Noniterative estimation and the choice of the number of factors in exploratory factor analysis

Based on the usual factor analysis model, this paper investigates the relationship between improper solutions and the number of factors, and discusses the properties of the noniterative estimation method of Ihara and Kano in exploratory factor analysis. The consistency of the Ihara and Kano estimator is shown to hold even for an overestimated number of factors, which provides a theoretical basis for the rare occurrence of improper solutions and for a new method of choosing the number of factors. The comparative study of their estimator and that based on maximum likelihood is carried out by a Monte Carlo experiment.The author would like to express his thanks to Masashi Okamoto and Masamori Ihara for helpful comments and to the editor and referees for critically reading the earlier versions and making many valuable suggestions. He also thanks Shigeo Aki for his comments on physical random numbers.     

MODIFYING LETTER AND NUMBER REVERSALS IN ELEMENTARY SCHOOL CHILDREN1

Children from regular and special-education classes were exposed to tutoring procedures designed to modify letter and number reversals. In Experiment I, two students showed reversals during letter-naming (e.g., saying p for q) and two-digit number (e.g., writing 31 for 13) exercises. In Experiment II, one subject made two-digit reversals, while the other child reversed single-digit numbers (e.g., 9 written with circle on right side of stem). The subject in Experiment III emitted letter reversals under naming, dictation, and copying exercises. The child in Experiment IV showed written letter reversals on both sides of the “body midline” under dictation procedures. Basic treatment procedures during all experiments involved modelling of correct and incorrect symbol formation, and differential experimenter feedback following student responses. During Experiments I and II, subjects were praised for each correct response, and informed when a reversal occurred. Experiment III included a Modelling Only Phase before these feedback procedures. Besides praise, treatment conditions in Experiment IV consisted of additional feedback following correct responses (e.g., charting correct responses), and temporal delays imposed between dictated letters and student responses. Except for occasional letter-naming reversals of one subject (Experiment I), and letter dictation errors of another (Experiment IV), reversals were eliminated when all experiments terminated. The Modelling Only Phase in Experiment III also reduced reversals to a low level. These findings suggest that a variety of reversal problems may be effectively assessed and remediated via simple modelling and reinforcement procedures. In addition, postcheck observations indicated that the effects were enduring. The present procedures should be easily implemented by school personnel.     

Determinants of pausing under variable-ratio schedules: Reinforcer magnitude, ratio size, and schedule configuration

Pigeons pecked a key under two-component multiple variable-ratio schedules that offered 8-s or 2-s access to grain. Phase 1 assessed the effects of differences in reinforcer magnitude on postreinforcement pausing, as a function of ratio size. In Phase 2, postreinforcement pausing and the first five interresponse times in each ratio were measured as a function of differences in reinforcer magnitude under equal variable-ratio schedules consisting of different configurations of individual ratios. Rates were also calculated exclusive of postreinforcement pause times in both phases. The results from Phase 1 showed that as ratio size increased, the differences in pausing educed by unequal reinforcer magnitudes also increased. The results of Phase 2 showed that the effects of reinforcer magnitude on pausing and IRT durations were a function of schedule configuration. Under one configuration, in which the smallest ratio was a fixed-ratio 1, pauses were unaffected by magnitude but the first five interresponse times were affected. Under the other configuration, in which the smallest ratio was a fixed-ratio 7, pauses were affected by reinforcer magnitude but the first five interresponse times were not. The effect of each configuration seemed to be determined by the value of the smallest individual ratio. Rates calculated exclusive of postreinforcement pause times were, in general, directly related to reinforcer magnitude, and the relation was shown to be a function of schedule configuration.     

FACAIC: Model selection algorithm for the orthogonal factor model using AIC and CAIC

This paper describes the authors' FORTRAN algorithm FACAIC for choosing the number of factors for an orthogonal factor model using Akaike's Information Criterion. FACAIC utilizes the IMSL subroutine OFCOMM.The authors dedicate this algorithm to Professor Hirotugu Akaike in appreciation of his pioneering work on AIC which was originally intended for the factor analysis and other statistical model identification problems.     

Within-session meal-size effects on induced drinking.

