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{{Hatnote|This article discusses the binary logit function only. See [[discrete choice]] for a discussion of [[multinomial logit]], conditional logit, nested logit, [[mixed logit]], exploded logit, and [[ordered logit]]. For the basic regression technique that uses the logit function, see [[logistic regression]].}}
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The '''logit''' ({{IPAc-en|ˈ|l|oʊ|dʒ|ɪ|t}} {{respell|LOH|jit}}) function is the [[inverse function|inverse]] of the [[sigmoid function|sigmoidal]] [[logistic function|"logistic" function]] used in [[mathematics]], especially in [[Data transformation (statistics)|statistics]]. When the function's parameter represents a probability {{mvar|p}}, the logit function gives the '''log-odds''', or the [[logarithm]] of the odds {{mvar|p}}/(1-{{mvar|p}}).<ref>http://itl.nist.gov/div898/software/dataplot/refman2/auxillar/logoddra.htm</ref>
 
==Definition==
 
The '''logit''' of a number ''p'' between 0 and 1 is given by the formula:
 
:<math>\operatorname{logit}(p)=\log\left( \frac{p}{1-p} \right) =\log(p)-\log(1-p)=-\log\left( \frac{1}{p} - 1\right). \!\,</math>
 
The base of the [[logarithm]] function used is of little importance in the present article, as long as it is greater than 1, but the [[natural logarithm]] with base [[e (mathematical constant)|e]] is the one most often used.
 
The [[logistic function|"logistic" function]] of any number <math>\alpha</math> is given by the inverse-logit:
 
:<math>\operatorname{logit}^{-1}(\alpha) = \frac{1}{1 + \operatorname{exp}(-\alpha)} = \frac{\operatorname{exp}(\alpha)}{ \operatorname{exp}(\alpha) + 1}</math>
 
If ''p'' is a [[probability]], then ''p''/(1 &minus; ''p'') is the corresponding [[odds]]; the logit of the probability is the logarithm of the odds. Similarly, the difference between the logits of two probabilities is the logarithm of the [[odds ratio]] (''R''), thus providing a shorthand for writing the correct combination of odds ratios [[additive function|only by adding and subtracting]]:
 
:<math>\operatorname{log}(R)=\log\left( \frac{{p_1}/(1-p_1)}{{p_2}/(1-p_2)} \right) =\log\left( \frac{p_1}{1-p_1} \right) - \log\left(\frac{p_2}{1-p_2}\right)=\operatorname{logit}(p_1)-\operatorname{logit}(p_2). \!\,</math>
 
[[Image:Logit.png|thumbnail|right|300px|Plot of logit(''p'') in the domain of 0 to 1, where the base of logarithm is ''e'']]
 
==History==
The logit model was introduced by [[Joseph Berkson]] in 1944, who coined the term. The term was borrowed by analogy from the very similar [[probit]] model developed by [[Chester Ittner Bliss]] in 1934.<ref name=Cramer2003>{{Cite web|url=http://www.cambridge.org/resources/0521815886/1208_default.pdf|author=J. S. Cramer|year=2003|title=The origins and development of the logit model|publisher=Cambridge UP}}</ref>  [[G. A. Barnard]] in 1949 coined the commonly used term ''log-odds''; the log-odds of an event is the logit of the probability of the event.{{Citation needed|date=March 2009}}
 
==Uses and properties==
 
* The '''logit''' in [[logistic regression]] is a special case of a link function in a [[generalized linear model]]: it is the canonical [[link function]] for the [[Bernoulli distribution]].
* The '''logit''' function is the negative of the [[derivative]] of the [[binary entropy function]].
* The '''logit''' is also central to the probabilistic [[Rasch model]] for [[measurement]], which has applications in psychological and educational assessment, among other areas.
* The '''inverse-logit''' function (i.e., the [[logistic function]]) is also sometimes referred to as the ''expit'' function.<ref>http://www.stat.ucl.ac.be/ISdidactique/Rhelp/library/msm/html/expit.html</ref>
* In '''plant disease epidemiology''' the logit is used to fit the data to a logistic model. With the Gompertz and Monomolecular models all three are known as Richards family models.
 
== Comparison with probit ==
[[File:Logit-probit.svg|right|300px|thumb|Comparison of the [[logit function]] with a scaled probit (i.e. the inverse [[cumulative distribution function|CDF]] of the [[normal distribution]]), comparing <math>\operatorname{logit}(x)</math> vs. <math>\Phi^{-1}(x)/\sqrt{\frac{\pi}{8}}</math>, which makes the slopes the same at the y-origin.]]
 
