On the sampling interpretation of confidence intervals and hypothesis tests in the context of conditional maximum likelihood estimation

In the context ofconditional maximum likelihood (CML) estimation, confidence intervals can be interpreted in three different ways, depending on the sampling distribution under which these confidence intervals contain the true parameter value with a certain probability. These sampling distributions are (a) the distribution of the data given theincidental parameters, (b) the marginal distribution of the data (i.e., with the incidental parameters integrated out), and (c) the conditional distribution of the data given the sufficient statistics for the incidental parameters. Results on the asymptotic distribution of CML estimates under sampling scheme (c) can be used to construct asymptotic confidence intervals using only the CML estimates. This is not possible for the results on the asymptotic distribution under sampling schemes (a) and (b). However, it is shown that theconditional asymptotic confidence intervals are also valid under the other two sampling schemes. I am indebted to Theo Eggen, Norman Verhelst and one of Psychometrika's reviewers for their helpful comments.     

标准参照测验中的信度估计公式

标准参照测验是与常模参照测验不同的一种测验,在标准参照测验中,一个人在测验上的分数不是和他人相比较而是和某个已经设定的标准作比较。如果测验是从某功课论域中随机抽样构造而成,则使用者希望知道考生在这份测验上的观测分数与其在该功课论域上的分数（假如已知）的接近程度;如果使用者想根据测验分数对考生作掌握分类,则他们关心这个推断与假设考生论域分数已知时所作推断一致程度有多高。本文对这两个问题的信度估计进行探讨,得到几个有用的估计公式。     

A parametric procedure for ultrametric tree estimation from conditional rank order proximity data

The psychometric and classification literatures have illustrated the fact that a wide class of discrete or network models (e.g., hierarchical or ultrametric trees) for the analysis of ordinal proximity data are plagued by potential degenerate solutions if estimated using traditional nonmetric procedures (i.e., procedures which optimize a STRESS-based criteria of fit and whose solutions are invariant under a monotone transformation of the input data). This paper proposes a new parametric, maximum likelihood based procedure for estimating ultrametric trees for the analysis of conditional rank order proximity data. We present the technical aspects of the model and the estimation algorithm. Some preliminary Monte Carlo results are discussed. A consumer psychology application is provided examining the similarity of fifteen types of snack/breakfast items. Finally, some directions for future research are provided.     

Estimating latent distributions in recurrent choice data

This paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data. These choice models are derived by specifying elements of the choice process at the individual level. Probability distributions are introduced to describe variations in the choice process among individuals and to obtain a representation of the aggregate choice behavior. Due to the explicit consideration of random effect sources, the choice models are parsimonious and readily interpretable. An easy to implement EM algorithm is presented for parameter estimation. Two applications illustrate the proposed approach.     

Ability estimation for conventional tests

Five different ability estimators—maximum likelihood [MLE ()], weighted likelihood [WLE ()], Bayesian modal [BME ()], expected a posteriori [EAP ()] and the standardized number-right score [Z ()]—were used as scores for conventional, multiple-choice tests. The bias, standard error and reliability of the five ability estimators were evaluated using Monte Carlo estimates of the unknown conditional means and variances of the estimators. The results indicated that ability estimates based on BME (), EAP () or WLE () were reasonably unbiased for the range of abilities corresponding to the difficulty of a test, and that their standard errors were relatively small. Also, they were as reliable as the old standby—the number-right score.     

学前儿童对时距的估计及其策略

该研究旨在探查学前儿童对时距的认识过程及其认识策略。使用2秒、4秒、6秒、8秒四种不同的时间间隔作为刺激物,在每次呈现之后要求儿童按键再现时距。5岁和6岁的学前儿童参加这一实验。主要结果表明:5、6岁儿童已能区分只有几秒钟差异的单一时距;在无声音参照条件下,他们对4秒钟的估计较为准确,而在有声音参照条件下,5岁儿童则对6秒钟的估计更趋准确。研究材料还证实了,儿童从5岁起初步能够使用时间标尺,开始把时间看成是可以计数的维量。     

Robust multidimensional scaling

A method for multidimensional scaling that is highly resistant to the effects of outliers is described. To illustrate the efficacy of the procedure, some Monte Carlo simulation results are presented. The method is shown to perform well when outliers are present, even in relatively large numbers, and also to perform comparably to other approaches when no outliers are present.This research was supported by Grant A8351 from the Natural Sciences and Engineering Research Council of Canada to Ian Spence.     

A comparison of three simple test theory models

In very simple test theory models such as the Rasch model, a single parameter is used to represent the ability of any examinee or the difficulty of any item. Simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available, and are themselves of real practical value for small or even medium samples. They can also serve a normative role in test design.As an alternative to the Rasch model, or the Rasch model with a correction for guessing, a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference. This model provides a natural account of guessing, and has other useful things to contribute as well. It also offers an alternative to the Rasch model with the usual correction for guessing. The three models are compared in terms of statistical properties and fits to actual data. The goal of the paper is to widen the range of minimal models available to test analysts.This research was supported by grant AP320 from the Natural Sciences and Engineering Research Council of Canada. The author is grateful for discussions with M. Abrahamowicz, I. Molenaar, D. Thissen, and H. Wainer.     

短时距估计中的标量特性

使用单任务研究程序,采用预期式研究范式和再现时距的研究方法,从心理物理学的视角,通过三个实验系统地考查了人类短时距估计的标量特性、变异源、时距估计中的转换点和韦伯函数的形态等问题。结果表明,刺激物的运动、变化、速度和物理时距是被试进行短时距估计的重要变异源;被试在实验中表现出高估较短时距和低估较长时距的倾向,时距估计的转换点为11.1s;计时过程中得到的韦伯函数是个分段连续函数, 韦伯函数的拐点有两个12s和21s,这两点与本研究得到的时距估计转换点具有部分一致性