Smooth coarea formula - Revision history

78.53.30.93 at 22:48, 16 April 2014

2014-04-16T22:48:43Z

← Older revision		Revision as of 00:48, 17 April 2014
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	~~In [[statistics]], '''marginal models''' (Heagerty & Zeger, 2000) are a technique for obtaining regression estimates in [[multilevel model]]ing, also called [[hierarchical linear models]]~~.		Hi there. Let me begin by introducing the writer, her title is Sophia Boon but she never truly liked that title. Her family members lives in Ohio but her husband desires them to move. The preferred hobby for him and his children is to play lacross and he'll be beginning some thing else alongside with it. Distributing production has been his profession for some time.<br><br>Here is my weblog :: [http://bigpolis.com/blogs/post/6503 live psychic reading] love [http://modenpeople.co.kr/modn/qna/292291 cheap psychic readings]; [http://conniecolin.com/xe/community/24580 simply click the up coming internet site],
	~~People often want to know~~ the ~~effect of a predictor/explanatory variable ''X''~~, ~~on a response variable ''Y''~~. ~~One way~~ to ~~get an estimate for such effects is through [[regression analysis]].~~

	~~==Why the name marginal model?==~~
	~~In a typical multilevel model, there are level 1 & 2 residuals (R and U variables)~~. The ~~two variables form a [[joint distribution]]~~ for ~~the response variable (<math>Y_{ij}</math>). In a marginal model, we collapse over the level 1 & 2 residuals~~ and ~~thus ''marginalize~~'~~' (see also [[conditional probability]]) the joint distribution into a univariate [[normal distribution]]~~. ~~We then fit the marginal model to data~~.

	~~For example, for the following hierarchical model,~~

	~~:level 1:~~ <~~math~~>~~Y_{ij} = \beta_{0j} + R_{ij}~~<~~/math~~>~~, the residual~~ is ~~<math>R_{ij}<~~/~~math>, and <math>var(R_{ij}) = \sigma^2<~~/~~math>~~

	~~:level 2: <math>\beta_{0j} = \gamma_{00} + U_{0j}<~~/~~math>, the residual is <math>U_{0j}<~~/~~math>, and <math>var(U_{0j}) = \tau_0^2<~~/~~math>~~

	~~Thus, the marginal model is,~~

	:~~<math>Y_{ij} \sim N(\gamma_{00},(\tau_0^2+\sigma^2))<~~/~~math>~~

	~~This model is what is used to fit to data in order to get regression estimates~~.

	~~==References==~~
	~~Heagerty, P~~. ~~J., & Zeger, S. L. (2000). Marginalized multilevel models and likelihood inference. ''Statistical Science, 15(1)'', 1-26.~~

	[~~[Category~~:~~Statistical models~~]]


	~~{{stats-stub}}~~

129.215.5.255 at 10:08, 25 October 2013

2013-10-25T10:08:16Z

← Older revision		Revision as of 12:08, 25 October 2013
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	~~Hi there~~, ~~I am Alyson Boon although it~~ is ~~not~~ the name ~~on my birth certification~~. ~~Office supervising is where her main earnings arrives from~~. ~~For~~ a ~~whilst I~~'~~ve been in Mississippi but now I~~'~~m contemplating other choices~~. ~~To play domino~~ is ~~some thing I really appreciate doing.~~<br><br>~~My web blog clairvoyance - [http~~://~~www~~.~~prograd~~.~~uff~~.~~br/novo/facts-about-growing-greater-organic-garden www~~.~~prograd~~.~~uff~~.br],		In [[statistics]], '''marginal models''' (Heagerty & Zeger, 2000) are a technique for obtaining regression estimates in [[multilevel model]]ing, also called [[hierarchical linear models]].
			People often want to know the effect of a predictor/explanatory variable ''X'', on a response variable ''Y''. One way to get an estimate for such effects is through [[regression analysis]].

			==Why the name marginal model?==
			In a typical multilevel model, there are level 1 & 2 residuals (R and U variables). The two variables form a [[joint distribution]] for the response variable (<math>Y_{ij}</math>). In a marginal model, we collapse over the level 1 & 2 residuals and thus ''marginalize'' (see also [[conditional probability]]) the joint distribution into a univariate [[normal distribution]]. We then fit the marginal model to data.

			For example, for the following hierarchical model,

			:level 1: <math>Y_{ij} = \beta_{0j} + R_{ij}</math>, the residual is <math>R_{ij}</math>, and <math>var(R_{ij}) = \sigma^2</math>

			:level 2: <math>\beta_{0j} = \gamma_{00} + U_{0j}</math>, the residual is <math>U_{0j}</math>, and <math>var(U_{0j}) = \tau_0^2</math>

			Thus, the marginal model is,

			:<math>Y_{ij} \sim N(\gamma_{00},(\tau_0^2+\sigma^2))</math>

			This model is what is used to fit to data in order to get regression estimates.

			==References==
			Heagerty, P. J., & Zeger, S. L. (2000). Marginalized multilevel models and likelihood inference. ''Statistical Science, 15(1)'', 1-26.

			[[Category:Statistical models]]


			{{stats-stub}}

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2012-01-01T03:17:42Z

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Hi there, I am Alyson Boon although it is not the name on my birth certification. Office supervising is where her main earnings arrives from. For a whilst I've been in Mississippi but now I'm contemplating other choices. To play domino is some thing I really appreciate doing.<br><br>My web blog clairvoyance - [http://www.prograd.uff.br/novo/facts-about-growing-greater-organic-garden www.prograd.uff.br],