Estimating the parameters of the latent population distribution

Under consideration is a test battery of binary items. The responses ofn individuals are assumed to follow a Rasch model. It is further assumed that the latent individual parameters are distributed within a given population in accordance with a normal distribution. Methods are then considered for estimating the mean and variance of this latent population distribution. Also considered are methods for checking whether a normal population distribution fits the data. The developed methods are applied to data from an achievement test and from an attitude test.     

Stepwise variable selection in factor analysis

It is very important to choose appropriate variables to be analyzed in multivariate analysis when there are many observed variables such as those in a questionnaire. What is actually done in scale construction with factor analysis is nothing but variable selection.In this paper, we take several goodness-of-fit statistics as measures of variable selection and develop backward elimination and forward selection procedures in exploratory factor analysis. Once factor analysis is done for a certain numberp of observed variables (thep-variable model is labeled the current model), simple formulas for predicted fit measures such as chi-square, GFI, CFI, IFI and RMSEA, developed in the field of the structural equation modeling, are provided for all models obtained by adding an external variable (so that the number of variables isp + 1) and for those by deleting an internal variable (so that the number isp – 1), provided that the number of factors is held constant.A programSEFA (Stepwise variable selection in Exploratory Factor Analysis) is developed to actually obtain a list of the fit measures for all such models. The list is very useful in determining which variable should be dropped from the current model to improve the fit of the current model. It is also useful in finding a suitable variable that may be added to the current model. A model with more appropriate variables makes more stable inference in general.The criteria traditionally often used for variable selection is magnitude of communalities. This criteria gives a different choice of variables and does not improve fit of the model in most cases.The URL of the programSEFA is http://koko15.hus.osaka-u.ac.jp/~harada/factor/stepwise/.     

JEAB: Past,present, and future

The effects of response force on microstructure were evaluated. A strain-gauge operandum permitted the manipulation of the force required to produce reinforcers (criterion responses) independently from the force defining response threshold. Thus, we could detect subcriterion forces that fell short of the force criterion. Eight rats earned food according to variable-interval (VI) 30- and 120-s schedules. The force requirements were set to 5.6 or 32.0 g; the response threshold was fixed at 5.6 g. Interresponse times were computed when subcriterion responses were both included and omitted from the analysis. Log-survivor functions of interresponse times showed that increasing force requirements elevated the mean between-bout interval of the VI 120-s schedule, but only if subcriterion behavior was excluded. Omitting subcriterion responses thus leads to overestimation of intervals separating response bouts. Increasing force requirements also increased the skewness of the between-bout distribution. A subsequent analysis found that subcriterion responses are most plentiful following reinforcer delivery, which helps to explain why their omission might inflate between-bout intervals, as this period is an important transition from reinforcer consumption to engagement in operant activity. The data suggest caution interpreting the effects of force on microstructure when subcriterion behavior is not or cannot be measured.     

Variable-ratio versus variable-interval schedules: response rate, resistance to change, and preference

Two experiments asked whether resistance to change depended on variable-ratio as opposed to variable-interval contingencies of reinforcement and the different response rates they establish. In Experiment 1, pigeons were trained on multiple random-ratio random-interval schedules with equated reinforcer rates. Baseline response rates were disrupted by intercomponent food, extinction, and prefeeding. Resistance to change relative to baseline was greater in the interval component, and the difference was correlated with the extent to which baseline response rates were higher in the ratio component. In Experiment 2, pigeons were trained on multiple variable-ratio variable-interval schedules in one half of each session and on concurrent chains in the other half in which the terminal links corresponded to the multiple-schedule components. The schedules were varied over six conditions, including two with equated reinforcer rates. In concurrent chains, preference strongly overmatched the ratio of obtained reinforcer rates. In multiple schedules, relative resistance to response-independent food during intercomponent intervals, extinction, and intercomponent food plus extinction depended on the ratio of obtained reinforcer rates but was less sensitive than was preference. When reinforcer rates were similar, both preference and relative resistance were greater for the variable-interval schedule, and the differences were correlated with the extent to which baseline response rates were higher on the variable-ratio schedule, confirming the results of Experiment 1. These results demonstrate that resistance to change and preference depend in part on response rate as well as obtained reinforcer rate, and challenge the independence of resistance to change and preference with respect to response rate proposed by behavioral momentum theory.     

Behavioral momentum in computer-presented discriminations in individuals with severe mental retardation

Behavioral momentum was examined in 2 individuals with severe mental retardation via within-subject manipulations of obtained reinforcer rates. Subjects performed self-paced discrimination problems presented on a touch screen computer monitor. Two different problems, Tasks A and B, alternated in blocks of 15 trials on a multiple schedule. Reinforcers were snack foods. The reinforcement schedule for Task A was continuous (fixed-ratio 1) and the schedule for Task B was continuous in some conditions and variable ratio in other conditions. Behavioral momentum was assessed in test sessions by prefeeding, presenting response-independent food, and making available alternatives to the tasks. When the obtained reinforcer rate for Task A was at least twice that for Task B, resistance to change was greater for Task A. When both reinforcer rates and response rates were a pproximately equal for the two tasks, resistance to change was approximately equal. These results are consistent with behavioral momentum effects. They extend previous findings with humans by examining momentum in self-initiated discrete-trial discrimination tasks with ratio schedules, and by isolating relative reinforcer rates as a controlling variable via within-subject manipulations.     

