Extending exploratory diagnostic classification models: Inferring the effect of covariates

Diagnostic models provide a statistical framework for designing formative assessments by classifying student knowledge profiles according to a collection of fine-grained attributes. The context and ecosystem in which students learn may play an important role in skill mastery, and it is therefore important to develop methods for incorporating student covariates into diagnostic models. Including covariates may provide researchers and practitioners with the ability to evaluate novel interventions or understand the role of background knowledge in attribute mastery. Existing research is designed to include covariates in confirmatory diagnostic models, which are also known as restricted latent class models. We propose new methods for including covariates in exploratory RLCMs that jointly infer the latent structure and evaluate the role of covariates on performance and skill mastery. We present a novel Bayesian formulation and report a Markov chain Monte Carlo algorithm using a Metropolis-within-Gibbs algorithm for approximating the model parameter posterior distribution. We report Monte Carlo simulation evidence regarding the accuracy of our new methods and present results from an application that examines the role of student background knowledge on the mastery of a probability data set.     

Stolen elections: How conspiracy beliefs during the 2020 American presidential elections changed over time

Conspiracy beliefs have been studied mostly through cross-sectional designs. We conducted a five-wave longitudinal study (N = 376; two waves before and three waves after the 2020 American presidential elections) to examine if the election results influenced specific conspiracy beliefs and conspiracy mentality, and whether effects differ between election winners (i.e., Biden voters) versus losers (i.e., Trump voters) at the individual level. Results revealed that conspiracy mentality kept unchanged over 2 months, providing first evidence that this indeed is a relatively stable trait. Specific conspiracy beliefs (outgroup and ingroup conspiracy beliefs) did change over time, however. In terms of group-level change, outgroup conspiracy beliefs decreased over time for Biden voters but increased for Trump voters. Ingroup conspiracy beliefs decreased over time across all voters, although those of Trump voters decreased faster. These findings illuminate how specific conspiracy beliefs are, and conspiracy mentality is not, influenced by an election event.     

A maximum likelihood method for latent class regression involving a censored dependent variable

The standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored. This model is generalized by developing a conditional mixture, maximum likelihood method for latent class censored regression. The proposed method simultaneously estimates separate regression functions and subject membership in K latent classes or groups given a censored dependent variable for a cross-section of subjects. Maximum likelihood estimates are obtained using an EM algorithm. The proposed method is illustrated via a consumer psychology application.     

Choice between delayed reinforcers and fixed-ratio schedules requiring forceful responding.

This experiment measured pigeons' choices between delayed reinforcers and fixed-ratio schedules in which a force of approximately 0.48 N was needed to operate the response key. In ratio-delay conditions, subjects chose between a fixed-ratio schedule and an adjusting delay. The delay was increased or decreased several times a session in order to estimate an indifference point--a delay duration at which the two alternatives were chosen about equally often. Each ratio-delay condition was followed by a delay-delay condition in which subjects chose between the adjusting delay and a variable-time schedule, with the components of this schedule selected to match the ratio completion times of the preceding ratio-delay condition. The adjusting delays at the indifference point were longer when the alternative was a fixed-ratio schedule than when it was a matched variable-time schedule, which indicated a preference for the matched variable-time schedules over the fixed-ratio schedules. This preference increased in a nonlinear manner with increasing ratio size. This nonlinearity was inconsistent with a theory that states that indifference points for both time and ratio schedules can be predicted by multiplying the choice response-reinforcer intervals of the two types of schedules by different multiplicative constants. Two other theories, which predict nonlinear increases in preference for the matched variable-time schedules, are discussed.     

Analyzing sequential categorical data: Individual variation in markov chains

Markov chains are probabilistic models for sequences of categorical events, with applications throughout scientific psychology. This paper provides a method for anlayzing data consisting of event sequences and covariate observations. It is assumed that each sequence is a Markov process characterized by a distinct transition probability matrix. The objective is to use the covariate data to explain differences between individuals in the transition probability matrices characterizing their sequential data. The elements of the transition probability matrices are written as functions of a vector of latent variables, with variation in the latent variables explained through a multivariate regression on the covariates. The regression is estimated using the EM algorithm, and requires the numerical calculation of a multivariate integral. An example using simulated cognitive developmental data is presented, which shows that the estimation of individual variation in the parameters of a probability model may have substantial theoretical importance, even when individual differences are not the focus of the investigator's concerns.Research contributing to this article was supported by B.R.S. Subgrant 5-35345 from the University of Virginia. I thank the DADA Group, Bill Fabricius, Don Hartmann, William Griffin, Jack McArdle, Ivo Molenaar, Ronald Schoenberg, Simon Tavaré, and several anonymous reviewers for their discussion of these points.     

Continuous and discrete latent structure models for item response data

Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizationss are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.     

内部分配改革的职务评价技术探新

建立工资标准系统的关键是确定职务工资率。职务间可比价值成分变异越大,对确定职务工资率的贡献也越大。根据以上研究设想采用方差分析方法进行职务评价。评价步骤包括：职务描述;对职务要素作主成分分析;对职务样本作聚类分析和判别分析;通过方差分析为可比价值各成分建构权重系数ωｉ。ωｉ‘满足：（１）ωｉ≥０;（２）Σωｉ＝１;（３）ωｉ,间可直接比较;（４）ωｉ的大小与对应的可比价值成分变异一致。最后将职务评价值线性变换为工资率。在线性方程中配一个常数。和调节系数α以适合组织的管理约束条件。配合两个企业内部分配改革的研究结果显示了方差分析法的有效性和实用性。     

Residualanalysis in the polytomous rasch model

Residuals for check of model fit in the polytomous Rasch model are examined. Comparisons are made between using counts for all response pattern and using item totals for score groups for the construction of the residuals. Comparisons are also, for the residuals based on score group totals, made between using as basis the item totals, or using the estimated item parameters. The developed methods are illustrated by two examples, one from a psychiatric rating scale, one from a Danish Welfare Study.     

An extension of the concept of specific objectivity

Comparisons of subjects are specifically objective if they do not depend on the items involved. Such comparisons are not restricted to the 1-parameter logistic latent trait model, but may also be defined within ordinal independence models and even within the 2-parameter logistic model.