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Latent Growth Modeling
Latent growth modeling is a statistical technique used in the structural equation modeling (SEM) framework to estimate growth trajectories. It is a longitudinal analysis technique to estimate growth over a period of time. It is widely used in the field of psychology, behavioral science, education and social science. It is also called latent growth curve analysis. The latent growth model was derived from theories of SEM. General purpose SEM software, such as OpenMx, lavaan (both open source packages based in R), AMOS, Mplus, LISREL, or EQS among others may be used to estimate growth trajectories. Background Latent Growth Models Tucker, L.R. (1958) Determination of parameters of a functional relation by factor analysis. ''Psychometrika'' 23, 19-23. Rao, C.R. (1958) Some statistical methods for the comparison of growth curves. ''Biometrics''. 14, 1-17. Scher, A.M., Young, A.C. & Meredith, W.M. (1960) Factor analysis of the electrocardiogram. ''Circulation Research'' 8, 519-526. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Equation Modeling
Structural equation modeling (SEM) is a label for a diverse set of methods used by scientists in both experimental and observational research across the sciences, business, and other fields. It is used most in the social and behavioral sciences. A definition of SEM is difficult without reference to highly technical language, but a good starting place is the name itself. SEM involves the construction of a ''model'', to represent how various aspects of an observable or theoretical phenomenon are thought to be causally structurally related to one another. The ''structural'' aspect of the model implies theoretical associations between variables that represent the phenomenon under investigation. The postulated causal structuring is often depicted with arrows representing causal connections between variables (as in Figures 1 and 2) but these causal connections can be equivalently represented as equations. The causal structures imply that specific patterns of connections should appe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Growth Curve (statistics)
The growth curve model in statistics is a specific multivariate linear model, also known as GMANOVA (Generalized Multivariate Analysis-Of-Variance). It generalizes MANOVA by allowing post-matrices, as seen in the definition. Definition Growth curve model: Let X be a ''p''×''n'' random matrix corresponding to the observations, A a ''p''×''q'' within design matrix with ''q'' ≤ ''p'', B a ''q''×''k'' parameter matrix, C a ''k''×''n'' between individual design matrix with rank(''C'') + ''p'' ≤ ''n'' and let Σ be a positive-definite ''p''×''p'' matrix. Then : X=ABC+\Sigma^E defines the growth curve model, where A and C are known, B and Σ are unknown, and E is a random matrix distributed as ''N''''p'',''n''(0,''I''''p'',''n''). This differs from standard MANOVA by the addition of C, a "postmatrix". History Many writers have considered the growth curve analysis, among them Wishart (1938), Box (1950) and Rao (1958). Potthoff and Roy in 1964 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OpenMx
OpenMx is an open source program for extended structural equation modeling. It runs as a package under R. Cross platform, it runs under Linux, Mac OS and Windows.S. Boker, M. Neale, H. Maes, M. Wilde, M. Spiegel, T. Brick, J. Spies, R. Estabrook, S. Kenny, T. Bates, P. Mehta and J. Fox. (2011). OpenMx: An Open Source Extended Structural Equation Modeling Framework. ''Psychometrika'', 76/ref> Overview OpenMx consists of an R library of functions and optimizers supporting the rapid and flexible implementation and estimation of Structural equation modeling, SEM models. Models can be estimated based on either raw data (with FIML modelling) or on correlation or covariance matrices. Models can handle mixtures of continuous and ordinal data. The current version is OpenMx 2, and is available on CRAN. Path analysis, Confirmatory factor analysis, Latent growth modeling, Mediation analysis are all implemented. Multiple group models are implemented readily. When a model is run, it r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R (programming Language)
