Bounds on the average causal effects in randomized trials with noncompliance by covariate adjustment.

In randomized trials with noncompliance, causal effects cannot be identified without strong assumptions. Therefore, several authors have considered bounds on the causal effects. Applying an idea of VanderWeele (), Chiba () gave bounds on the average causal effects in randomized trials with noncompliance using the information on the randomized assignment, the treatment received and the outcome under monotonicity assumptions about covariates. But he did not consider any observed covariates. If there are some observed covariates such as age, gender, and race in a trial, we propose new bounds using the observed covariate information under some monotonicity assumptions similar to those of VanderWeele and Chiba. And we compare the three bounds in a real example.

Accelerating L1-penalized expectation maximization algorithm for latent variable selection in multidimensional two-parameter logistic models.

One of the main concerns in multidimensional item response theory (MIRT) is to detect the relationship between observed items and latent traits, which is typically addressed by the exploratory analysis and factor rotation techniques. Recently, an EM-based L1-penalized log-likelihood method (EML1) is proposed as a vital alternative to factor rotation. Based on the observed test response data, EML1 can yield a sparse and interpretable estimate of the loading matrix. However, EML1 suffers from high computational burden. In this paper, we consider the coordinate descent algorithm to optimize a new weighted log-likelihood, and consequently propose an improved EML1 (IEML1) which is more than 30 times faster than EML1. The performance of IEML1 is evaluated through simulation studies and an application on a real data set related to the Eysenck Personality Questionnaire is used to demonstrate our methodologies.

Latent variable sdelection 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.