David J. Strauss

Pseudolikelihood Estimation for Social Networks

Abstract Interest in log-linear modeling for social-network data has grown steadily since Holland and Leinhardt (1981) proposed their p 1 model. That model was designed for a single binary relationship (directed graph) representing interactions between individuals. It assumed that interactions between pairs of individuals are mutually independent. Subsequent work has extended the model in various ways, including block-modeling and the case of dependence between pairs of individuals. In empirical work it would often be desirable to fit a wide variety of these models, as the differences in predictions or goodness of fit are likely to provide insights into the data. This has not been common practice, however, because estimation for some of the models has been difficult, and the maximum likelihood schemes developed for others involve different computer programs not always available in standard packages. The focus of this article is on a general estimation technique that maximizes the pseudolikelihood, the pro...

Classical confidence intervals and Bayesian probability estimates for ends of local taxon ranges

The observed local range of a fossil taxon in a stratigraphic section is almost certainly a truncated version of the true local range. True endpoints are parameters that may be estimated using only the assumption that fossil finds are distributed randomly between them. If thickness is rescaled so that true endpoints lie at 0 and 1, the joint distribution of gap lengths between fossil finds is given by the Dirichlet distribution. Observed ends of the range are maximum likelihood estimators of true endpoints, but they are biased seriously. Extension of the observed range at each end by a distance equal to the average gap length yields unbiased point estimators. Classical statistics can generate confidence intervals for ends of the taxon range; but with Bayesian inference, the probability that true endpoints lie in a certain region can be stated. For a 95% confidence level (classical) or a 95% probability (Bayesian), the range extensions exceed the observed range if the range is established on less than six finds; if only two finds are used, such range extensions are an order of magnitude longer than the observed range. Evidently the standard biostratigraphic practice that identifies zonal boundaries as horizons rather than confidence intervals may not be justified at the resolution of typical fossiliferous sections.

Spatial Prediction of Soil Salinity Using Electromagnetic Induction Techniques: 1. Statistical Prediction Models: A Comparison of Multiple Linear Regression and Cokriging

We describe a regression-based statistical methodology suitable for predicting field scale spatial salinity (EC,) conditions from rapidly acquired electromagnetic induction (EC,) data. This technique uses multiple linear regression (MLR) models to estimate soil salinity from EC, survey data. The MLR models incorporate multiple EC, measurements and trend surface parameters to increase the prediction accuracy and can be fitted from limited amounts of EC, calibration data. This estimation technique is compared to some commonly recommended cokriging techniques, with respect to statistical modeling assumptions, calibration sample size requirements, and prediction capabilities. We show that MLR models are theoretically equivalent to and cost-effective relative to cokriging for estimating a spatially distributed random variable when the residuals from the regression model are spatially uncorrelated. MLR modeling and prediction techniques are demonstrated with data from three salinity surveys.

Spatial Prediction of Soil Salinity Using Electromagnetic Induction Techniques: 2. An Efficient Spatial Sampling Algorithm Suitable for Multiple Linear Regression Model Identification and Estimation

In our companion paper we described a regression-based statistical methodology for predicting field scale salinity (EC,) patterns from rapidly acquired electromagnetic induction (EC,) measurements. This technique used multiple linear regression (MLR) models to construct both point and conditional probability estimates of soil salinity from EC, survey data. In this paper we introduce a spatial site selection algorithm designed to identify a minimal number of calibration sites for MLR model estimation. The algorithm selects sites that are spatially representative of the entire survey area and simultaneously facilitate the accurate estimation of model parameters. Additionally, we introduce two statistical criteria that are useful for selecting optimal MLR variable combinations, describe a technique for identifying faulty signal data, and explore some of the differences between our recommended model-based sampling plan are some more commonly used design-based sampling plans. Survey data from two of the fields analyzed in the previous paper are used to demonstrate these techniques.

Life expectancy of children with cerebral palsy

Risk factors for mortality of young children with cerebral palsy were studied using a sample of 12,709 children aged 0.5-3.5 years with cerebral palsy who had received services from the State of California between 1980 and 1995. The most powerful prognostic factors for survival were simple functional items: mobility and feeding skills. Once these were known, factors such as severity of mental retardation and presence of quadriplegia contributed relatively little. Children with fair motor and eating skills had good survival prospects, with 90% or more reaching adulthood, but those without such skills had much poorer prospects. Among children who were unable to lift their heads, median survival time was 7 additional years for those who were tube fed (n = 557) and 14 years for those fed entirely by others (n = 997). Although a childs approximate survival chances can be assessed from such functional classifications, we indicate the manner in which additional information on the childs condition can be used to obtain more accurate survival data.

