This paper addresses the problem of inference for a multinomial regression model in the presence of likelihood monotonicity. This paper proposes translating the multinomial regression problem into a conditional logist...This paper addresses the problem of inference for a multinomial regression model in the presence of likelihood monotonicity. This paper proposes translating the multinomial regression problem into a conditional logistic regression problem, using existing techniques to reduce this conditional logistic regression problem to one with fewer observations and fewer covariates, such that probabilities for the canonical sufficient statistic of interest, conditional on remaining sufficient statistics, are identical, and translating this conditional logistic regression problem back to the multinomial regression setting. This reduced multinomial regression problem does not exhibit monotonicity of its likelihood, and so conventional asymptotic techniques can be used.展开更多
In this paper, covariance structures with polytomous variables in several populations are analyzed. A computationally efficient multistage procedure is proposed to estimate the thresholds and the covariance structure ...In this paper, covariance structures with polytomous variables in several populations are analyzed. A computationally efficient multistage procedure is proposed to estimate the thresholds and the covariance structure parameters.Statistical properties of the estimators are derived, and a computer program is implemented to obtain the solution. An artificial example is presented to illustrate the method.展开更多
Cognitive diagnosis is the judgment of the student’s cognitive ability, is a wide-spread concern in educational science. The cognitive diagnosis model (CDM) is an essential method to realize cognitive diagnosis measu...Cognitive diagnosis is the judgment of the student’s cognitive ability, is a wide-spread concern in educational science. The cognitive diagnosis model (CDM) is an essential method to realize cognitive diagnosis measurement. This paper presents new research on the cognitive diagnosis model and introduces four individual aspects of probability-based CDM and deep learning-based CDM. These four aspects are higher-order latent trait, polytomous responses, polytomous attributes, and multilevel latent traits. The paper also sorts on the contained ideas, model structures and respective characteristics, and provides direction for developing cognitive diagnosis in the future.展开更多
文摘This paper addresses the problem of inference for a multinomial regression model in the presence of likelihood monotonicity. This paper proposes translating the multinomial regression problem into a conditional logistic regression problem, using existing techniques to reduce this conditional logistic regression problem to one with fewer observations and fewer covariates, such that probabilities for the canonical sufficient statistic of interest, conditional on remaining sufficient statistics, are identical, and translating this conditional logistic regression problem back to the multinomial regression setting. This reduced multinomial regression problem does not exhibit monotonicity of its likelihood, and so conventional asymptotic techniques can be used.
基金This research is supported in part by a research grant DA01070 from the U.S. Public Health Service
文摘In this paper, covariance structures with polytomous variables in several populations are analyzed. A computationally efficient multistage procedure is proposed to estimate the thresholds and the covariance structure parameters.Statistical properties of the estimators are derived, and a computer program is implemented to obtain the solution. An artificial example is presented to illustrate the method.
基金supported by the National Natural Science Foundation(Grant Nos.U1811261,62137001,61902055)the Fundamental Research Funds for the Central Universities(N180716010,N2117001).
文摘Cognitive diagnosis is the judgment of the student’s cognitive ability, is a wide-spread concern in educational science. The cognitive diagnosis model (CDM) is an essential method to realize cognitive diagnosis measurement. This paper presents new research on the cognitive diagnosis model and introduces four individual aspects of probability-based CDM and deep learning-based CDM. These four aspects are higher-order latent trait, polytomous responses, polytomous attributes, and multilevel latent traits. The paper also sorts on the contained ideas, model structures and respective characteristics, and provides direction for developing cognitive diagnosis in the future.