As a control for the effects of session duration and hunger on the relation between food magnitude and induced drinking, four food-deprived rats were exposed to a variable-time 50-s schedule of food delivery in which the size of each food delivery varied randomly within sessions. Food-related behavior and schedule-induced drinking per opportunity were examined as functions of meal size and postfood time. All rats showed an inverted-U-shaped relation between drinking per opportunity and meal size. This relation was caused by variation in the percentage of intervals that contained drinking and by variation in the number of drinking bouts per interval, rather than by bout duration or by the amount of drinking within those intervals that actually contained drinking. Head-in-feeder time increased linearly with meal size. Schedule-induced drinking was entrained by food delivery in 3 of 4 subjects; the entrainment was due to regulation of the starting time of each drinking bout rather than to regulation of bout duration.     

On the distinction between open and closed economies.

Open and closed economies have been assumed to produce opposite relations between responding and the programmed density of reward (the amount of reward divided by its cost). Experimental procedures that are treated as open economies typically dissociate responding and total reward by providing supplemental income outside the experimental session; procedures construed as closed economies do not. In an open economy responding is assumed to be directly related to reward density, whereas in a closed economy responding is assumed to be inversely related to reward density. In contrast to this predicted correlation between response-reward relations and type of economy, behavior regulation theory predicts both direct and inverse relations in both open and closed economies. Specifically, responding should be a bitonic function of reward density regardless of the type of economy and is dependent only on the ratio of the schedule terms rather than on their absolute size. These predictions were tested by four experiments in which pigeons' key pecking produced food on fixed-ratio and variable-interval schedules over a range of reward magnitudes and under several open- and closed-economy procedures. The results better supported the behavior regulation view by showing a general bitonic function between key pecking and food density in all conditions. In most cases, the absolute size of the schedule requirement and the magnitude of reward had no effect; equal ratios of these terms produced approximately equal responding.     

Confirmation of linear system theory prediction: Rate of change of Herrnstein's kappa as a function of response-force requirement

Four human subjects worked on all combinations of five variable-interval schedules and five reinforcer magnitudes (¢/reinforcer) in each of two phases of the experiment. In one phase the force requirement on the operandum was low (1 or 11 N) and in the other it was high (25 or 146 N). Estimates of Herrnstein's κ were obtained at each reinforcer magnitude. The results were: (1) response rate was more sensitive to changes in reinforcement rate at the high than at the low force requirement, (2) κ increased from the beginning to the end of the magnitude range for all subjects at both force requirements, (3) the reciprocal of κ was a linear function of the reciprocal of reinforcer magnitude for seven of the eight data sets, and (4) the rate of change of κ was greater at the high than at the low force requirement by an order of magnitude or more. The second and third findings confirm predictions made by linear system theory, and replicate the results of an earlier experiment (McDowell & Wood, 1984). The fourth finding confirms a further prediction of the theory and supports the theory's interpretation of conflicting data on the constancy of Herrnstein's κ.     

4～5岁儿童对书面数符号的表征和理解能力的发展

本研究对61名中班儿童的书面数符号表征和理解能力进行了跟踪调查。一年中三次个别面试的结果表明,约40％的4岁儿童已能运用1—10的书面数符号表征数量。至中班末期,大多数5岁儿童能够较熟练地运用至少1一17的书面数符号来表征数量,尽管其中有人在两位数的表征和数字的正确写法上有困难。儿童的书面数符号表征与他们的基数概念发展水平密切相关。大学附属幼儿园4—5岁儿童的书面数符号表征能力好于为工人家庭服务的幼儿园儿童的能力。     

任务框架、损益值大小对自恋者风险偏好的影响

以234名大学生为被试,探讨了任务框架、损益值大小对显性/隐性自恋者风险偏好的影响。结果表明：(1)框架效应较稳定的出现在中等风险水平情境下,且在大损益值条件下更易出现。(2)在获益框架下,被试为小金额决策更冒险,在损失框架下,则为大金额决策更冒险。(3)在损失框架下,高显性自恋者比低显性自恋者更为冒险,在获益框架下,高隐性自恋者比低隐性自恋者更为保守;高隐性自恋者的风险偏好受到任务框架和损益值大小的共同影响。     

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.