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Nonlinear Mixed-effects Model
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. Definition While any statistical model containing both fixed effects and random effects is an example of a nonlinear mixed-effects model, the most commonly used models are members of the class of nonlinear mixed-effects models for repeated measures :_ = f(\phi_,_) + \epsilon_,\quad i =1,\ldots, M, \, j = 1,\ldots, n_i where *M is the number of groups/subjects, *n_i is the number of observations for the ith group/subject, *f is a real-valued differentiable function of a group-specific parameter vector \theta_ and a covariat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample data (and similar data from a larger Statistical population, population). A statistical model represents, often in considerably idealized form, the data-generating process. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman J. Adèr, Herman Adèr quoting Kenneth A. Bollen, Kenneth Bollen). All Statistical hypothesis testing, statistical hypothesis tests and all Estimator, statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference. Introduction Informally, a statistical model can be thought of as a statistical assumption (or set of statistical assumptions) with a certain property: that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Progressive Disease
Progressive disease or progressive illness is a disease or physical ailment whose course in most cases is the worsening, growth, or spread of the disease. This may happen until death, serious debility, or organ failure occurs. Some progressive diseases can be halted and reversed by treatment (surgical, dietary, or lifestyle interventions). Many can be slowed by medical therapy. Some cannot be altered by current treatments. Though the time distinctions are imprecise, diseases can be ''rapidly progressive'' (typically days to weeks) or ''slowly progressive'' (months to years). The time course of a disease affects whether it is considered acute or chronic. By definition, virtually all slowly progressive diseases are also chronic diseases. Biologically, many of these are also referred to as degenerative diseases due to the cellular changes. Not all chronic diseases are progressive: a chronic, non-progressive disease may be referred to as a ''static'' condition. ''Progressive dise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Growth
When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth. More precisely, the reciprocal function 1/x has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as x \to 0 is infinite: any similar graph is said to exhibit hyperbolic growth. Description If the output of a function is inversely proportional to its input, or inversely proportional to the difference from a given value x_0, the function will exhibit hyperbolic growth, with a singularity at x_0. In the real world hyperbolic growth is created by certain non-linear positive feedback mechanisms. Comparisons with other growth Like exponential growth and logistic growth, hyperbolic growth is highly nonlinear, but differs in important respects. These functions can be confused, as exponential growth, hyperbolic growth, and the first half of logistic growth are convex functions; however their asymptotic behavior (behavior as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Function
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation f(x) = \frac, where For values of x in the domain of real numbers from -\infty to +\infty, the S-curve shown on the right is obtained, with the graph of f approaching L as x approaches +\infty and approaching zero as x approaches -\infty. The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks. A generalization of the logistic function is the hyperbolastic function of type I. The standard logistic function, where L=1,k=1,x_0=0, is sometimes simply called ''the sigmoid''. It is also sometimes called the ''expit'', being the inverse of the logit. History The logistic function was introduced in a series of three papers by Pierre François Verhulst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Estimation Of A Mean Height Curve For Boys From The Berkeley Growth Study With And Without Warping
Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is derived from the best information available.C. Lon Enloe, Elizabeth Garnett, Jonathan Miles, ''Physical Science: What the Technology Professional Needs to Know'' (2000), p. 47. Typically, estimation involves "using the value of a statistic derived from a sample to estimate the value of a corresponding population parameter".Raymond A. Kent, "Estimation", ''Data Construction and Data Analysis for Survey Research'' (2001), p. 157. The sample provides information that can be projected, through various formal or informal processes, to determine a range most likely to describe the missing information. An estimate that turns out to be incorrect will be an overestimate if the estimate exceeds the actual result and an underestimate if the estimate fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ADAS-Cog
The Alzheimer's Disease Assessment Scale-Cognitive Subscale (ADAS-Cog) is a brief neuropsychological assessment used to assess the severity of cognitive symptoms of dementia. It is one of the most widely used cognitive scales in clinical trials and is considered to be the “gold standard” for assessing antidementia treatments. The ADAS-Cog is one half of the Alzheimer's Disease Assessment Scale (ADAS), which also contains a non-cognitive subscale (ADAS-Noncog), which includes 10 tasks which assess mood and behavioural changes which may occur in Alzheimer's disease and other forms of dementia. The ADAS-Cog consist of 11 questions: *Word Recall Task *Naming Objects and Fingers *Following Commands *Constructional Praxis *Ideational Praxis *Orientation *Word Recognition Task *Remembering Test Directions *Spoken Language *Comprehension *Word-Finding Difficulty Different versions Since its original creation in 1980s there have been many alternate versions of the ADAS-Cog created for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). If the constant of proportionality is negative, then the quantity decreases over time, and is said to be undergoing exponential decay instead. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay since the function values form a geometric progression. The formula for exponential growth of a variable at the growth rate , as time goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is x_t = x_0(1+r)^t where is the value of at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dementia
