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Topic: Saturated model

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	Saturated model - Wikipedia, the free encyclopedia
		In mathematical logic, and in particular model theory, a saturated model M is one which realizes as many complete types as may be "reasonably expected" given its size.
		Saturated models exist: for instance, (Q, <) is saturated and the countable random graph is saturated.
		The notion of saturated model is dual to the notion of prime model in the following way: let T be a countable theory in a first-order language (that is, a set of mutually consistent sentences in that language) and let P be a prime model of T.
	en.wikipedia.org /wiki/Saturated_model (694 words)

	Type (model theory) - Wikipedia, the free encyclopedia
		In model theory, a type is a set of formulae in first-order logic such that all the formulae could be consistent descriptions of a certain element (or several elements) of the model.
		A model that realizes the maximum possible variety of types is called a saturated model, and the ultrapower construction provides one way of producing saturated models.
		The field of algebraic numbers is a model omitting this type, and the algebraic closure of any transcendental extension of the rationals is a model realizing this type.
	en.wikipedia.org /wiki/Type_(model_theory) (866 words)

	Saturated Model
		The -2 log likelihood of the saturated model is needed to compute the deviance of a model.
		The saturated model is loosely defined as the model where the number of parameters equals the number of data points.
		These models assume that an animal can enter the study on any occasion, so the saturated model is computed with the parameter estimate as the number of animals with the encounter history divided by the total number of animals encountered.
	www.cnr.colostate.edu /~gwhite/mark/markhelp/saturatedmodel.htm (573 words)

	Information Technology Services (Site not responding. Last check: 2007-10-09)
		AMOS performs this operation for two distinct models: the first model is a saturated model in which the number of estimated parameters is equal to the number of known inputs: means, variances, and covariances.
		This model is saturated: There are an equal number of parameters estimated as there are known inputs to the analysis, so the chi-square test of model fit output by AMOS is 0.
		The nested model comparison of the third to the second model tests whether the mean of X is equal to the mean of Y and that the variance of X is equal to the variance of Y, simultaneously.
	www.utexas.edu /its/rc/answers/amos/amos5.html (1594 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.
		A saturated log-linear model is one which incorporates all possible effects: a 1-way effect for each variable, all 2-way effects for models with two or more variables, all 3-way effects for models with three or more variables, and so on..
		This means this model is not significantly different from the saturated model in accounting for the distribution of data in the table.
	www2.chass.ncsu.edu /garson/pa765/logit.htm (14783 words)

	PA 765: AMOS Output for Structural Equation Modeling
		The "independence model" is the model in which variables are assumed to be uncorrelated with the dependent(s), so if the fit for "your model" is no better than for the "independence model," then your model should certainly be rejected.
		The "saturated model" is one with no constraints and will always fit any data perfectly, so normally your model will have a measure of fit between the saturated and independence models.
		PRATIO is the parsimony ratio, which is the ratio of the degrees of freedom in your model to degrees of freedom in the independence (null) model.
	www2.chass.ncsu.edu /garson/pa765/semAMOS1.htm (2450 words)

	ipedia.com: Model theory Article (Site not responding. Last check: 2007-10-09)
		Model theory is then concerned with what is provable within given mathematical systems, and how these systems relate to each other.
		Completeness in model theory is defined as the property that every statement in a language or its opposite is provable from some theory.
		Model theory is usually concerned with first order logic and many important results (such as the compactness theorem) fail in second order logic or other alternatives.
	www.ipedia.com /model_theory.html (833 words)

	Effect of Liquefaction on Lateral Response of Piles by Centrifuge...
		An end-bearing model pile, with its tip fixed to the bottom of the box, is surrounded by saturated sand having a relative density, Dr Seismic shaking of limited duration is applied in-flight to the base of the rigid container to induce an excess pore pressure in the sand.
		The purpose of this centrifuge model is to establish the effect of excess pore pressure in the sand on the p-y curves at different depths along the pile.
		After saturation, the loading unit is installed on the model, the computer-operated actuator locks the pile head electronically in a neutral position and a zero slope boundary condition at the pile head during the test is secured.
	mceer.buffalo.edu /research/HighwayPrj/bullarticles/Jan95Vol9No1Pg8.asp (2161 words)

	[No title]
		They model the means of cell counts in contingency tables by describing the association patterns among a set of categorical variables without specifying any variable as a response (dependent) variable.
		It compares the specified model with the saturated model and is equal to -2 times the difference of the log likelihoods for the specified and the saturated models.
		Since the Likelihood Ratio statistic compares the model without the third order interaction (xyz) with the saturated model, it is the likelihood ratio test for the significance of xyz, that is, it tests the same hypothesis as the Wald test for xyz in the previous "Maximum Likelihood Analysis of Variance" table (for the saturated model).
	www.uky.edu /ComputingCenter/SSTARS/LoglinearModelAnalysisinSASandSPSS.htm (2045 words)

