The paper develops a two-stage robust procedure for structural equation modeling (SEM) and an R package rsem to facilitate the use of the procedure by applied researchers. In the first stage, M-estimates of the saturated mean vector and covariance matrix of all variables are obtained. Those corresponding to the substantive variables are then fitted to the structural model in the second stage. A sandwich-type covariance matrix is used to obtain consistent standard errors (SE) of the structural parameter estimates. Rescaled, adjusted as well as corrected and F-statistics are proposed for overall model evaluation. Using R and EQS, the R package rsem combines the two stages and generates all the test statistics and consistent SEs. Following the robust analysis, multiple model fit indices and standardized solutions are provided in the corresponding output of EQS. An example with open/closed book examination data illustrates the proper use of the package. The method is further applied to the analysis of a data set from the National Longitudinal Survey of Youth 1997 cohort, and results show that the developed procedure not only gives a better endorsement of the substantive models but also yields estimates with uniformly smaller standard errors than the normal-distribution-based maximum likelihood.

Assuming item parameters on a test are known constants, the reliability coefficient for item response theory (IRT) ability estimates is defined for a population of examinees in two different ways: as (a) the product-moment correlation between ability estimates on two parallel forms of a test and (b) the squared correlation between the true abilities and estimates. Due to the bias of IRT ability estimates, the parallel-forms reliability coefficient is not generally equal to the squared-correlation reliability coefficient. It is shown algebraically that the parallel-forms reliability coefficient is expected to be greater than the squared-correlation reliability coefficient, but the difference would be negligible in a practical sense.

In a number of psychological studies, answers to reasoning vignettes have been shown to result from both intuitive and deliberate response processes. This paper utilizes a psychometric model to separate these two response tendencies. An experimental application shows that the proposed model facilitates the analysis of dual-process item responses and the assessment of individual-difference factors, as well as conditions that favor one response tendency over another one.

We propose a new method of structural equation modeling (SEM) for longitudinal and time series data, named Dynamic GSCA (Generalized Structured Component Analysis). The proposed method extends the original GSCA by incorporating a multivariate autoregressive model to account for the dynamic nature of data taken over time. Dynamic GSCA also incorporates direct and modulating effects of input variables on specific latent variables and on connections between latent variables, respectively. An alternating least square (ALS) algorithm is developed for parameter estimation. An improved bootstrap method called a modified moving block bootstrap method is used to assess reliability of parameter estimates, which deals with time dependence between consecutive observations effectively. We analyze synthetic and real data to illustrate the feasibility of the proposed method.

This paper focuses on two estimators of ability with logistic item response theory models: the Bayesian modal (BM) estimator and the weighted likelihood (WL) estimator. For the BM estimator, Jeffreys’ prior distribution is considered, and the corresponding estimator is referred to as the Jeffreys modal (JM) estimator. It is established that under the three-parameter logistic model, the JM estimator returns larger estimates than the WL estimator. Several implications of this result are outlined.

Many psychological processes are characterized by recurrent shifts between distinct regimes or states. Examples that are considered in this paper are the switches between different states associated with premenstrual syndrome, hourly fluctuations in affect during a major depressive episode, and shifts between a “hot hand” and a “cold hand” in a top athlete. We model these processes with the regime switching state-space model proposed by Kim (J. Econom. 60:1–22, 1994), which results in both maximum likelihood estimates for the model parameters and estimates of the latent variables and the discrete states of the process. However, the current algorithm cannot handle missing data, which limits its applicability to psychological data. Moreover, the performance of standard errors for the purpose of making inferences about the parameter estimates is yet unknown. In this paper we modify Kim’s algorithm so it can handle missing data and we perform a simulation study to investigate its performance in (relatively) short time series in cases of different kinds of missing data and in case of complete data. Finally, we apply the regime switching state-space model to the three empirical data sets described above.