Dementia is a disorder which manifests as a set of related symptoms, which usually surfaces when the brain is damaged by injury or disease. The symptoms involve progressive impairments in memory, thinking, and behavior, which negatively affects a person's ability to function and carry out everyday activities. Aside from memory impairment and a disruption in thought patterns, the most common symptoms include emotional problems, difficulties with language, and decreased motivation. The symptoms may be described as occurring in a continuum over several stages. Consciousness is not affected. Dementia ultimately has a significant effect on the individual, caregivers, and on social relationships in general. A diagnosis of dementia requires the observation of a change from a person's usual mental functioning, and a greater cognitive decline than what is caused by normal aging. Several diseases and injuries to the brain, such as a stroke, can give rise to dementia. However, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mild Cognitive Impairment
Mild cognitive impairment (MCI) is a neurocognitive disorder which involves cognitive impairments beyond those expected based on an individual's age and education but which are not significant enough to interfere with instrumental activities of daily living. MCI may occur as a transitional stage between normal aging and dementia, especially Alzheimer's disease. It includes both memory and non-memory impairments. The cause of the disorder remains unclear, as well as both its prevention and treatment, with some 50 percent of people diagnosed with it going on to develop Alzheimer's disease within five years. The diagnosis can also serve as an early indicator for other types of dementia, although MCI may remain stable or even remit. Mild cognitive impairment has been relisted as mild neurocognitive disorder in DSM-5, and in ICD-11, the latter effective on 1 January 2022. Classification MCI can present with a variety of symptoms, but is divided generally into two types. Amnestic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alzheimer's Disease
Alzheimer's disease (AD) is a neurodegeneration, neurodegenerative disease that usually starts slowly and progressively worsens. It is the cause of 60–70% of cases of dementia. The most common early symptom is difficulty in short-term memory, remembering recent events. As the disease advances, symptoms can include primary progressive aphasia, problems with language, Orientation (mental), disorientation (including easily getting lost), mood swings, loss of motivation, self-neglect, and challenging behaviour, behavioral issues. As a person's condition declines, they often withdraw from family and society. Gradually, bodily functions are lost, ultimately leading to death. Although the speed of progression can vary, the typical life expectancy following diagnosis is three to nine years. The cause of Alzheimer's disease is poorly understood. There are many environmental and genetic risk factors associated with its development. The strongest genetic risk factor is from an alle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cognitive Testing
Cognitive tests are assessments of the cognitive capabilities of humans and other animals. Tests administered to humans include various forms of IQ tests; those administered to animals include the mirror test (a test of visual self-awareness) and the T maze test (which tests learning ability). Such study is important to research concerning the philosophy of mind and psychology, as well as determination of human and animal intelligence. Modern cognitive tests originated through the work of James McKeen Cattell who coined the term "mental tests". They followed Francis Galton's development of physical and physiological tests. For example, Galton measured strength of grip and height and weight. He established an "Anthropometric Laboratory" in the 1880s where patrons paid to have physical and physiological attributes measured. Galton's measurements had an enormous influence on psychology. Cattell continued the measurement approach with simple measurements of perception. Cattell's tests ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cognitive Reserve
Cognitive reserve is the mind's and brain's resistance to damage of the brain. The mind's resilience is evaluated behaviorally, whereas the neuropathological damage is evaluated histologically, although damage may be estimated using blood-based markers and imaging methods. There are two models that can be used when exploring the concept of "reserve": ''brain reserve'' and ''cognitive reserve''. These terms, albeit often used interchangeably in the literature, provide a useful way of discussing the models. Using a computer analogy brain reserve can be seen as hardware and cognitive reserve as software. All these factors are currently believed to contribute to global reserve. Cognitive reserve is commonly used to refer to both brain and cognitive reserves in the literature. In 1988 a study published in ''Annals of Neurology'' reporting findings from post-mortem examinations on 137 elderly persons unexpectedly revealed that there was a discrepancy between the degree of Alzheimer's dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
