On the Generalized S−X2–Test of Item Fit: Some Variants, Residuals, and a Graphical Visualization

The generalized [Formula: see text]–test is a test of item fit for items with polytomous responses format. The test is based on a comparison of the observed and expected number of responses in strata defined by the test score. In this article, we make four contributions. We demonstrate that the performance of the generalized [Formula: see text]–test depends on how sparse cells are pooled. We propose alternative implementations of the test within the framework of limited information testing. We derive the distribution of the [Formula: see text]–residuals that can be used for post hoc analyses. We suggest a diagnostic plot that visualizes the form of the misfit. The performance of the alternative implementations is investigated in a simulation study. The simulation study suggests that the alternative implementations are capable of controlling the Type-I error rate well and have high power. An empirical application concludes this article.

Simultaneous modeling of Binary Responses: A sequence of binary models and Ordinal multinomial with Bayesian estimates impacting HIV/AIDS

Background: In this research, we examined several binary factors impact binary outcomes simultaneous and how the information of HIV/AIDS is perceived by the public is associated with outcomes to HIV/AIDS.Methods: We used polytomous responses through a sequence of binary models and a multinomial logistic regression model with Bayesian estimates to analyze the 2009 Mozambique survey data as it pertains to blood test, heard of HIV/AIDS and heard about campaign.Results: The analysis reveals that both heard about HIV and heard about the campaign are represented differentially in testing positive. Wealth, education and thinking of risk is positively associated with heard about HIV and heard about the campaign regardless of HIV. However, religious is a positive factor for social efforts of hearing of HIV/AIDS and the campaign. Both the polytomous response model and the ordinal model with model gave the same findings in regards to the marginal mean. However, the polytomous (conditional) models gave additional information about education.Conclusions: While knowledge of the disease continues to be important, the future social effort to combat HIV in Mozambique may need different strategies in different subpopulation groups.

The Bipolarity of Attitudes: Unfolding the Implications of Ambivalence

Recently, some attitude researchers have argued that the traditional bipolar model of attitudes should be replaced, claiming that a bivariate model is superior in several ways, foremost of which is its ability to account for ambivalent attitudes. This study argues that ambivalence is not at odds with bipolarity per se, but rather the conventional view of bipolarity, and that the psychometric evidence supporting a bivariate interpretation has been flawed. To demonstrate this, a scale developed out of the bivariate approach was examined using a unidimensional unfolding item response theory model: general hyperbolic cosine model for polytomous responses. The results were consistent with a bipolar interpretation, providing support for the argument that ambivalent evaluations are the correct middle-point of a bipolar evaluative dimension. Thus, it is argued that attitudinal ambivalence does not necessitate moving beyond bipolarity, but rather, moving beyond the conventional conceptualization and assessment of attitudes.

Estimation of an IRT Model by Mplus for Dichotomously Scored Responses Under Different Estimation Methods

The purpose of this article is twofold. The first is to provide evaluative information on the recovery of model parameters and their standard errors for the two-parameter item response theory (IRT) model using different estimation methods by Mplus. The second is to provide easily accessible information for practitioners, instructors, and students about the relationships between IRT and item factor analysis (FA) parameterizations. Specifically, this is done using the “Theta” and “Delta” parameterizations in Mplus for unidimensional and multidimensional modeling with dichotomous and polytomous responses with and without the scaling constant D. The first objective aims at investigating differences that may occur when using different estimation methods in Mplus for binary response modeling. The second objective was motivated by practical interest observed among graduate students and applied researchers. The relations between IRT and Mplus FA “Theta” and “Delta” parameterizations are described using expressions without the use of matrices, which can be understood efficiently by applied researchers and students.