Civil Rights
Movements, leaders, victories and the continuing fight for equality.
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THE BHP WIRE —
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Explore the people, places, events, achievements, struggles and stories that shaped our journey.
Movements, leaders, victories and the continuing fight for equality.
Innovation, patents, science, technology and world-changing contributions.
Pioneers, champions, Negro Leagues, records, activism and excellence.
Meet the people whose lives, choices and achievements shaped the journey.
Black towns, communities, institutions and places where history happened.
Moments that changed communities, movements, institutions and the nation.
Katherine Johnson’s mathematical calculations helped guide some of America’s most important early space missions while she confronted the racial and gender barriers faced by Black women in twentieth-century America.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
Nonlinear mixed-effects models constitute a class of statistical models generalizing linear mixed-effects models. Like linear mixed-effects models, they are particularly useful in settings where there are multiple measurements within the same statistical units or when there are dependencies between measurements on related statistical units. Nonlinear mixed-effects models are applied in many fields including medicine, public health, pharmacology, and ecology.
A mixed model, mixed-effects model or mixed error-component model is a statistical model containing both fixed effects and random effects. These models are useful in a wide variety of disciplines in the physical, biological and social sciences. They are particularly useful in settings where repeated measurements are made on the same statistical units (see also longitudinal study), or where measurements are made on clusters of related statistical units. Mixed models are often preferred over traditional analysis of variance regression models because they don't rely on the independent observations assumption. Further, they have their flexibility in dealing with missing values and uneven spacing of repeated measurements. The Mixed model analysis allows measurements to be explicitly modeled in a wider variety of correlation and variance-covariance avoiding biased estimations structures. This page will discuss mainly linear mixed-effects models rather than generalized linear mixed models or nonlinear mixed-effects models.
NONMEM is a non-linear mixed-effects modeling software package developed by Stuart L. Beal and Lewis B. Sheiner in the late 1970s at University of California, San Francisco, and expanded by Robert Bauer at Icon PLC. Its name is an acronym for nonlinear mixed effects modeling but it is especially powerful in the context of population pharmacokinetics, pharmacometrics, and PK/PD models. NONMEM models are written in NMTRAN, a dedicated model specification language that is translated into FORTRAN, compiled on the fly and executed by a command-line script. Results are presented as text output files including tables. There are multiple interfaces to assist modelers with housekeeping of files, tracking of model development, goodness-of-fit evaluations and graphical output, such as PsN and xpose and Wings for NONMEM. Current version for NONMEM is 7.5.
Nonlinear mixed-effects models are a special case of regression analysis for which a range of different software solutions are available. The statistical properties of nonlinear mixed-effects models make direct estimation by a BLUE estimator impossible. Nonlinear mixed effects models are therefore estimated according to Maximum Likelihood principles. Specific estimation methods are applied, such as linearization methods as first-order (FO), first-order conditional (FOCE) or the laplacian (LAPL), approximation methods such as iterative-two stage (ITS), importance sampling (IMP), stochastic approximation estimation (SAEM) or direct sampling. A special case is use of non-parametric approaches. Furthermore, estimation in limited or full Bayesian frameworks is performed using the Metropolis-Hastings or the NUTS algorithms. Some software solutions focus on a single estimation method, others cover a range of estimation methods and/or with interfaces for specific use cases.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Mae Jemison, aboard Space Shuttle Endeavour in 1992.
