An overview of applied robust methods

Data in social sciences are typically non-normally distributed and characterized by heavy tails. However, most widely used methods in social sciences are still based on the analyses of sample means and sample covariances. While these conventional methods continue to be used to address new substantive issues, conclusions reached can be inaccurate or misleading. Although there is no ‘best method’ in practice, robust methods that consider the distribution of the data can perform substantially better than the conventional methods. This article gives an overview of robust procedures, emphasizing a few that have been repeatedly shown to work well for models that are widely used in social and behavioural sciences. Real data examples show how to use the robust methods for latent variable models and for moderated mediation analysis when a regression model contains categorical covariates and product terms. Results and logical analyses indicate that robust methods yield more efficient parameter estimates, more reliable model evaluation, more reliable model/data diagnostics, and more trustworthy conclusions when conducting replication studies. R and SAS programs are provided for routine applications of the recommended robust method.     

On scaling models applied to data from several groups

Statistical methods are presented to facilitate a more complete analysis of results obtained when a scaling model is applied to data from two or more groups. These methods can be used to (a) compare the corresponding estimated latent distributions obtained using the scaling model applied to the different groups, (b) compare the corresponding estimated item reliabilities (or item response error rates) for the different groups, and (c) test whether the scaling model applied to the several groups can be replaced by a more parsimonious scaling model that includes various homogeneity constraints (i.e., constraints that describe which parameters in the model are the same for the several groups). Various kinds of scaling models are considered here in the multiple-group context.Support for this research was provided in part by the National Science Foundation, to Clogg by Grant No. SES-7823759 and to Goodman by Grant No. SES-8303838. Clogg and Goodman were Fellows at the Center for Advanced Study in the Behavioral Sciences when part of the research was done, with financial support provided in part by National Science Foundation grant BNS-8011494 to the Center. The authors are indebted to Mark P. Becker and James W. Shockey for helpful comments.     

Conjunctive item response theory kernels

Conjunctive item response models are introduced such that (a) sufficient statistics for latent traits are not necessarily additive in item scores; (b) items are not necessarily locally independent; and (c) existing compensatory (additive) item response models including the binomial, Rasch, logistic, and general locally independent model are special cases. Simple estimates and hypothesis tests for conjunctive models are introduced and evaluated as well. Conjunctive models are also identified with cognitive models that assume the existence of several individually necessary component processes for a global ability. It is concluded that conjunctive models and methods may show promise for constructing improved tests and uncovering conjunctive cognitive structure. It is also concluded that conjunctive item response theory may help to clarify the relationships between local dependence, multidimensionality, and item response function form.I appreciate the many helpful suggestions that were given by the reviewers and Ivo Molenaar.     

Speech acts and arguments

Speech act theory seems to provide a promising avenue for the analysis of the functional organization of argument. The theory, however, might be taken to suggest that arguments are a homogenous class of speech act with a specifiable illocutionary force and a single set of felicity conditions. This suggestion confuses the analysis of the meaning of speech act verbs with the analysis of the pragmatic structure of actual language use. Suggesting that arguments are conveyed through a homogeneous class of linguistic action overlooks the way in which the context of activity and the form of expression organize the argumentative functions performed in using language. An alternative speech act analysis would treat folk terminology as a heuristic entry point into the development of a technical analysis of the myriad argumentative functions and structures to be found in natural language use. This would lead to a thorough-going pragmatic analysis of the rational and functional design of speech acts in argumentation.     

Dynamic factor analysis of nonstationary multivariate time series

A dynamic factor model is proposed for the analysis of multivariate nonstationary time series in the time domain. The nonstationarity in the series is represented by a linear time dependent mean function. This mild form of nonstationarity is often relevant in analyzing socio-economic time series met in practice. Through the use of an extended version of Molenaar's stationary dynamic factor analysis method, the effect of nonstationarity on the latent factor series is incorporated in the dynamic nonstationary factor model (DNFM). It is shown that the estimation of the unknown parameters in this model can be easily carried out by reformulating the DNFM as a covariance structure model and adopting the ML algorithm proposed by Jöreskog. Furthermore, an empirical example is given to demonstrate the usefulness of the proposed DNFM and the analysis.     

Sequential sampling designs for the two-parameter item response theory model

In optimal design research, designs are optimized with respect to some statistical criterion under a certain model for the data. The ideas from optimal design research have spread into various fields of research, and recently have been adopted in test theory and applied to item response theory (IRT) models. In this paper a generalized variance criterion is used for sequential sampling in the two-parameter IRT model. Some general principles are offered to enable a researcher to select the best sampling design for the efficient estimation of item parameters.     

Extensions of Rasch's multiplicative poisson model

Consideration will be given to a model developed by Rasch that assumes scores observed on some types of attainment tests can be regarded as realizations of a Poisson process. The parameter of the Poisson distribution is assumed to be a product of two other parameters, one pertaining to the ability of the subject and a second pertaining to the difficulty of the test. Rasch's model is expanded by assuming a prior distribution, with fixed but unknown parameters, for the subject parameters. The test parameters are considered fixed. Secondly, it will be shown how additional between- and within-subjects factors can be incorporated. Methods for testing the fit and estimating the parameters of the model will be discussed, and illustrated by empirical examples.     

人眼深度运动知觉的研究

人类的深度运动知觉,是通过检测二维平面内的相对运动而形成的。本文在心理物理学实验基础上,揭示该机制的数学与生理学实现形式。视觉系统中存在对视平面内的相对运动敏感的神经元,构成深度运动的检测机制,产生单眼深度运动知觉与双眼深度运动知觉。在心理学上,视觉利用物体视角变化及大小知觉的恒常性判断深度运动。文中还初步讨论了人类的深度运动知觉与蜜蜂,家蝇等昆虫的深度运动知觉的区别。     

樟柳碱所致学习和记忆障碍动物模型的探讨

本实验采用水迷津法、步下法和步入法,用樟柳碱制备学习和记忆障碍的动物模型。结果表明,樟柳碱(10毫克/公斤)可使小鼠引起学习障碍,其表现为通过水迷津全程的时间延长,而且小鼠进入盲路的错误次数明显增多。樟柳碱(10毫克/公斤)可使小鼠引起记忆障碍,在樟柳碱的影响下,小鼠步下平台或步入暗箱的潜伏期明显缩短,并使它们的错误次数增多。本实验结果进一步表明,测定小鼠的记忆障碍,步入法似乎比步下法更为敏感。