Assessing the Effect of Model Misspecifications on Parameter Estimates in Structural Equation Models

Model misspecifications may have a systematic effect on parameters, causing biases in their estimates. In the application of structural equation models, every interesting model is fallible. When simultaneously evaluating a model, it is of interest to study whether all parameters are affected by a misspecification. This paper provides three procedures for evaluating such an effect: (1) analyzing the path, (2) using a functional relationship, and (3) using a significance test. Analyzing the path is illustrated through a confirmatory factor model. This method is ad hoc but intuitive. A more rigorous approach is built upon the concept of orthogonality of two sets of parameters. When parameter a is orthogonal to parameter b, omitting parameter b will not affect the estimation of parameter a. The functional relationship of two sets of parameters is used to check their orthogonality. The distribution of the difference between estimates based on different models is obtained, which provides a Hausman–like way to check significant parameter differences that are due to biases. Examples illustrate that these procedures can provide valuable information on identifying parameter estimates that are systematically affected by a model misspecification.     

Three Likelihood-Based Methods For Mean and Covariance Structure Analysis With Nonnormal Missing Data

Survey and longitudinal studies in the social and behavioral sciences generally contain missing data. Mean and covariance structure models play an important role in analyzing such data. Two promising methods for dealing with missing data are a direct maximum-likelihood and a two-stage approach based on the unstructured mean and covariance estimates obtained by the EM-algorithm. Typical assumptions under these two methods are ignorable nonresponse and normality of data. However, data sets in social and behavioral sciences are seldom normal, and experience with these procedures indicates that normal theory based methods for nonnormal data very often lead to incorrect model evaluations. By dropping the normal distribution assumption, we develop more accurate procedures for model inference. Based on the theory of generalized estimating equations, a way to obtain consistent standard errors of the two-stage estimates is given. The asymptotic efficiencies of different estimators are compared under various assumptions. We also propose a minimum chi-square approach and show that the estimator obtained by this approach is asymptotically at least as efficient as the two likelihood-based estimators for either normal or nonnormal data. The major contribution of this paper is that for each estimator, we give a test statistic whose asymptotic distribution is chi-square as long as the underlying sampling distribution enjoys finite fourth-order moments. We also give a characterization for each of the two likelihood ratio test statistics when the underlying distribution is nonnormal. Modifications to the likelihood ratio statistics are also given. Our working assumption is that the missing data mechanism is missing completely at random. Examples and Monte Carlo studies indicate that, for commonly encountered nonnormal distributions, the procedures developed in this paper are quite reliable even for samples with missing data that are missing at random.     

Nesting Monte Carlo EM for high-dimensional item factor analysis

The item factor analysis model for investigating multidimensional latent spaces has proved to be useful. Parameter estimation in this model requires computationally demanding high-dimensional integrations. While several approaches to approximate such integrations have been proposed, they suffer various computational difficulties. This paper proposes a Nesting Monte Carlo Expectation-Maximization (MCEM) algorithm for item factor analysis with binary data. Simulation studies and a real data example suggest that the Nesting MCEM approach can significantly improve computational efficiency while also enjoying the good properties of stable convergence and easy implementation.     

The demand for leisure time in the presence of constrained work hours

This article presents a labor supply model designed to address situations of overemployment or underemployment in the labor market. Previous labor supply models have taken the possibility of work hour constraints into consideration but typically assumed that the existence of fixed work hours only influenced the decision of labor force participation. This ignores situations in which individuals choose to be employed at fixed-hour jobs even though these jobs do not offer the desired work hours.     

Maximum likelihood estimation in a model with interval data

It is suggested that in some situations, observations for random variables should be collected in the form of intervals. In this paper, the unknown parameters in a bivariate normal model are estimated based on a set of point and interval observations via the maximum likelihood approach. The Newton-Raphson algorithm is used to find the estimates, and asymptotic properties of the estimator are provided. Monte Carlo studies are conducted to study the performance of the estimator. An example based on real-life data is presented to demonstrate the practical applicability of the method.     

Characterizing parameters of multivariate elliptical distributions*

This paper defines new parameters characterizing multivariate elliptical distributions. Mardia's coefficient of multivariate kurtosis is shown to be essentially one of these parameters. A simple relation is established between centered multivariate product moments and second moments of the variables. The general results are verified on the contaminated normal distribution as an example.     

A financial survey of mergers during the years 1968–70

This paper is concerned with the financial objectives of mergers and acquisitions and the way in which considerations in the merger transaction, such as the price paid and the method of payment used, may affect such objectives subsequent to the merger. The analysis is based on a sample of 65 mergers during the years 1968–70 inclusive [2].     

Test of linear trend in eigenvalues of k covariance matrices with applications in common principal components analysis

A test for linear trend among a set of eigenvalues of k covariance matrices is developed. A special case of this test is Flury's (1986) test for the equality of eigenvalues. The linear trend hypothesis appears to be more relevant to data analysis than the equality hypothesis. Examples show how the linear trend hypothesis can be acceptable while the equality hypothesis is rejected.