Causes of excess mortality in cerebral palsy

It is well known that individuals with cerebral palsy (CP) are subject to higher mortality than the general population but the causes of this have not been systematically analysed. This study investigates mortality in a Californian population of 45 292 individuals with CP, 4028 of whom died during the 1986 to 1995 study period. The aims of this study were to identify diseases that may be causally linked with CP, and diseases whose diagnosis and/or treatment need improvement. Overall, the standardized mortality ratio (SMR) was 8.4. Mortality from breast cancer was three times that of the general population, suggesting poorer detection and/or treatment. The dramatic elevation of mortality due to brain cancer, especially in children (SMR=24), raises the possibility of a link between this and CP. Cause of death was non‐specific in some individuals. Therefore, these SMRs are conservative. As expected, SMRs due to respiratory diseases were very high but, contrary to anecdotal reports, such diseases did not account for most deaths. High SMRs were also found for diseases of the circulatory and digestive systems. Finally, a marked elevation of deaths was due to external causes, including drowning and being hit by motor vehicles.

Causes of death in autism

The objective of this study was to determine which causes of death are more frequent in persons with autism, and by how much, compared with the general population. Subjects were 13,111 ambulatory Californians with autism, followed between 1983 and 1997. The units of study were person-years, each linked to the subjects age, sex, and cause of death (if any) for the specific year. Observed numbers of cause-specific deaths were compared with numbers expected according to general population mortality rates. Standardized mortality rates (SMRs) were computed for each mental retardation level. Elevated death rates were observed for several causes, including seizures and accidents such as suffocation and drowning; elevated mortality due to respiratory disease was observed among persons with severe mental retardation. Overall, excess mortality was especially marked for persons with severe mental retardation, but life expectancy is reduced even for persons who are fully ambulatory and who have only mild mental retardation.

Mortality and causes of death in persons with Down syndrome in California

This study investigated mortality and causes of death between 1988 and 1999 in 14781 persons (6702 female) with Down syndrome in California, comparing age, sex, ethnicity, and other factors. Mean age at the start of follow-up was 14 years 8 months (SD 14y 10mo). During the study period 600 persons died. The standardized mortality ratio (SMR) for the population was 5.5. Blacks were at greater risk than whites, Hispanics, or Asians (relative risk = 1.5). Mortality declined during the period, especially for children with congenital heart defects. Leukemia (SMR = 17), respiratory illnesses (SMR = 27), congenital anomalies (SMR = 72), and circulatory diseases (SMR = 5.3) accounted for most of the excess mortality. With the exception of leukemia, cancer mortality was not different from that of the general population.

Growth patterns in a population of children and adolescents with cerebral palsy

This study examined growth of children and adolescents with cerebral palsy (CP) who received services from the California Department of Developmental Services from 1987 to 2002. In all, 141 961 measurements of height and weight were taken from 24920 patients with CP (14103 males, 10817 females). Centiles of weight and height were determined by age, sex, and five levels of functional ability ranging from fully ambulatory to unable to walk, crawl, or feed self, and fed via gastrostomy tube. Resulting charts of height and weight centiles were compared with Centers for Disease Control and Prevention weight and height charts for the general population of the US. Centiles of height and weight of patients with CP were close to those of the general population for the highest functioning groups with CP, but lagged substantially for other groups. Presence of a feeding tube was associated with greater height and weight in the lowest functioning groups, with centiles for weight being 2 to 5kg higher for those with gastrostomy tubes. The charts may assist in early identification of nutritional or metabolic difficulties beyond what might be expected for patients with similar functional disabilities.

Bivariate Distributions with Exponential Conditionals

Abstract It is frequently easier to visualize conditional distributions of experimental variables rather than joint distributions. In this article we consider the most general class of bivariate distributions such that both sets of conditional densities are exponential. The class proves to be remarkably simple to describe: The joint density must be proportional to exp(- λx - μy - νxy), where the constant of proportionality depends on the classical exponential integral. The joint distribution has marginals that are not exponential and a negative correlation coefficient, except in the special case of independence. After deriving some distributional results, we develop methods for parameter estimation and simulation. A simple method-of-moments estimator appears to give reasonable results. We also briefly discuss generalizations to higher dimensions and to distributions with conditionals in a general exponential family.