Additive and multiplicative models for gamma distributed random variables,and their application as psychometric models for response times

A class of models for gamma distributed random variables is presented. These models are shown to be more flexible than the classical linear models with respect to the structure that can be imposed on the expected value. In particular, both additive, multiplicative, and combined additive-multiplicative models can be formulated. As a special case, a class of psychometric models for reaction times is presented, together with their psychological interpretation. By means of a comparison with existing models, this class of models is shown to offer some possibilities that are not available in existing methods. Parameter estimation by means of maximum likelihood (ML) is shown to have some attractive properties, since the models belong to the exponential family. Then, the results of a simulation study of the bias in the ML estimates are presented. Finally, the application of these models is illustrated by an analysis of the data from a mental rotation experiment. This analysis is preceded by an evaluation of the appropriateness of the gamma distribution for these data.     

What Causes the Mean Bias of the Likelihood Ratio Statistic with Many Variables?

Abstract

Survey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. However, conventional SEM methods are not crafted to handle data with a large number of variables (p). A large p can cause T_ml, the most widely used likelihood ratio statistic, to depart drastically from the assumed chi-square distribution even with normally distributed data and a relatively large sample size N. A key element affecting this behavior of T_ml is its mean bias. The focus of this article is to determine the cause of the bias. To this end, empirical means of T_ml via Monte Carlo simulation are used to obtain the empirical bias. The most effective predictors of the mean bias are subsequently identified and their predictive utility examined. The results are further used to predict type I errors of T_ml. The article also illustrates how to use the obtained results to determine the required sample size for T_ml to behave reasonably well. A real data example is presented to show the effect of the mean bias on model inference as well as how to correct the bias in practice.     

我国乡镇卫生资源二次配置模式探讨

长期以来,我国卫生资源配置城乡不均衡的局面比较严峻,大量优质卫生资源主要积聚在大中城市,而乡镇基层医疗机构的卫生资源比较稀缺。以增加政府财政投入,引入私人资本与第三部门力量等方式来提高农村卫生资源增量势必会遇到投入缓慢、资金不足、技术瓶颈等现实障碍。通过改革公立医院,调整城市卫生资源存量,把大中城市公立医院中的富余卫生资源以二次配置方式转移到农村卫生服务机构,是破解农村卫生资源存量不足、增长缓慢的困境,提高农村卫生服务能力和水平,改善农民就医问药问题的新途径。     

Display size effects in visual search: Analyses of reaction time distributions as mixtures

In a reanalysis of data from Cousineau and Shiffrin (2004) and two new visual search experiments, we used a likelihood ratio test to examine the full distributions of reaction time (RT) for evidence that the display size effect is a mixture-type effect that occurs on only a proportion of trials, leaving RT in the remaining trials unaffected, as is predicted by serial self-terminating search models. Experiment 1 was a reanalysis of Cousineau and Shiffrin's data, for which a mixture effect had previously been established by a bimodal distribution of RTs, and the results confirmed that the likelihood ratio test could also detect this mixture. Experiment 2 applied the likelihood ratio test within a more standard visual search task with a relatively easy target/distractor discrimination, and Experiment 3 applied it within a target identification search task within the same types of stimuli. Neither of these experiments provided any evidence for the mixture-type display size effect predicted by serial self-terminating search models. Overall, these results suggest that serial self-terminating search models may generally be applicable only with relatively difficult target/distractor discriminations, and then only for some participants. In addition, they further illustrate the utility of analysing full RT distributions in addition to mean RT.     

A Bayesian psychophysical model for angular variables

Bayesian theories of perception provide a link between observed response distributions and theoretical constructs from Bayesian decision theory. Using Bayesian psychophysics we derive response distributions for two cases, one based on a normal distribution and one on a von Mises distribution for angular variables. Interestingly, where the theoretical response distribution is always unimodal in the case of normal distributions, it can become bimodal in the angular setting in the case when prior and likelihood are about equally strong.