	The saturated model
		This model is not interesting per se, because the goal of any analysis to build a model as parsimonious as possible (using a minimum number of parameters) that satisfactorily fit a set of data.
		It is nonetheless useful as a reference model; since it completely accounts for the "variance" of the matrix, subsequent models are to compared with it.
		The smaller the difference between a specified model and this one, the better the fit (and conversely).
	tecfa.unige.ch /~lemay/thesis/THX-Doctorat/node236.html (164 words)

	When (Site not responding. Last check: 2007-10-09)
		Such a model is called a saturated model as it is as completely full as possible (saturated) with parameters.
		Such a model is sometimes useful as it serves as a benchmark to quantify how well a simpler model (one with fewer parameters) fits the data.
		A saturated model by itself isn't biologically very useful; the whole intent of a "model" is to achieve some synthetic simplification of set of observations (data points), whereas a saturated model isn't a simplification and provides no greater interpretability than just looking at the raw data points themselves.
	www.absc.usgs.gov /staff/WTEB/jschmutz/joel/snowfall_saturated.htm (196 words)

	PlanetMath: deviance
		to be served as a base model in case when more than one models are being assessed.
		are the null model and the saturated model.
		Cross-references: degrees, statistic, hypothesis testing, distribution, regression models, squares, sum, residual, maximum likelihood estimate, observations, independent, identity, general linear model, normal, vector, MLE, log-likelihood function, outcome, base, difference, link function, mean, model, one way, explanatory variable, response variable, generalized linear model
	planetmath.org /encyclopedia/Deviance.html (294 words)

	Selection of Models
		Among the two-group models we distinguish further between models of the PCFA type, that is models with predictors and criteria.
		The first aspect concerns the model for the predictors, the second aspect concerns the model for the criteria, and the third aspect concerns the model for the dependence of the criteria on the predictors.
		Possible models are marked with a ``x'' and models that are excluded because of the variables’ sampling characteristics or status are marked with a ``-''.
	www.dgps.de /fachgruppen/methoden/mpr-online/issue5/art5/node6.html (948 words)

	Ed231C: Loglinear Regression Models
		This model accounts for the association between cigarettes and marijuana controlling for alochol and for the association between alcohol and marijuana controlling for cigarettes.
		In this model all three pairs of variables are conditionally dependent on the third variable and is denoted (am,cm,ac).
		The constant in the glm model is the log of the expected frequency for cell a=0, c=0, m=0, thus exp(4.172538) = 64.879909.
	www.gseis.ucla.edu /courses/ed231c/notes3/loglin.html (950 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The difference between -2LL values for two models is a likelihood ratio test statistic and this is distributed approximately as the chi-squared distribution with degrees of freedom (df) equal to the difference in number of parameters between the two models.
		This shows that the final model for stage 1 is not a significantly worse fit to the data than a saturated model with 8 more parameters (8 more parameters in the saturated model explain why these test statistics have 8 df).
		The saturated model treats the covariate as if it were a factor with 4 levels, thus requiring 3 (=4-1) parameters compared with 1 parameter for each effect including the covariate.
	homepages.gold.ac.uk /aphome/answers2002.doc (5843 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The saturated SEM model would have the cognitive style variables, independence and interdependence, predicted by sex (male 1, female 2), and ethnic (Anglo 1, Asian 2) with correlated residuals.
		The mediation model suggests that some of the direct paths in the saturated model are not needed.
		On the basis of the saturated model, eliminate paths that seem to be no different from zero.
	www.nyu.edu /classes/shrout/G89-2247/04EX4.doc (481 words)

	Example 29.3: Modeling Long Seasonal Patterns
		The table in Figure 29.3.1 shows the fit statistics for this model, and the plot in Figure 29.3.2 shows the fit of the model on the withheld data.
		This model fits the data well; however, it takes a considerable amount of time to estimate because the dimension of the state vector in the underlying state space model is large, about 60 (see "Details").
		More importantly, this model does not offer any insight into the structure of the particular seasonal pattern present at this call center; for example, it may be possible that a similar calling pattern may repeat during each day of the week except for different mean number of calls for different days of the week.
	support.sas.com /91doc/getDoc/etsug.hlp/ucm_sect38.htm (684 words)

	[No title]
		A question as to whether the saturated zone can be considered to be well-mixed in terms of chemistry could not be answered, primarily because boreholes were pumped over large intervals for sampling, and the appearance of uniform compositions may be an artifact of the manner in which the samples were acquired.
		Saturated zone studies would be expected to contribute to identification of the shortest flow paths to the accessible environment.
		Saturated zone models could also be used in a transient mode to simulate the progressive lowering of the regional potentiometric surface during Quaternary time, as inferred by Ike Winograd some years ago, from paleohydrologic evidence.
	www.ocrwm.doe.gov /qa/reports/fy96/ym96a012.htm (6151 words)

