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Topic: Linear model

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Generalized linear model

	PlanetMath: regression model
		Some well known non-normal regression models are the logistic regression for binary data and the Poisson regression for count data.
		Linear regression models belong to a more general class of statistical models called the general linear model, where explanatory variables are no longer restricted to be continuous ones only.
		This is version 7 of regression model, born on 2004-07-29, modified 2006-09-24.
	planetmath.org /encyclopedia/RegressionModel.html (472 words)

	PlanetMath: general linear model
		A linear regression model is a special case of the general linear model where all explanatory variables are assumed to be continuous.
		Analysis of variance model, or ANOVA, is another special case of the general linear model, where all of the explantory variables are categorical in nature (for example, gender, marital status, etc..).
		This is version 3 of general linear model, born on 2004-08-03, modified 2006-09-18.
	planetmath.org /encyclopedia/ANOVA.html (340 words)

	Linear model - Wikipedia, the free encyclopedia
		The general linear model (or multivariate regression model) is a linear model with multiple measurements per object.
		ANOVA, or analysis of variance, is historically a precursor to the development of linear models.
		Here the model parameters themselves are not computed, but X column contributions and their significance are identified using the ratios of within-group variances to the error variance and applying the F test.
	en.wikipedia.org /wiki/Linear_model (318 words)

	General Linear Models (GLM)
		Linear combinations of responses reflecting a repeated measure effect (for example, the difference of responses on a measure under differing conditions) can be constructed and tested for significance using either the univariate or multivariate approach to analyzing repeated measures in the general linear model.
		In using the general linear model, one must keep in mind that finding a particular arbitrary solution to the normal equations is primarily a means to the end of accounting for responses on the dependent variables, and not necessarily an end in itself.
		Add a provision for analyzing linear combinations of multiple dependent variables, add a method for dealing with redundant predictor variables and recoded categorical predictor variables, and the major limitations of multiple regression are overcome by the general linear model.
	www.statsoft.com /textbook/stglm.html (13045 words)

	Linear Regression Model : Advantages / Limitations l Linear Regression Software
		Linear regression is a statistical procedure for predicting the value of a dependent variable from an independent variable when the relationship between the variables can be described with a linear model.
		An equivalent formulation which explicitly shows the linear regression as a model of conditional expectation is with the conditional distribution of y given x essentially the same as the distribution of the error term.
		Linear regression implements a statistical model that, when relationships between the independent varibles and the dependent variable are almost linear, shows optimal results.
	www.camo.com /rt/Resources/linear_regression_model.html (569 words)

	Surface Evolver Documentation - Mathematical model (Site not responding. Last check: 2007-09-10)
		Quadratic or Lagrange models may be changed to linear with the M 1 or linear commands.
		As a generalization of the torus model, you may declare the domain to be the quotient space of R^n with respect to some symmetry group.
		This is the underlying symmetry for the torus model.
	www.susqu.edu /brakke/evolver/html/model.htm (4292 words)

	Methods and Measurements: Log Linear Analysis
		Another conceivable model would be that age is related to work status, and disability is related to work status, but the two (age and disability) independent variables do not interact in their effect.
		If the model is appropriate for the table, then all residual frequencies should be "random noise," that is, consist of positive and negative values of approximately equal magnitudes that are distributed evenly across the cells of the table.
		For example, if we first fit a model with the age by work status interaction and the disability by work status interaction, and then fit a model with the age by disability by work status (three-way) interaction, then the second model is a superset of the previous model.
	colfa.utsa.edu /Sociology/masters/loglinear.htm (1829 words)

	4.1.4.1. Linear Least Squares Regression
		Just as models that are linear in the statistical sense do not have to be linear with respect to the explanatory variables, nonlinear models can be linear with respect to the explanatory variables, but not with respect to the parameters.
		Linear models with nonlinear terms in the predictor variables curve relatively slowly, so for inherently nonlinear processes it becomes increasingly difficult to find a linear model that fits the data well as the range of the data increases.
		This means that linear models may not be effective for extrapolating the results of a process for which data cannot be collected in the region of interest.
	www.itl.nist.gov /div898/handbook/pmd/section1/pmd141.htm (883 words)

	Linear regression
		Linear regression analyzes the relationship between two variables, X and Y. For each subject (or experimental unit), you know both X and Y and you want to find the best straight line through the data.
		In general, the goal of linear regression is to find the line that best predicts Y from X. Linear regression does this by finding the line that minimizes the sum of the squares of the vertical distances of the points from the line.
		The goal of linear regression is to adjust the values of slope and intercept to find the line that best predicts Y from X. More precisely, the goal of regression is to minimize the sum of the squares of the vertical distances of the points from the line.
	www.curvefit.com /linear_regression.htm (2787 words)

	Log-Linear Analysis of Frequency Tables
		Another conceivable model would be that age is related to hair color, and stress is related to hair color, but the two (age and stress) factors do not interact in their effect.
		For example, if we first fit a model with the age by hair color interaction and the stress by hair color interaction, and then fit a model with the age by stress by hair color (three-way) interaction, then the second model is a superset of the previous model.
		In general, two models are hierarchically related to each other if one can be produced from the other by either adding terms (variables or interactions) or deleting terms (but not both at the same time).
	www.statsoft.com /textbook/stloglin.html (1647 words)