R is a programming language for statistical computing and graphics supported by the R Core Team and the R Foundation for Statistical Computing. Created by statisticians Ross Ihaka and Robert Gentleman, R is used among data miners, bioinformaticians and statisticians for data analysis and developing statistical software. Users have created packages to augment the functions of the R language. According to user surveys and studies of scholarly literature databases, R is one of the most commonly used programming languages used in data mining. R ranks 12th in the TIOBE index, a measure of programming language popularity, in which the language peaked in 8th place in August 2020. The official R software environment is an open-source free software environment within the GNU package, available under the GNU General Public License. It is written primarily in C, Fortran, and R itself (partially self-hosting). Precompiled executables are provided for various operating systems. R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AMOS (statistical Software Package)
Amos or AMOS may refer to: Arts and entertainment * Amos Records, an independent record label established in Los Angeles, California, in 1968 * Amos (band), an American Christian rock band * ''Amos'' (album), an album by Michael Ray * ''Amos'' (film), a 1985 American made-for-television drama film People and religious figures * Amos (name), a given name, nickname and surname Technology * AMOS or Advanced Mortar System, a 120 mm automatic twin barreled, breech loaded mortar turret * AMOS (programming language), a dialect of BASIC on the Amiga computer * Alpha Micro Operating System, a proprietary operating system used in Alpha Microsystems minicomputers * AMOS (statistical software package), a statistical software package used in structural equation modeling * Air Force Maui Optical and Supercomputing observatory, an Air Force Research Laboratory operating on Maui, Hawaii * Amos (satellite), series of Israeli IAI-built civilian communications satellites ** AMOS (sate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LISREL
LISREL (linear structural relations) is a proprietary statistical software package used in structural equation modeling (SEM) for manifest and latent variables. It requires a "fairly high level of statistical sophistication". History LISREL was developed in the 1970s by Karl Jöreskog, then a scientist at Educational Testing Service in Princeton, New Jersey, and Dag Sörbom, later both professors of Uppsala University in Sweden. The most current version is LISREL 11 and can be downloaded from https://ssicentral.com/index.php/products/lisrel/. Command language, graphical user interface and delivery LISREL is mainly syntax-based, although recent versions have featured a graphical user interface (GUI). SSI (Scientific Software International) has recently changed from e-Academy to a "home-built" solution for distributing the rental (6- or 12-month) versions of their software. See also * Confirmatory factor analysis * Multivariate analysis * Path analysis (statistics) * Structural eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
EQS (software)
EQS may refer to: * Etixx-Quick-Step, a professional cycling team * Mercedes-Benz EQS, an electric sedan * Mercedes-Benz EQS SUV, an electric sport utility vehicle * Environmental Quality Standard, an environmental standard for environmental quality * Esquel Airport Esquel Airport ( es, Aeropuerto de Esquel, ) is an international airport in Chubut Province, Argentina serving the city of Esquel Esquel is a town in the northwest of Chubut Province in Argentine Patagonia. It is located in Futaleufú Depart ... (IATA airport code: EQS), Esquel, Chubut Province, Argentina See also * EQ (other) * {{dab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factor Analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modelled as linear combinations of the potential factors plus "error" terms, hence factor analysis can be thought of as a special case of errors-in-variables models. Simply put, the factor loading of a variable quantifies the extent to which the variable is related to a given factor. A common rationale behind factor analytic methods is that the information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a dataset. Factor analysis is commonly used in psychometrics, persona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalised Logistic Function
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959. Definition Richards's curve has the following form: :Y(t) = A + where Y = weight, height, size etc., and t = time. It has five parameters: *A: the lower (left) asymptote; *K: the upper (right) asymptote when C=1. If A=0 and C=1 then K is called the carrying capacity; *B: the growth rate; *\nu > 0 : affects near which asymptote maximum growth occurs. *Q: is related to the value Y(0) *C: typically takes a value of 1. Otherwise, the upper asymptote is A + The equation can also be written: :Y(t) = A + where M can be thought of as a starting time, at which Y(M) = A + . Including both Q and M can be convenient: :Y(t) = A + this representation simplifies the ... [...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] |
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] |
