Inference is considered for the marginal distribution of X, when (X, Y) has a truncated bivariate normal distribution. The Y variable is truncated, but only the X values are observed. The relationship of this distribution to Azzalini's “skew-normal” distribution is obtained. Method of moments and maximum likelihood estimation are compared for the three-parameter Azzalini distribution. Samples that are uniformative about the skewness of this distribution may occur, even for large n. Profile likelihood methods are employed to describe the uncertainty involved in parameter estimation. A sample of 87 Otis test scores is shown to be well-described by this model.

Structural equation models (SEM) are widely used for modeling complex multivariate relationships among measured and latent variables. Although several analytical approaches to interval estimation in SEM have been developed, there lacks a comprehensive review of these methods. We review the popular Wald-type and lesser known likelihood-based methods in linear SEM, emphasizing profile likelihood-based confidence intervals (CIs). Existing algorithms for computing profile likelihood-based CIs are described, including two newer algorithms which are extended to construct profile likelihood-based confidence regions (CRs). Finally, we illustrate the use of these CIs and CRs with two empirical examples, and provide practical recommendations on when to use Wald-type CIs and CRs versus profile likelihood-based CIs and CRs. OpenMx example code is provided in an Online Appendix for constructing profile likelihood-based CIs and CRs for SEM.

In relational event networks, endogenous statistics are used to summarize the past activity between actors. Typically, it is assumed that past events have equal weight on the social interaction rate in the (near) future regardless of the time that has transpired since observing them. Generally, it is unrealistic to assume that recently past events affect the current event rate to an equal degree as long-past events. Alternatively one may consider using a prespecified decay function with a prespecified rate of decay. A problem then is that the chosen decay function could be misspecified yielding biased results and incorrect conclusions. In this paper, we introduce three parametric weight decay functions (exponential, linear, and one-step) that can be embedded in a relational event model. A statistical method is presented to decide which memory decay function and memory parameter best fit the observed sequence of events. We present simulation studies that show the presence of bias in the estimates of effects of the statistics whenever the decay, as well as the memory parameter, are not properly estimated, and the ability to test different memory models against each other using the Bayes factor. Finally, we apply the methodology to two empirical case studies.

While Perron and Wada (2009) maximum likelihood estimation approach suggests that postwar US real GDP follows a trend stationary process (TSP), our Bayesian approach based on the same model and the same sample suggests that it follows a difference stationary process (DSP). We first show that the results based on the approach should be interpreted with caution, as they are relatively more subject to the ‘pile-up problem’ than those based on the Bayesian approach. We then directly estimate and compare the two competing TSP and DSP models of real GDP within the Bayesian framework. Our empirical results suggest that a DSP model is preferred to a TSP model both in terms of in-sample fits and out-of-sample forecasts.

Dynamic models which predict changes in the intensity of schistosome infection with host age are fitted to pre-intervention Schistosoma mansoni data from Kenya. Age-specific post-treatment-reinfection data are used to estimate the force of infection, thus enabling investigation of the rate of worm death. An empirical and statistical approach is taken to the model fitting: where possible, distributional properties and function relationships are obtained from the data rather than assumed from theory. Attempts are made to remove known sources of bias. Maximum likelihood techniques, employed to allow for error in both the pre-intervention and reinfection data, yield confidence intervals for the worm life-span (CI95% = 5·7–10·5 years) and demonstrate that the worm death rate is unlikely to vary with host age. The possibilities and limitations of fitting dynamic models to data are discussed. We conclude that a detailed, quantitative approach will be necessary if progress is to be made with the interpretation of epidemiological data and the models intended to describe them.