Biased Mentalizing in Children Aged Seven to 11: Latent Class Confirmation of Response Styles to Social Scenarios and Associations with Psychopathology

A new approach to the measurement of mentalizing is introduced. Instead of measuring the presence or absence of mentalizing capacity, the current study aimed at developing a mentalizing task that focuses on investigating biases in mentalizing through the use of ambiguous peer‐related social scenarios. The response consistency of 659 children was investigated in a community sample of children aged seven to 11. Confirmatory latent class analysis allocated children to three groups on the basis of their responses: an overly positive style (OP), a rational/neutral style (R) or an overly negative style (ON). Children classed as OP showed a greater likelihood of being above cut‐off on a population screen for externalizing disorder. Over a two‐year follow‐up period, the children who were classified as R were most likely to remain so whereas the OP and ON children were found to change group. The results are discussed in the context of social‐cognitive research in this age group. Further studies should examine the external validity of the mentalizing task because the results reported here concern only internal construct validity.     

Practical Methods for Bounding Type I Error Rate with an Internal Pilot Design

New analytic forms for distributions at the heart of internal pilot theory solve many problems inherent to current techniques for linear models with Gaussian errors. Internal pilot designs use a fraction of the data to re-estimate the error variance and modify the final sample size. Too small or too large a sample size caused by an incorrect planning variance can be avoided. However, the usual hypothesis test may need adjustment to control the Type I error rate. A bounding test achieves control of Type I error rate while providing most of the advantages of the unadjusted test. Unfortunately, the presence of both a doubly truncated and an untruncated chi-square random variable complicates the theory and computations. An expression for the density of the sum of the two chi-squares gives a simple form for the test statistic density. Examples illustrate that the new results make the bounding test practical by providing very stable, convergent, and much more accurate computations. Furthermore, the new computational methods are effectively never slower and usually much faster. All results apply to any univariate linear model with fixed predictors and Gaussian errors, with the t-test a special case.     

An alternative to unit root tests: Bridge estimators differentiate between nonstationary versus stationary models and select optimal lag

This paper introduces a novel way of differentiating a unit root from stationary alternatives using so-called “Bridge” estimators; this estimation procedure can potentially generate exact zero estimates of parameters. We exploit this property and treat this as a model selection problem. We show that Bridge estimators can select the correct model with probability tending to 1. They estimate “zero” parameter on the lagged dependent variable as zero (nonstationarity), if this is nonzero (stationary), estimate the coefficient with standard normal limit. In this sense, we extend the statistics literature as well, since that literature only deals with model selection among only stationary variables.     

State estimation for nonlinear state-space transmission models of tuberculosis

Given the high prevalence of tuberculosis (TB) and the mortality rate associated with the disease, numerous models, such as the Gammaitoni and Nucci (GN) model, were developed to model the risk of transmission. These models typically rely on a quanta generation rate as a measurement of infectivity. Since the quanta generation rate cannot be measured directly, the unique contribution of this work is to develop state estimators to estimate the quanta generation rate from available measurements. To estimate the quanta generation rate, the GN model is adapted into an augmented single-room GN model and a simplified two-room GN model. Both models are shown to be observable, i.e., it is theoretically possible to estimate the quanta generation rate given available measurements. Kalman filters are used to estimate the quanta generation rate. First, a continuous-time extended Kalman filter is used for both adapted models using a simulation and measurement sampling rate of 60 s. Accurate quanta generate rate estimates are achieved in both cases. A more realistic scenario is also considered with a measurement sampling rate of one day. For these estimates, a hybrid extended Kalman filter (HEKF) is used. Accurate quanta generation rate estimates are achieved for the more realistic scenario. Future work could potentially use the HEKFs, the adapted models, and real-time measurements in a control system feedback loop to reduce the transmission of TB in confined spaces such as hospitals.     

MODELING DEMAND DURING LEAD TIME*

This paper treats some of the important considerations in constructing an analytical model for the distribution of demand during lead time. It presents a formal model that can be developed along one of two lines. The first has order size and order intensity leading to a compound distribution of period demand, then period demand and lead time giving rise to a compound distribution of demand during lead time. The second has order intensity and lead time giving rise to a compound distribution of lead-time order intensity, then lead-time order intensity and order size leading to a compound distribution of demand during lead time. The paper also condenses the state of the art in a table and proposes some simple classification schemes that could help researchers extend that state of the art.