Closely related to the logit function (and [[logit model]]) are the [[probit function]] and [[probit model]]. The logit and probit are both [[sigmoid function]]s with a domain between 0 and 1, which makes them both [[quantile function]]s — i.e. inverses of the [[cumulative distribution function]] (CDF) of a [[probability distribution]].  In fact, the logit is the quantile function of the [[logistic distribution]], while the probit is the quantile function of the [[normal distribution]]. The probit function is denoted <math>\Phi^{-1}(x)</math>, where <math>\Phi(x)</math> is the CDF of the normal distribution, as just mentioned:
 
:<math>\Phi(x) = \int_{-\infty}^{x} \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}} \operatorname{d}\!x</math>
 
As shown in the graph, the logit and probit functions are extremely similar, particularly when the probit function is scaled so that its slope at y=0 matches the slope of the logit. As a result, [[probit model]]s are sometimes used in place of [[logit model]]s because for certain applications (e.g. in [[Bayesian statistics]]) the implementation is easier.
 
== See also ==
* [[Discrete choice]] on binary logit, multinomial logit, conditional logit, nested logit, mixed logit, exploded logit, and ordered logit
* [[Limited dependent variable]]
* [[Daniel McFadden]], a [[Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel]] winner for development of a particular logit model used in economics<ref name=Cramer2003/>
* [[Logit analysis (in marketing)|Logit analysis in marketing]]
* [[Multinomial logit]]
* [[Perceptron]]
* [[Probit]] another function with the same domain and range as the logit
* [[Ridit scoring]]
* [[Data transformation (statistics)]]
 
== References ==
{{More footnotes|date=November 2010}}
 
{{Reflist}}
 
==Further reading==
*{{cite book|last=Ashton|first=Winifred D.|title=The Logit Transformation: with special reference to its uses in Bioassay|year=1972|publisher=Charles Griffin|isbn=0-85264-212-1|series=Griffin's Statistical Monographs & Courses|volume= 32}}
 
[[Category:Categorical data]]
[[Category:Functions and mappings]]

Revision as of 03:15, 4 March 2014

With thus many weight reduction diets, plans, programs and unusual techniques popping up like popcorn, it's actually getting difficult to identify the number one way to lose fat.

Whatever choice of diet you choose to take, the advice of a doctor or nutritionist is important for your success plus healthy fat loss. If you follow the above mentioned guidelines then the experience is enjoyable plus fruitful. You should have realistic goals set for the fat loss to avoid disillusionment while paying close attention to guarantee we fully understand what are the best diet plans swiftly for females the planet over.

Similar to the 1200 calorie diet plan, a 1500 calorie diet is a diet which limits the amount of calories to be consumed inside a day, to 1500. Two such sample diet plans are provided below inside a tabular form.

Fruits plus greens are the most important things for a healthy diet plus fat loss. Fruits are the method to go when you're craving something sweet, since they contain natural sugars and vitamins which create them healthier than sweet junk foods. A healthy amount of calories originates from fruits as well, and your body requires calories to function. Fruit also contains fiber that works with proteins by helping to break them down and it furthermore keeps you feeling full. So, when you want to eat less, grab some fruit. Vegetables plus fruits both are full of fiber, however greens tend to not have the additional calories plus sugars that fruit has.

The calories which are necessary by the human body are regarding 1200 calories per day. In truth, rather of any of the diets to get rid of fat immediately, I would suggest that we take the menu 1200 calorie diet. This type of diet plan includes a perfect measure of the suggested calories per day and also involves a balance of nutrition. The balance of nutrition means that 75% of the diet involves foods conveniently digested plus 25% includes foods which are not, and are intended to be stored. These foods are stored because fat, several kinds of proteins and carbohydrates, whenever consumed in excessive amounts (over 25%) lead to issues including overweight and weight.

Many of the skin diet is good sense. Fisher encourages fresh fruit and vegetable intake plus the usage of wholegrains plus fish. If you can't stand fish, she recommends linseeds, otherwise well-known as flaxseeds. But, the dietary system moreover includes other goods that are potent skin improvers, including dandelion tea and turmeric. She additionally lists foods to avoid because they can aggravate particular skin conditions. Some of these items, like chocolate and alcohol, will likely not surprise. But, a few of the items on the list of foods might not be thus apparent. As an example, rosacea sufferers could avoid pineapple and strawberries.

We have considered all of the above citations to choose diet medications which function. Our goal is to guide you by acquiring carefully selected good quality fat loss supplements, made of all-natural resources and clinically proven to bring we the greatest results possible. Choose within the best and lose weight with confidence. The trim plus appealing you're possible. Create the research plus slender down the healthy technique with top quality diet supplements.

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