NONLINEAR REGRESSION FOR SPLIT PLOT EXPERIMENTS

Split plot experimental designs are common in studies of the effects of air pollutants on crop yields. Nonlinear functions such the Weibull function have been used extensively to model the effect of ozone exposure on yield of several crop species. The usual nonlinear regression model, which assumes independent errors, is not appropriate for data from nested or split plot designs in which there is more than one source of random variation. The nonlinear model with variance components combines a nonlinear model for the mean with additive random effects to describe the covariance structure. We propose an estimated generalized least squares (EGLS) method of estimation for this model. The variance components are estimated two ways: by analysis of variance, and by an approximate MINQUE method. These methods are demonstrated and compared with results from ordinary nonlinear least squares for data from the National Crop Loss Assessment Network (NCLAN) program regarding the effects of ozone on soybeans. In this example all methods give similar point estimates of the parameters of the Weibull function. The advantage of estimated generalized least squares is that it produces proper estimates of the variances of the parameters and of estimated yields, which take the covariance structure into account. A computer program that fits the nonlinear model with variance components by the EGLS method is available from the authors

A conversation about implicit bias

Explicit bias reflects our perceptions at a conscious level. In contrast, implicit bias is unintentional and operates at a level below our conscious awareness. Implicit stereotypes shaping implicit biases are widely studied in criminal justice, medicine, CEO selection at Fortune 500 companies, etc. However, the problem of unconscious bias remains. E.g., while women constitute an increasing proportion of all STEM undergraduates, they still make up only a small proportion of faculty members at research universities, and they are substantially under-represented in organizational leadership and as recipients of professional awards and prizes. Can we afford to have unintentional perceptions continue to hinder the success and advancement of women and other underrepresented groups? Can we afford to continue to underuse human capital in science? This session at the 2015 Joint Statistical Meetings (JSM) aimed to illuminate what statisticians need to know and do to break the glass ceiling of implicit bias

Validity of Spatial Analyses for Large Field Trials.

A number of recent articles report that analyses which account for spatial variation in field trials in terms of correlations between plot errors are more efficient than the classical randomized blocks analysis of variance. In most cases, these efficiency comparisons are in terms of model-based or 'predicted' estimates of precision. The validity of estimates of precision has not been generally demonstrated for these correlated errors (CE) analyses, however. We describe a simulation study to assess validity (as well as efficiency) of several CE and alternative fixed effects spatial analyses. We focus on situations typical of large field trials with limited replication, and with realistic levels of both fixed and random components of spatial variation. Results show that when spatial autocorrelation is present the CE analyses are robust with respect to validity, except when strong fixed trend is underfitted in the analysis. Also, when spatial autocorrelation is present, efficiency of the ..

Retention and promotion of women and underrepresented minority faculty in science and engineering at four large land grant institutions.

In the most recent cohort, 2002-2015, the experiences of men and women differed substantially among STEM disciplines. Female assistant professors were more likely than men to leave the institution and to leave without tenure in engineering, but not in the agricultural, biological and biomedical sciences and natural resources or physical and mathematical sciences. In contrast, the median times to promotion from associate to full professor were similar for women and men in engineering and the physical and mathematical sciences, but one to two years longer for women than men in the agricultural, biological and biomedical sciences and natural resources.URM faculty hiring is increasing, but is well below the proportions earning doctoral degrees in STEM disciplines. The results are variable and because of the small numbers of URM faculty, the precision and power for comparing URM faculty to other faculty were low. In three of the four institutions, lower fractions of URM faculty than other faculty hired in the 2002-2006 time frame left without tenure. Also, in the biological and biomedical and physical and mathematical sciences no URM faculty left without tenure. On the other hand, at two of the institutions, significantly more URM faculty left before their tenth anniversary than other faculty and in engineering significantly more URM faculty than other faculty left before their tenth anniversary. We did not find significant differences in promotion patterns between URM and other faculty

Logistic Regression for Southern Pine Beetle Outbreaks with Spatial and Temporal Autocorrelation

Regional outbreaks of southern pine beetle (Dendroctonus frontalis Zimm.) show marked spatial and temporal patterns. While these patterns are of interest in themselves, we focus on statistical methods for estimating the effects of underlying environmental factors in the presence of spatial and temporal autocorrelation. The most comprehensive available information on outbreaks consist of binary data, annual presence or absence of outbreak for individual counties within the southern United States. We demonstrate a method for modeling spatially correlated proportions, such as the proportion of years that a county experiences outbreak, based on annual outbreak presence or absence data for counties in three states (NC, SC, and GA) over 31 years. In the proposed method the proportion of years in outbreak is predicted using a marginal logistic regression model with spatial autocorrelation among counties, with adjustment of variance terms to account for temporal autocorrelation. This type of m..

A likelihood ratio test for separability of covariances

We propose a formal test of separability of covariance models based on a likelihood ratio statistic. The test is developed in the context of multivariate repeated measures (for example, several variables measured at multiple times on many subjects), but can also apply to a replicated spatio-temporal process and to problems in meteorology, where horizontal and vertical covariances are often assumed to be separable. Separable models are a common way to model spatio-temporal covariances because of the computational benefits resulting from the joint space-time covariance being factored into the product of a covariance function that depends only on space and a covariance function that depends only on time. We show that when the null hypothesis of separability holds, the distribution of the test statistic does not depend on the type of separable model. Thus, it is possible to develop reference distributions of the test statistic under the null hypothesis. These distributions are used to evaluate the power of the test for certain nonseparable models. The test does not require second-order stationarity, isotropy, or specification of a covariance model. We apply the test to a multivariate repeated measures problem.Kronecker product Multivariate regression Multivariate repeated measures Nonstationary Separable covariance Spatio-temporal process