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This article is an empirical evaluation of the choice of fixed cutoff points in assessing the root mean square error of approximation (RMSEA) test statistic as a measure of goodness-of-fit in Structural Equation Models. Using simulation data, the authors first examine whether there is any empirical evidence for the use of a universal cutoff, and then compare the practice of using the point estimate of the RMSEA alone versus that of using it jointly with its related confidence interval. The results of the study demonstrate that there is little empirical support for the use of .05 or any other value as universal cutoff values to determine adequate model fit, regardless of whether the point estimate is used alone or jointly with the confidence interval. The authors' analyses suggest that to achieve a certain level of power or Type I error rate, the choice of cutoff values depends on model specifications, degrees of freedom, and sample size. KeywordsRMSEA; SEM; goodness-of-fit; computer simulations Structural Equation Modeling (SEM) has been widely used in sociological, psychological, and social science research. One of the appealing attributes of SEM is that it allows for tests of theoretically derived models against empirical data. For researchers using SEM techniques, evaluation of the fit of a hypothesized model to sample data is crucial to the analysis. A key feature of SEM is the test of the null hypothesis of ∑ = ∑ = (θ), also known as the test of exact fit, where ∑ is the population covariance matrix, ∑(θ) is the covariance matrix implied by a specific model, and θ is a vector of free parameters defined by the model. The model test statistic T enables an asymptotic test of the null hypothesis of H 0 : ∑ = ∑ (θ). A significant T, often reported as the model chi-square, would suggest misspecification of the model. However, such a test of exact fit of the proposed model is generally unrealistic, as hardly any model using real data is without error (e.g., Browne and Cudeck 1993). A trivial misspecification, particularly with large sample sizes, can lead to rejection of the model even when it may otherwise adequately reproduce the population covariance matrix.

In this article, the authors examine the most common type of improper solutions: zero or negative error variances. They address the causes of, consequences of, and strategies to handle these issues. Several hypotheses are evaluated using Monte Carlo simulation models, including two structural equation models with several misspecifications of each model. Results suggested several unique findings. First, increasing numbers of omitted paths in the measurement model were associated with decreasing numbers of improper solutions. Second, bias in the parameter estimates was higher in samples with improper solutions than in samples including only proper solutions. Third, investigations of the consequences of using constrained estimates in the presence of improper solutions indicated that inequality constraints helped some samples achieve convergence. Finally, the use of confidence intervals as well as four other proposed tests yielded similar results when testing whether the error variance was greater than or equal to zero.

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In the wake of the Cold War, democracy has gained the status of a mantra. Yet there is no consensus about how to conceptualize and measure regimes such that meaningful comparisons can be made through time and across countries. In this prescriptive article, we argue for a new approach to conceptualization and measurement. We first review some of the weaknesses among traditional approaches. We then lay out our approach, which may be characterized ashistorical,multidimensional,disaggregated,andtransparent.We end by reviewing some of the payoffs such an approach might bring to the study of democracy.

Women's political representation, once considered unacceptable by politicians and their publics, is now actively encouraged by powerful international actors. In this article, the authors ask how the growth and discourse of the international women's movement affected women's acquisition of political power over time. To answer this question, they use event history techniques to address women's political representation in more than 150 countries over 110 years (1893–2003). They consider multiple political outcomes: female suffrage, first female parliamentarian, and achievement of 10, 20, and 30 percent women in a country's national legislature. The findings show that increasing global pressure for the inclusion of women in international politics and the changing discourse of the international women's movement help to explain women's acquisition of these multiple political outcomes. Furthermore, by adding these concepts to traditional domestic models of women in politics, the authors demonstrate that country-level political, social structural, and cultural characteristics cause countries to act in conjunction with, or in opposition to, these global pressures. This is the first time that research on women in politics has considered such a comprehensive list of countries, time points, and outcomes.