	[No title]
		The finite difference method is used to approximate the flow equation, which is developed by combining the law of conservation of fluid mass with a nonlinear form of Darcy's equation, and the advection-dispersion equation.
		Saturated hydraulic conductivities are evaluated at cell boundaries by using distance-weighted harmonic means.
		DATA REQUIREMENTS A conceptual model of the geometry and boundaries of the region to be simulated is of prime importance.
	esm.versar.com /emlimes/desc/vs2dt.txt (700 words)

	comments about Ch. 5 of H & L
		It seems like it can be described as a difference in log-likelihoods: the log-likelihood of the saturated model minus the log-likelihood of the fitted model under consideration.
		P. 13 indicates that the likelihood of the saturated model is 1, which can only be if each factor in the likelihood product is 1, which can only be if each success has an associated probability of 1 and each failure has an associated probability of 1.
		There are 628 cases in all, so if one fit a model to all but 5 of them, it could be thought to be good about 99% of the time.
	mason.gmu.edu /~csutton/HL5.html (1143 words)

	[No title]
		Since this is a hierarchical model, all lowerorder effects included in the retained higherorder effects are also retained, that is, the model also includes the effects of Plattr x Deattr, Plattr x Verdict, Deattr x Verdict, Plattr, Deattr, Verdict, and Gender.
		When deciding between any two particular models, we may test the significance of their differences if and only if one is nested within the other.
		Of course, each model is automatically compared to the fully saturated model with the goodnessoffit (2 SPSS gives us, and we don't want to accept a model that is significantly bad in fit.
	core.ecu.edu /psyc/wuenschk/MV/LogLin/Logit.doc (2411 words)

	Summary of Lehman & Associates Studies
		In order to evaluate an alternative conceptual model of saturated zone flow for the area around and including Yucca Mountain based on previous work done by LLA and other State of Nevada researchers, a numerical model was assembled and tested.
		The implications of this conceptual model are significant.
		The conceptual model emphasizes focused flow paths in the saturated zone along structural zones and weakness.
	www.state.nv.us /nucwaste/yucca/lehman01.htm (1775 words)

	Model Theory of Fields: Suggested Reading (Site not responding. Last check: 2007-10-09)
		A survey on the model theory of the real numbers with exponentiation that appeared in the Notices of the AMS.
		D. Marker, An introduction to the Model Theory of Fields.
		An introduction to geometric model theory and Hrushovski's proof of the Mordell-Lang conjecture.
	www.math.uic.edu /~marker/mtf-reading.html (125 words)

	Stata FAQ: How to generate saturated model in a loglinear model using DESMAT?
		Sometimes, we need to generate a saturated model.
		One thing that one often wants to do after running a saturated model is to compare it with other models.
		We can issue the command lrtest to save the likelihood ratio for the saturated model after the saturated model is created.
	www.ats.ucla.edu /stat/stata/faq/desmat_saturated_Model.htm (552 words)

	Types of models (Site not responding. Last check: 2007-10-09)
		As in analysis of variance the degrees of freedom have to be computed.
		Then the constraints imposed on the model reduce the degrees of freedom.
		Three types of model are defined according to the constraints: the saturated model, the independence model and the intermediary non-saturated model.
	tecfa.unige.ch /~lemay/thesis/THX-Doctorat/node235.html (46 words)

	Logistic Regr - 5 comments
		First, only the first row of the table is represented as comparing the current model with a saturated model in the User's Guide.
		This is not true for the situation represented in the SPSS LOGISTIC REGRESSION procedure, in which you have generally as many cells in your design as cases, because the approximation there is based on asymptotics as the number of cases in a cell becomes large.
		The difference between two nested models involving some parameters is indeed chi square distributed on df equal to the number of parameters by which the two models differ.
	www.pitt.edu /~wpilib/statfaq/97logis.html (1551 words)

	Benoît Mariou
		In the early eighties, answering a question of A. Macintyre, J.H. Schmerl ([1]) proved that every countable recursively saturated structure, equipped with a function ß encoding the finite functions, is the ß-closure of an infinite indiscernible sequence.
		This result implies that every countably saturated structure, in a countable but not necessarily recursive language, is an Ehrenfeucht-Mostowski model, by which we mean that the structure expands, in a countable language, to the Skolem hull of an infinite indiscernible sequence (in the new language).
		More recently, D. Lascar ([2]) showed that the saturated model of cardinality aleph1 of an omega-stable theory is also an Ehrenfeucht-Mostowski model.
	www.logique.jussieu.fr /www.mariou/abstract1.html (276 words)

	PC-Progress Discussion Forums
		I mean i create tank model (unsaturated-saturated model) for studying movement of heavy metal when it leak from the containment from topsoil to groundwater and i want to set groundwater flow have a slope 0.001.
		Kd should be the same in the unsaturated and saturated zone (I think).
		This is because the wetted surface area is the same in the unsaturated and saturated zone (there is always some small film of water at soil surface).
	www.pc-progress.cz /_forum/topic.asp?TOPIC_ID=433 (361 words)

	Example 22.9: Repeated Measures, Two Repeated Measurement Factors
		For the initial model, the response functions are marginal probabilities, and the repeated measurement factors are Time and Treatment.
		The analysis of variance table for the reduced model (Output 22.9.8) shows that the model fits (since the Residual is nonsignificant) and that the treatment effect is significant.
		The ANOVA table shows that an additive model fits, that there is a significant effect of time, and that the sensitivity is significantly different from the specificity.
	www.asu.edu /sas/sasdoc/sashtml/stat/chap22/sect48.htm (504 words)

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