Marginal maximum likelihood estimation for a psychometric model of discontinuous development

Item response theory models posit latent variables to account for regularities in students' performances on test items. Wilson's “Saltus” model extends the ideas of IRT to development that occurs in stages, where expected changes can be discontinuous, show different patterns for different types of items, or even exhibit reversals in probabilities of success on certain tasks. Examples include Piagetian stages of psychological development and Siegler's rule-based learning. This paper derives marginal maximum likelihood (MML) estimation equations for the structural parameters of the Saltus model and suggests a computing approximation based on the EM algorithm. For individual examinees, empirical Bayes probabilities of learning-stage are given, along with proficiency parameter estimates conditional on stage membership. The MML solution is illustrated with simulated data and an example from the domain of mixed number subtraction. The authors' names appear in alphabetical order. We would like to thank Karen Draney for computer programming, Kikumi Tatsuoka for allowing us to use the mixed-number subtraction data, and Eric Bradlow, Chan Dayton, Kikumi Tatsuoka, and four anonymous referees for helpful suggestions. The first author's work was supported by Contract No. N00014-88-K-0304, R&T 4421552, from the Cognitive Sciences Program, Cognitive and Neural Sciences Division, Office of Naval Research, and by the Program Research Planning Council of Educational Testing Service. The second author's work was supported by a National Academy of Education Spencer Fellowship and by a Junior Faculty Research Grant from the Committee on Research, University of California at Berkeley. A copy of the Saltus computer program can be obtained from the second author.     

A maximum likelihood approach to test validation with missing and censored dependent variables

A maximum likelihood approach is described for estimating the validity of a test (x) as a predictor of a criterion variable (y) when there are both missing and censoredy scores present in the data set. The missing data are due to selection on a latent variable (y _s ) which may be conditionally related toy givenx. Thus, the missing data may not be missing random. The censoring process in due to the presence of a floor or ceiling effect. The maximum likelihood estimates are constructed using the EM algorithm. The entire analysis is demonstrated in terms of hypothetical data sets.     

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.     

Exploratory longitudinal factor analysis in multiple populations

For multiple populatios, a longtidinal factor analytic model which is entirely exploratory, that is, no explicit identification constraints, is proposed. Factorial collapse and period/practice effects are allowed. An invariant and/or stationary factor pattern is permitted. This model is formulated stochastically. To implement this model a stagewise EM algorithm is developed. Finally a numerical illustration utilizing Nesselroade and Baltes' data is presented.The authors wish to thank Barbara Mellers and Henry Kaiser for their helpful comments and John Nesselroade for providing us the data for our illustration. This research wwa supported in part by a grant (No. AG03164) from the National Institute on Aging to William Meredith. Details of the derivations and a copy of the PROC MATRIX program are available upon request from the first author.     

IRT中最小化χ2/EM参数估计方法

对IRT的双参数Logistic模型（2PLM）中未知参数估计问题,给出了一个新的估计方法――最小化χ2/EM估计。新方法在充分考虑项目反应理论(IRT)与经典测量理论(CTT)之间的差异的前提下,从统计计算的角度改进了Berkson的最小化χ2估计,取消了Berkson实施最小化χ2估计时需要已知能力参数的不合实际的前提,扩大了应用范围。实验结果表明新方法能力参数的估计结果与BILOG相比,精确度要高,且当样本容量超过2000时,项目参数的估计结果也优于BILOG。实验还表明新方法稳健性好     

Wendy's Story: analytic perspectives on J. M. Barrie's Peter and Wendy

This essay is a study of Peter and Wendy, J. M. Barrie's 1911 novel based on his 1904 play Peter Pan. Utilizing Jungian and Kleinian theory, the tale is treated as an expression of Wendy's psyche in transformation, tracking her passage into puberty and the transition from omnipotent narcissism towards depressive concern which accompanied her differentiation from idealized identification with her mother. The resultant changes in Wendy's parental imagos are given particular emphasis, especially the moves towards the integration of her split paternal imago, symbolized by Peter Pan and Captain Hook. This enables Wendy's fuller engagement with the Oedipus situation, resulting in her assimilation of unconscious aspects of the instinctual feminine. In turn, she opens to a conception of parental intercourse which is more reality orientated and allows an internal sense of coupledom vital for her own capacity to form adult relationships.     

Generation of referring expressions: assessing the Incremental Algorithm

A substantial amount of recent work in natural language generation has focused on the generation of 'one-shot' referring expressions whose only aim is to identify a target referent. Dale and Reiter's Incremental Algorithm (IA) is often thought to be the best algorithm for maximizing the similarity to referring expressions produced by people. We test this hypothesis by eliciting referring expressions from human subjects and computing the similarity between the expressions elicited and the ones generated by algorithms. It turns out that the success of the IA depends substantially on the 'preference order' (PO) employed by the IA, particularly in complex domains. While some POs cause the IA to produce referring expressions that are very similar to expressions produced by human subjects, others cause the IA to perform worse than its main competitors; moreover, it turns out to be difficult to predict the success of a PO on the basis of existing psycholinguistic findings or frequencies in corpora. We also examine the computational complexity of the algorithms in question and argue that there are no compelling reasons for preferring the IA over some of its main competitors on these grounds. We conclude that future research on the generation of referring expressions should explore alternatives to the IA, focusing on algorithms, inspired by the Greedy Algorithm, which do not work with a fixed PO.     

How to administer the Initial Preference Task

Individuals like their name letters more than non‐name letters. This effect has been termed the Name Letter Effect (NLE) and is widely exploited to measure implicit (i.e. automatic, unconscious) self‐esteem, predominantly by means of the Initial Preference Task (IPT). Methodological research on how to best administer the IPT is, however, scarce. In order to bridge this gap, the present paper assessed the advantages and disadvantages of different types of IPT administrations with two meta‐analyses (k = 49; N = 11,514) and a follow‐up experiment (N = 449). As a result, a new type of administration is recommended which (1) treats the effects of the first and the last name initials separately, (2) uses a duplicate administration for reliability reasons, (3) uses the likability as well as the attractiveness item wording and (4) exploits not only letters but also numbers (i.e. birthday number effect) to measure implicit self‐esteem. Copyright © 2011 John Wiley & Sons, Ltd.     

Latent variable selection in multidimensional item response theory models using the expectation model selection algorithm

The aim of latent variable selection in multidimensional item response theory (MIRT) models is to identify latent traits probed by test items of a multidimensional test. In this paper the expectation model selection (EMS) algorithm proposed by Jiang et al. (2015) is applied to minimize the Bayesian information criterion (BIC) for latent variable selection in MIRT models with a known number of latent traits. Under mild assumptions, we prove the numerical convergence of the EMS algorithm for model selection by minimizing the BIC of observed data in the presence of missing data. For the identification of MIRT models, we assume that the variances of all latent traits are unity and each latent trait has an item that is only related to it. Under this identifiability assumption, the convergence of the EMS algorithm for latent variable selection in the multidimensional two-parameter logistic (M2PL) models can be verified. We give an efficient implementation of the EMS for the M2PL models. Simulation studies show that the EMS outperforms the EM-based L₁ regularization in terms of correctly selected latent variables and computation time. The EMS algorithm is applied to a real data set related to the Eysenck Personality Questionnaire.