	The linear model lin-1
		The linear model is one of the most popular models used in data analysis.
		The most prominent deficiency of the linear model, is its strong assumptions about the true relationship in the data; for data which do not conform well to a linear model, predictions may be inaccurate.
		The strategy of fitting a linear model is well known and the only heuristics necessary is a principled way of handling the situation where the linear system used to determine the parameters of the model is close to singular.
	www.cs.toronto.edu /~delve/methods/lin-1/hypertext/lin-1.html (700 words)

	General Linear Model (Site not responding. Last check: 2007-09-10)
		The General Linear Model (GLM) underlies most of the statistical analyses that are used in applied and social research.
		If the model is misspecified, the estimates of the coefficients (the b-values) are likely to be biased (i.e., wrong) and the resulting equation will not describe the data accurately.
		In complex situations, this model specification problem can be a serious and difficult one (see, for example, the discussion of model specification in the statistical analysis of the regression-discontinuity design).
	www.socialresearchmethods.net /kb/genlin.htm (1023 words)

	Beyond the Linear Damping Model for Mechanical Harmonic Oscillators (Site not responding. Last check: 2007-09-10)
		When an oscillator described by a linear damping model is driven, motion at the natural frequency of the oscillator decays toward zero as a transient.
		Model predicted response to drive at 1/2 the resonance frequency and using anisotropic friction.
		The nonlinear model with symmetric friction cannot duplicate the essential (non-noisy) spectrum that is the right-side graph of Fig.
	physics.mercer.edu /petepag/debunk.html (3062 words)

	The Intangible Economy: Linear model of innovation
		The basic linear model of innovation posits a process that moves from one stage to another: Basic Research...
		Rather, he argues, the linear model of innovation originally gained acceptance and continues to this day because of the availability and power of the statistics used in the model.
		The model took hold as part of the general mindset - and the statistics were development to reinforce the model.
	www.athenaalliance.org /weblog/archives/2006/05/linear_model_of.html (677 words)

	Generalized linear model - Wikipedia, the free encyclopedia
		In statistics, the generalized linear model (GLM) is a useful generalization of ordinary least squares regression.
		The linear predictor is a quantity which relate to the expectation of the data (thus, "predictor") through the link function.
		The model's primary merit is that near p=0.5 it is approximately a linear transformation of the probit and logit — econometricians sometimes call this the Harvard model.
	en.wikipedia.org /wiki/Generalized_linear_model (744 words)

	Linear Models of Reality
		Linear models can exhibit quite complex behavior when they have multiple inputs and outputs, and even the simplest models predict wave-like oscillating motion and exponential increasing or fading away, and combinations of these.
		A linear system may also be unstable, which means that even in the absence of input, the output rapidly explodes toward infinity.
		Although in many areas of science linear models do a good job of predicting the things that are predictable, there is a special reason for the relevance in engineering.
	www.cs.cmu.edu /People/ram/art/essay/linear (863 words)

	SPSS Advanced Models \| Data Analysis (Site not responding. Last check: 2007-09-10)
		General linear model (GLM): The GLM gives you flexible design and contrast options to estimate means and variances and to test and predict means.
		Linear mixed models, also known as hierarchical linear models (HLM): If you work with data that display correlation and non-constant variability, such as data that represent students nested within classrooms or consumers nested within families, use the linear mixed models procedure to model means, variances, and covariances in your data.
		You can also use linear mixed models if you're working with repeated measures data, including situations in which there are different numbers of repeated measurements, different intervals for different cases, or both.
	www.spss.com /advanced_models/data_analysis.htm (424 words)

	PA 765: Logit, Probit, and Log-linear Models
		There are several possible purposes to undertake log-linear modeling, the primary being to determine the most parsimonious model which is not significantly different from the saturated model which fully but trivially accounts for the cell frequencies of a table.
		This is because the constant in a loglinear model is a function of the means, and the means are determined by the marginals, which are known.
		Note that the probability of the dependent is not a linear function of Z, but rather is a cumulative normal function of Z. This means that the effect of a unit change in the independent on the probability of the dependent depends on the level of the independents.
	www2.chass.ncsu.edu /garson/pa765/logit.htm (14875 words)

	Linear Programming Model (Site not responding. Last check: 2007-09-10)
		Every network flow model has a linear programming model, that is a model with algebraic linear expressions describing the objective function and constraints.
		For construction of the model, it is convenient to number the nodes and arcs for reference as in Fig.
		The linear programming model is an algebraic description of the objective to be minimized and the constraints to be satisfied by the variables.
	www.me.utexas.edu /~jensen/models/network/net2.html (129 words)

