Semi-automated Rasch analysis using in-plus-out-of-questionnaire log likelihood

Rasch analysis is a popular statistical tool for developing and validating instruments that aim to measure human performance, attitudes and perceptions. Despite the availability of various software packages, constructing a good instrument based on Rasch analysis is still considered to be a complex, labour-intensive task, requiring human expertise and rather subjective judgements along the way. In this paper we propose a semi-automated method for Rasch analysis based on first principles that reduces the need for human input. To this end, we introduce a novel criterion, called in-plus-out-of-questionnaire log likelihood (IPOQ-LL). On artificial data sets, we confirm that optimization of IPOQ-LL leads to the desired behaviour in the case of multi-dimensional and inhomogeneous surveys. On three publicly available real-world data sets, our method leads to instruments that are, for all practical purposes, indistinguishable from those obtained by Rasch analysis experts through a manual procedure.     

Sample size requirements for estimating pearson, kendall and spearman correlations

Interval estimates of the Pearson, Kendall tau-a and Spearman correlations are reviewed and an improved standard error for the Spearman correlation is proposed. The sample size required to yield a confidence interval having the desired width is examined. A two-stage approximation to the sample size requirement is shown to give accurate results.     

Adjusting for information inflation due to local dependency in moderately large item clusters

When multiple items are clustered around a reading passage, the local independence assumption in item response theory is often violated. The amount of information contained in an item cluster is usually overestimated if violation of local independence is ignored and items are treated as locally independent when in fact they are not. In this article we provide a general method that adjusts for the inflation of information associated with a test containing item clusters. A computational scheme was presented for the evaluation of the factor of adjustment for clusters in the restrictive case of two items per cluster, and the general case of more than two items per cluster. The methodology was motivated by a study of the NAEP Reading Assessment. We present a simulated study along with an analysis of a NAEP data set.The research was supported under the National Assessment of Educational Progress (Grant No. R999G30002) as administered by the Office of Educational Research and Improvement, U.S. Department of Education. This work was started when the author was at the Division of Statistics and Psychometrics at the Educational Testing Service. The author thanks Juliet Shaffer, Bob Mislevy, Eric Bradlow, three reviewers and an associate editor for their helpful comments on the paper.     

An estimate of the covariance between variables which are not jointly observed

Situations sometimes arise in which variables collected in a study are not jointly observed. This typically occurs because of study design. An example is an equating study where distinct groups of subjects are administered different sections of a test. In the normal maximum likelihood function to estimate the covariance matrix among all variables, elements corresponding to those that are not jointly observed are unidentified. If a factor analysis model holds for the variables, however, then all sections of the matrix can be accurately estimated, using the fact that the covariances are a function of the factor loadings. Standard errors of the estimated covariances can be obtained by the delta method. In addition to estimating the covariance matrix in this design, the method can be applied to other problems such as regression factor analysis. Two examples are presented to illustrate the method. This research was partially supported by NIMH grant MH5-4576     

On equivariance and invariance of standard errors in three exploratory factor models

Current practice in factor analysis typically involves analysis of correlation rather than covariance matrices. We study whether the standardz-statistic that evaluates whether a factor loading is statistically necessary is correctly applied in such situations and more generally when the variables being analyzed are arbitrarily rescaled. Effects of rescaling on estimated standard errors of factor loading estimates, and the consequent effect onz-statistics, are studied in three variants of the classical exploratory factor model under canonical, raw varimax, and normal varimax solutions. For models with analytical solutions we find that some of the standard errors as well as their estimates are scale equivariant, while others are invariant. For a model in which an analytical solution does not exist, we use an example to illustrate that neither the factor loading estimates nor the standard error estimates possess scale equivariance or invariance, implying that different conclusions could be obtained with different scalings. Together with the prior findings on parameter estimates, these results provide new guidance for a key statistical aspect of factor analysis.We gratefully acknowledge the help of the Associate Editor and three referees whose constructive comments lead to an improved version of the paper. This work was supported by National Institute on Drug Abuse Grants DA01070 and DA00017 and by the University of North Texas Faculty Research Grant Program.     

On computing ELECTRE's credibility indices under partial information

The ELECTRE family of decision aid methods is a well‐known approach to help decision makers (DMs) advance in a decision process. Among the most recent methods in the family, ELECTRE IS, III, and TRI compute fuzzy indices for the credibility of a given action outranking some other. We consider the case when the DMs are unsure which values each parameter should take, which may result from insufficient, imprecise or contradictory information, as well as from different preferences among a group of DMs. In the framework of a robustness analysis approach, where DMs provide only partial information on the parameter values (through constraints on acceptable combinations), we study how to find whether an outranking among two actions in an ELECTRE method is robust. In this context, we study the resulting nonlinear problems of optimizing a credibility index (under the type of constraints that we consider to appear in practice) and present some examples. Copyright © 1999 John Wiley & Sons, Ltd.     

Lexicographic order preservation and stochastic dominance

Stochastic dominance concerns conditions on outcome probabilities that are necessary and sufficient for one act to be (strictly) preferred to another according to all preference relations that share certain properties, one of which customarily is an Archimedean property sufficient to entail existence of real-valued representations. We relax this assumption to permit linear lexicographic utility of finite and known dimensionality. In some situations, levels of the lexicographic hierarchy could correspond to explicit criteria or attributes. In our model, subjective probabilities emerge as matrix premultipliers of the outcome utility vectors. We thus obtain matrix probability generalizations of the familiar cumulative probability conditions for stochastic dominance.     

父亲参与教养对小学生攻击行为的影响:母亲育儿压力的部分中介效应

本研究旨在考察父亲参与教养对小学生攻击行为的影响以及母亲育儿压力在二者之间的中介作用,采用同伴提名法和问卷法对604名1~6年级小学生及其家长进行调查。潜变量结构方程模型拟合检验结果显示：父亲参与教养（互动性、可及性、责任性）对小学生攻击行为（身体攻击、关系攻击）具有显著的负向预测作用;在父亲参与教养与小学生关系攻击之间,母亲的育儿愁苦和亲子互动失调具有显著的部分中介作用;在父亲参与教养与小学生身体攻击之间,只有母亲的育儿愁苦具有显著的部分中介作用。上述结果表明,父亲参与教养可以通过减少母亲的育儿愁苦来降低儿童的关系攻击和身体攻击,还能通过减少母子互动失调来降低儿童的关系攻击。     

Selecting polychoric instrumental variables in confirmatory factor analysis: An alternative specification test and effects of instrumental variables

The polychoric instrumental variable (PIV) approach is a recently proposed method to fit a confirmatory factor analysis model with ordinal data. In this paper, we first examine the small-sample properties of the specification tests for testing the validity of instrumental variables (IVs). Second, we investigate the effects of using different numbers of IVs. Our results show that specification tests derived for continuous data are extremely oversized at all sample sizes when applied to ordinal variables. Possible modifications for ordinal data are proposed in the present study. Simulation results show that the modified specification tests with all available IVs are able to detect model misspecification. In terms of estimation accuracy, the PIV approach where the IVs outnumber the endogenous variables by one produces a lower bias but a higher variation than the PIV approach with more IVs for correctly specified factor loadings at small samples.