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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 \phi_ and a covariate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latent Variable
In statistics, latent variables (from Latin: present participle of ) are variables that can only be inferred indirectly through a mathematical model from other observable variables that can be directly observed or measured. Such '' latent variable models'' are used in many disciplines, including engineering, medicine, ecology, physics, machine learning/artificial intelligence, natural language processing, bioinformatics, chemometrics, demography, economics, management, political science, psychology and the social sciences. Latent variables may correspond to aspects of physical reality. These could in principle be measured, but may not be for practical reasons. Among the earliest expressions of this idea is Francis Bacon's polemic the ''Novum Organum'', itself a challenge to the more traditional logic expressed in Aristotle's Organon: In this situation, the term ''hidden variables'' is commonly used, reflecting the fact that the variables are meaningful, but not observable ... [...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, data-generating process. When referring specifically to probability, probabilities, the corresponding term is probabilistic model. 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. 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). Introduction Informally, a ... [...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 dis ... [...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 functions 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 behav ... [...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 the equation f(x) = \frac where The logistic function has domain the real numbers, the limit as x \to -\infty is 0, and the limit as x \to +\infty is L. The exponential function with negated argument (e^ ) is used to define the standard logistic function, depicted at right, where L=1, k=1, x_0=0, which has the equation f(x) = \frac and is sometimes simply called the sigmoid. It is also sometimes called the expit, being the inverse function of the logit. 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. There are various generalizations, depending on the field. History The logistic function was introduced in a series of three papers by Pier ... [...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 fal ... [...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 consists of 11 tasks: *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 var ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Growth
Exponential growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present size. For example, when it is 3 times as big as it is now, it will be growing 3 times as fast as it is now. In more technical language, its instantaneous rate of change (that is, the derivative) of a quantity with respect to an independent variable is proportional to the quantity itself. Often the independent variable is time. 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). Exponential growth is the inverse of logarithmic growth. Not all cases of growth at an always increasing rate are instances of exponential growth. For example the function f(x) = x^3 grows at an ever increasing rate, but is much slower than growing exponentially. For example, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dementia
Dementia is a syndrome associated with many neurodegenerative diseases, characterized by a general decline in cognitive abilities that affects a person's ability to perform activities of daily living, everyday activities. This typically involves problems with memory, thinking, behavior, and motor control. Aside from memory impairment and a thought disorder, disruption in thought patterns, the most common symptoms of dementia include emotional problems, difficulties with language, and decreased motivation. The symptoms may be described as occurring in a continuum (measurement), continuum over several stages. Dementia is a life-limiting condition, having a significant effect on the individual, their caregivers, and their 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 might be caused by the normal aging process. Several diseases and injuries to the brain, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mild Cognitive Impairment
Mild cognitive impairment (MCI) is a diagnosis that reflects an intermediate stage of cognitive impairment that is often, but not always, a transitional phase from cognitive changes in normal aging to those typically found in dementia, especially dementia due to Alzheimer's disease (Alzheimer's dementia). MCI may include both memory and non-memory neurocognitive impairments. About 50 percent of people diagnosed with MCI have Alzheimer's disease and go on to develop Alzheimer's dementia within five years. MCI can also serve as an early indicator for other types of dementia, although MCI may also remain stable or remit. Many definitions of MCI exist. A common feature of many of these is that MCI involves cognitive impairments that are measurable but that are not significant enough to interfere with instrumental activities of daily living. The DSM-5 introduces the concept of mild neurocognitive disorder (mNCD), which is designed to be largely equivalent to MCI. The International Clas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alzheimer's Disease
Alzheimer's disease (AD) is a neurodegenerative disease and the cause of 60–70% of cases of dementia. The most common early symptom is difficulty in remembering recent events. As the disease advances, symptoms can include problems with language, disorientation (including easily getting lost), mood swings, loss of motivation, self-neglect, and 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 average life expectancy following diagnosis is three to twelve years. The causes of Alzheimer's disease remain poorly understood. There are many environmental and genetic risk factors associated with its development. The strongest genetic risk factor is from an allele of apolipoprotein E. Other risk factors include a history of head injury, clinical depression, and high blood pressure. The progression of the di ... [...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 testing is used in psychology and psychometrics, as well as other fields studying 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 were eventually abandoned ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