Response rate viewed as engagement bouts: effects of relative reinforcement and schedule type.

The rate of a reinforced response is conceptualized as a composite of engagement bouts (visits) and responding during visits. Part I of this paper describes a method for estimating the rate of visit initiations and the average number of responses per visit from log survivor plots: the proportion) of interresponse times (IRTs) longer than some elapsed time (log scale) plotted as a function of elapsed time. In Part 2 the method is applied to IRT distributions from rats that obtained food pellets by nose poking a lighted key under various multiple schedules of reinforcement. As expected, total response rate increased as a function of (a) increasing the rate of reinforcement (i.e., variable-interval [VI] 4 min vs. VI 1 mi), (b) increasing the amount of the reinforcer (one food pellet vs. four pellets), (c) increasing the percentage of reinforcers that were contingent on nose poking (25% vs. 100%), and (d) requiring additional responses after the end of the VI schedule (i.e., adding a tandem variable-ratio [VR] 9 requirement). The first three of these variables (relative reinforcement) increased the visit-initiation rate. The tandem VR, in contrast, increased the number of responses per visit. Thus, variables that have similar effects on total response rate can be differentiated based on their effects on the componemts of response rate.     

The general matching law describes choice on concurrent variable-interval schedules of wheel-running reinforcement.

Six male Wistar rats were exposed to concurrent variable-interval schedules of wheel-running reinforcement. The reinforcer associated with each alternative was the opportunity to run for 15 s, and the duration of the changeover delay was 1 s. Results suggested that time allocation was more sensitive to relative reinforcement rate than was response allocation. For time allocation, the mean slopes and intercepts were 0.82 and 0.008, respectively. In contrast, for response allocation, mean slopes and intercepts were 0.60 and 0.03, respectively. Correction for low response rates and high rates of changing over, however, increased slopes for response allocation to about equal those for time allocation. The results of the present study suggest that the two-operant form of the matching law can be extended to wheel-running reinforcement. 'I'he effects of a low overall response rate, a short Changeover delay, and long postreinforcement pausing on the assessment of matching in the present study are discussed.     

工作嵌入的概念、测量及相关变量

工作嵌入代表个体与工作的嵌入程度,用于解释个体为什么留在组织中的一系列因素,具有非情感性、多维度的特点。工作嵌入明显区别于工作满意度、组织承诺等组织行为学变量,包括匹配、联结以及牺牲三个维度。该文明确了工作嵌入与相关变量的概念区别,重点介绍了工作嵌入测量方法的发展以及其在组织行为领域中的研究成果,并指出了今后有必要对其影响因素、测量工具、维度以及结果变量拓展等四个方面进行探讨     

Multilevel and Latent Variable Modeling with Composite Links and Exploded Likelihoods

Composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models. Applications considered include survival or duration models, models for rankings, small area estimation with census information, models for ordinal responses, item response models with guessing, randomized response models, unfolding models, latent class models with random effects, multilevel latent class models, models with log-normal latent variables, and zero-inflated Poisson models with random effects. Some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation. We wish to thank The Research Council of Norway for a grant supporting our collaboration.     

Multilevel Modeling with Correlated Effects

When there exist omitted effects, measurement error, and/or simultaneity in multilevel models, explanatory variables may be correlated with random components, and standard estimation methods do not provide consistent estimates of model parameters. This paper introduces estimators that are consistent under such conditions. By employing generalized method of moments (GMM) estimation techniques in multilevel modeling, the authors present a series of estimators along a robust to efficient continuum. This continuum depends on the assumptions that the analyst makes regarding the extent of the correlated effects. It is shown that the GMM approach provides an overarching framework that encompasses well-known estimators such as fixed and random effects estimators and also provides more options. These GMM estimators can be expressed as instrumental variable (IV) estimators which enhances their interpretability. Moreover, by exploiting the hierarchical structure of the data, the current technique does not require additional variables unlike traditional IV methods. Further, statistical tests are developed to compare the different estimators. A simulation study examines the finite sample properties of the estimators and tests and confirms the theoretical order of the estimators with respect to their robustness and efficiency. It further shows that not only are regression coefficients biased, but variance components may be severely underestimated in the presence of correlated effects. Empirical standard errors are employed as they are less sensitive to correlated effects when compared to model-based standard errors. An example using student achievement data shows that GMM estimators can be effectively used in a search for the most efficient among unbiased estimators. This research was supported by the National Academy of Education/Spencer Foundation and the National Science Foundation, grant number SES-0436274. We thank the editor, associate editor, and referees for detailed feedback that helped improve the paper.