	Linear regression
		For a linear model, the sum-sqaured error is a quadratic function of the model parameters.
		Change the model parameters so that we move a short distance in the direction of the greatest rate of decrease of the error, i.e., in the direction of -G. Repeat steps 2 and 3 until G gets close to zero.
		Our linear model of equation 1 can in fact be implemented by the simple neural network shown in Fig.
	www.willamette.edu /~gorr/classes/cs449/linear1.html (662 words)

	Linear Growth
		Linear growth means that the relationship between the variables is a straight line relationship.
		An example of a linear relationship is the relationship between temperature in Fahrenheit and Celsius is F=(9/5)*C + 32.
		Here the slope (or the rate at which F changed when C changes one unit) is 9/5 and the intercept (or displacement in F when C is zero) is 32.
	www.trinity.edu /slibs/MathModels/linear.htm (324 words)

	4.1.4.2. Nonlinear Least Squares Regression
		Unlike linear regression, there are very few limitations on the way parameters can be used in the functional part of a nonlinear regression model.
		Linear models do not describe processes that asymptote very well because for all linear functions the function value can't increase or decrease at a declining rate as the explanatory variables go to the extremes.
		With functions that are linear in the parameters, the least squares estimates of the parameters can always be obtained analytically, while that is generally not the case with nonlinear models.
	www.itl.nist.gov /div898/handbook/pmd/section1/pmd142.htm (691 words)

	A non-linear model of information seeking behaviour
		The new model of inter-disciplinary information seeking is represented in terms of three core processes and three levels of contextual interaction in Figure 1 (Foster, 2004: 232).
		The two dimensional model represents one slice of a temporal continuum within which a palette of non-linear behaviour exists, but it is a continuum without fixed stages.
		The model already allows the generation of hypotheses and question development, expansion of the implications of a non-linear perspective: but the implications of the model are necessarily at the beginning of an evolutionary process and will develop through further research, testing, and experimentation using a wide range of methods.
	informationr.net /ir/10-2/paper222.html (7017 words)

	Simple linear regression with PHP, Part 2
		The data-exploration tool you are building implements the statistical decision procedure for a linear model (the T test) and provides summary data that can be used to construct the theoretical and statistical arguments necessary to establish a linear model.
		This means that a linear model is a useful predictor of Y values (better than the mean of the Y values) for the range of X values observed in the study.
		Even though simple linear regression only uses one variable to account for, or predict, the variance in another variable, looking for simple linear relations between all your study variables is often the first step in exploratory data analysis.
	www-106.ibm.com /developerworks/web/library/wa-linphp2 (3844 words)

	Linear model order reduction
		Model Order reduction techniques for linear dynamical systems are developed rather properly, though there are still quite a lot of issues to address.
		The model reduction for such kind of systems is considered in thesis of Tatjana Stykel [2] and [3].
		The goal of the model order reduction is: given a large system in the form (1) or (2), to provide another state-space system in the same form (1) or (2), but of lower order q << n, which approximates (in some sense) input-output relationships for the original system.
	web.mit.edu /mor/Linear_mor.html (971 words)

	General Log-Linear Model
		Furthermore, if more than one stress is present, one could choose to apply a different transformation to each stress to create combination models, similar to the ones discussed in the Temperature-Humidity and Temperature-NonThermal chapters.
		The power of the model and this formulation becomes evident once one realizes that 6,651 unique life-stress relationships are possible (when allowing a maximum of eight stresses).
		When combined with the life distributions available in ALTA 6 PRO, almost 20,000 models can be created.
	www.weibull.com /AccelTestWeb/general_log_linear_model.htm (228 words)

	Linear Recumbent Bicycles - About Linear Recumbent Bicycles
		Linear Manufacturing began building quality aluminum recumbents in Iowa in the mid '80's.
		We purchased the assets of Linear Inc. Our first stem was to re-design the popular Linear LWB model.
		Many of them prefer a Linear LWB or CLWB to the other brands they try, even before they hear the Linear is half the price of some of the others.
	www.linearrecumbent.com /linear_models.htm (530 words)

	MMU - Research Design, Biol Sci Stats and RDGeneral linear model (Site not responding. Last check: 2007-09-10)
		Because the model assumes additive components it is called a linear model, or more specifically a General Linear Model (GLM).
		There is another class of linear models known as Generalised Linear Models.
		In the previous examples the observed values were a linear function of a number of predictors plus a residual term.
	obelia.jde.aca.mmu.ac.uk /rd/linmodel.htm (615 words)

	Good Math, Bad Math : The Categorical Model of Linear Logic
		Linear types are types where referencing the value corresponding to the type consumes it.
		Take the linear implication operator; mix it with the categorical exponent; and what you get still behaves linearly: that is, if "X -o Y"; that is, one X can be consumed to produce one Y, then 2 Xs can be consumed to produce 2 Ys; and N Xs can be consumed to produce N Ys.
		So a linear category behaves cleanly with exponents; t has a linear implication; it has an eval operator (from the fact that it's a cartesian category) to perform the linear implications; it has tensor for producing groups of resources.
	scienceblogs.com /goodmath/2006/07/the_categorical_model_of_linea.php (1114 words)

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