-fitting model, working memory contributed to letter and math skills, over and above inhibition, social understanding, age, and vocabulary. Inhibition and social understanding did not uniquely contribute to letter and math skills, but significant relations were found among working memory, inhibition, and social understanding. Findings are discussed with respect to improving ways to examine the complex relations among preschoolers’ executive function, social understanding, and school readiness skills.     

COMPARING PLEASURE AND PAIN: THE FUNDAMENTAL MATHEMATICAL EQUIVALENCE OF REWARD GAIN AND SHOCK REDUCTION UNDER VARIABLE INTERVAL SCHEDULES

The relationship between positive and negative reinforcement and the symmetry of Thorndike's law of effect are unresolved issues in operant psychology. Here we show that, for a given pattern of responding on variable interval (VI) schedules with the same programmed rate of food rewards (positive reinforcement VI) or electric shocks (negative reinforcement VI), there is a fundamental mathematical equivalence between reward gain and shock reduction. We also provide the first normative account of how animals should respond on a negative VI schedule, showing that it is better to space responses evenly than to respond with a variable interresponse time (IRT). Published data from rats, however, indicate that these animals respond irregularly, often with a burst of activity immediately following a shock. While this is irrational in the experimental setting, it may represent an appropriate response to the heterogeneity of stimuli commonly encountered in natural environments. We discuss the broader implications of our analysis for understanding how animals evaluate appetitive and aversive stimuli.     

Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities

The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the population distribution. A simulation study shows that the new procedure is feasible in practice, and that when the latent distribution is not well approximated as normal, two-parameter logistic (2PL) item parameter estimates and expected a posteriori scores (EAPs) can be improved over what they would be with the normal model. An example with real data compares the new method and the extant empirical histogram approach.     

存在问题的逻辑语言维度

存在问题在分析哲学的背景下取得了深入细致的研究成果。在“何谓存在”问题上,围绕“存在”是不是个体的属性从而是不是逻辑谓词的争论呈现出三派观点:弗雷格、罗素等从一阶逻辑出发,认为“存在”不是逻辑谓词,而是量词;皮尔士、斯特劳森等结合精致的自然语言分析,认为“存在”在某些特殊情况下表达了个体的属性,是一种特殊的谓词;自由逻辑学家则从自由逻辑的角度给出了肯定的答案。在“何物存在”问题上,蒯因“存在就是约束变项的值”的本体论承诺标准机智地揭示了存在问题的语言学实质。可以说,利用一阶逻辑解释存在问题的方法是比较成功的。如果将弗雷格、罗素的一阶语言扩展到高阶语言,则既能与蒯因的理论连贯一致,又能避免无谓的“存在”本体论纷争。这种做法的结果是“存在”具有了层次性的特征。掌握一定的逻辑学基础知识,有助于我们深入研究西方哲学。     

Maximizing present value: A model to explain why moderate response rates obtain on variable-interval schedules

In Phases 1 and 3, two Japanese monkeys responded on a multiple variable-ratio 80 variable-interval X schedule, where the value of X was adjusted to ensure equal between-schedule reinforcement rates. Components strictly alternated following the delivery of a food pellet, and each session ended following 50 components. Phase 2 differed from the others only in that the 50 pellets previously earned during the session were delivered together at session's end. Variable-ratio response rates did not decrease across phases, but variable-interval response rates decreased substantially during the Phase 2 procedure. This rate decrease was attributed to the food-at-session's-end manipulation removing the greater immediacy of reinforcement provided by short interresponse times relative to long interresponse times. Without this time preference for short interresponse times, the variable-interval interresponse-time reinforcement feedback function largely controlled response emission, dictating a response-rate reduction. This result was explained in terms of the economic notion of “maximizing present value.”     

Discriminative properties of briefly presented stimuli

In Experiment I, pigeons' responses produced food according to a fixed-interval schedule while responses on the key also produced brief stimuli according to a variable-interval schedule. Each brief stimulus reset the fixed interval. Thus, a brief stimulus occurred irregularly but a fixed minimum time separated the occurrence of food from a brief stimulus. Pauses followed brief stimuli and were followed by an accelerated response rate until another brief stimulus or food occurred. In Experiment II, four control procedures were examined. (1) Brief-stimulus presentations were omitted, producing a loss of response patterning. (2) A second-order schedule was studied with fixed-interval components. This schedule produced patterning following brief stimuli similar in kind and degree to that found in Experiment I. (3) A conjoint schedule was arranged in which food was no longer separated from the stimulus by a fixed time; pauses following the stimulus no longer resulted. (4) A brief food reinforcer replaced the brief visual stimulus, resulting in a constant response rate with no pausing following the brief food stimulus. The results suggest that the brief-stimulus effects were due to discriminative functions produced by the fixed temporal relation separating the stimulus from food.     

Schedule-induced defecation.

Excessive defecation, typically considered to be a concomitant of stress, was experimentally induced or eliminated under specific schedules of positive reinforcement of lever pressing by rats. The schedules were, by and large, those under which polydipsia is typically induced. In the first of three experiments, rats under fixed-interval 32-second schedules and variable interval 32-second schedules for food and water reinforcers defecated profusely, but not under fixed-interval one-second schedules or other small interval schedules. Somewhat higher rates of defecation were observed on variable interval 32-second schedules than on fixed-interval 32-second schedules. In a second experiment, fixed-ratio schedules were used, some of which resulted in responding such that reinforcement densities were similar to those on the interval schedules that induced defecation. Defecation was not systematically induced by these ratio schedules. In a third experiment, fixed-time schedules of food presentations were utilized. High rates of defecation were induced comparable to those induced by interval schedules of the same time parameter. No other behavior commonly termed "emotional" was observed in any of these experiments.