Generalized linear modeling of a panel mobility index with correlated multivariate categorical responses

Data with multivariate, longitudual categorical responses often occur in applications. It can be difficult to analyze and model such data while simultaneously taking into account explanatory variables and correlations between the responses over time. We take a generalized linear model approach to this problem in analyzing panel data from the Health and Retirement Survey (HRS) that includes older Americans’ mobility over several years as a response. We provide a general formula for the likelihood of such data and apply it to the case when there are three binary responses. This approach can be taken, with computational limits, for data with multivariate, categorical responses with any number of categories. We consider, simultaneously, interpretations of coefficients, dependence of responses and goodness-of-fit in reduced models for parsimony while taking into account explanatory data. The gradient of the objective function is provided for use in gradient descent and the coded optimization algorithm is tested with a Monte Carlo simulation. Dependence of responses in mobility is shown before taking explanatory variables into account, and dependence is shown in a Markov logistic regression model and in the generalized linear model taking into account race, age, gender and interactions between them.

A multidimensional IRT model for continuous and graded responses with error in persons and items

This article proposes two multidimensional extensions of existing DMs: the M-DTCRM, intended for (approximately) continuous responses, and the M-DTGRM, intended for ordered-categorical responses (including binary). A rationale for the extension to the multiple-content-dimensions case, which is based on the concept of the multidimensional location index, is first proposed and discussed. Then, the models are described using both the factor-analytic and the IRT parameterizations. Procedures for (a) calibrating the items, (b) scoring individuals, (c) assessing model appropriateness, and (d) assessing measurement precision are finally discussed. The proposals are submitted to be of particular interest for the case of multidimensional questionnaires in which the number of items per scale would not be enough for arriving at stable estimates.

A multidimensional IRT model for continuous and graded responses with error in persons and items

This article proposes two multidimensional extensions of existing DMs: the M-DTCRM, intended for (approximately) continuous responses, and the M-DTGRM, intended for ordered-categorical responses (including binary). A rationale for the extension to the multiple-content-dimensions case, which is based on the concept of the multidimensional location index, is first proposed and discussed. Then, the models are described using both the factor-analytic and the IRT parameterizations. Procedures for (a) calibrating the items, (b) scoring individuals, (c) assessing model appropriateness, and (d) assessing measurement precision are finally discussed. The proposals are submitted to be of particular interest for the case of multidimensional questionnaires in which the number of items per scale would not be enough for arriving at stable estimates.

The Appropriateness of Sum Scores as Estimates of Factor Scores in the Multiple Factor Analysis of Ordered-Categorical Responses

Unit-weight sum scores (UWSSs) are routinely used as estimates of factor scores on the basis of solutions obtained with the nonlinear exploratory factor analysis (EFA) model for ordered-categorical responses. Theoretically, this practice results in a loss of information and accuracy, and is expected to lead to biased estimates. However, the practical relevance of these limitations is far from clear. In this article, we adopt an empirical view and propose indices and procedures (some of them new) for assessing the appropriateness of UWSSs in nonlinear EFA applications. A new automated approach for obtaining UWSSs that maximize fidelity and correlational accuracy is proposed. The appropriateness of UWSSs under different conditions and the behavior of the present proposal in comparison with other more common approaches are assessed with a simulation study. A tutorial for interested practitioners is presented using an illustrative example based on a well-known personality questionnaire. All the procedures proposed in the article have been implemented in a well-known noncommercial EFA program.

The appropriateness of sum scores as estimates of factor scores in the multiple factor analysis of ordered-categorical responses.

<p>Unit-weight sum scores (UWSSs) are routinely used as estimates of factor scores on the basis of solutions obtained with the non-linear exploratory factor analysis (EFA) model for ordered-categorical responses. Theoretically, this practice results in a loss of information and accuracy, and is expected to lead to biased estimates. However, the practical relevance of these limitations is far from clear. In this article we adopt an empirical view, and propose indices and procedures (some of them new) for assessing the appropriateness of UWSSs in non-linear EFA applications. A new automated approach for obtaining UWSSs that maximize fidelity and correlational accuracy is proposed. The appropriateness of UWSSs under different conditions and the behavior of the present proposal in comparison with other more common approaches are assessed with a simulation study. A tutorial for interested practitioners is presented using an illustrative example based on a well-known personality questionnaire. All the procedures proposed in the article have been implemented in a well-known noncommercial EFA program. </p>

The appropriateness of sum scores as estimates of factor scores in the multiple factor analysis of ordered-categorical responses.

<p>Unit-weight sum scores (UWSSs) are routinely used as estimates of factor scores on the basis of solutions obtained with the non-linear exploratory factor analysis (EFA) model for ordered-categorical responses. Theoretically, this practice results in a loss of information and accuracy, and is expected to lead to biased estimates. However, the practical relevance of these limitations is far from clear. In this article we adopt an empirical view, and propose indices and procedures (some of them new) for assessing the appropriateness of UWSSs in non-linear EFA applications. A new automated approach for obtaining UWSSs that maximize fidelity and correlational accuracy is proposed. The appropriateness of UWSSs under different conditions and the behavior of the present proposal in comparison with other more common approaches are assessed with a simulation study. A tutorial for interested practitioners is presented using an illustrative example based on a well-known personality questionnaire. All the procedures proposed in the article have been implemented in a well-known noncommercial EFA program. </p>