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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]].}}
| | If your computer is running slow, we have probably gone by the different stages of rage plus frustration. Having such a perfect tool like a computer can appear like a curse along with a blessing simultaneously when this arises. It is excellent when it is actually running quickly plus smooth, but then when it begins acting weird and slows technique down, frustration sets in. How can something as fabulous because a computer create a person so mad?<br><br>The PC registry begins to get errors plus fragmented the more you utilize the computer because we enter more information every time, also as make changes in our systems plus setup. When the registry starts to get overloaded plus full of mistakes, a computer might eventually crash. It can be done to fix it on your however, surprisingly dangerous, especially in the event you have no extensive experience inside doing so. Therefore, do NOT even attempt to do this oneself.<br><br>The error is basically a result of issue with Windows Installer package. The Windows Installer is a tool utilized to install, uninstall plus repair the most programs on your computer. Let you discuss a limited factors which helped a lot of people that facing the similar problem.<br><br>If that does not work you need to try and repair the issue with a 'registry cleaner'. What arises on numerous computers is that their registry database becomes damaged and unable to show the computer where the DLL files that it requirements are. Every Windows PC has a central 'registry' database that shops information about all of the DLL files on the computer.<br><br>After which, I also bought the Regtool [http://bestregistrycleanerfix.com/registry-reviver registry reviver] Software, plus it further secure my laptop having system crashes. All my registry problems are fixed, plus I will function peacefully.<br><br>S/w connected error handling - If the blue screen bodily memory dump occurs after the installation of s/w application or a driver it could be which there is system incompatibility. By booting into safe mode plus removing the software we can rapidly fix this error. We could furthermore try out a "system restore" to revert to an earlier state.<br><br>Reboot PC - Just reboot your PC to find when the error is gone. Frequently, rebooting the PC readjusts the internal settings plus software and hence fixes the problem. If it doesn't then move on to follow the instructions below.<br><br>All of these difficulties is conveniently solved by the clean registry. Installing the registry cleaner allows you to employ a PC without worries behind. You will capable to use you program without being afraid which it's going to crash in the center. Our registry cleaner usually fix a host of mistakes on a PC, identifying lost, invalid or corrupt settings in a registry. |
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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> | |
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| ==Definition==
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| The '''logit''' of a number ''p'' between 0 and 1 is given by the formula: | |
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| :<math>\operatorname{logit}(p)=\log\left( \frac{p}{1-p} \right) =\log(p)-\log(1-p)=-\log\left( \frac{1}{p} - 1\right). \!\,</math>
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| 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. | |
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| The [[logistic function|"logistic" function]] of any number <math>\alpha</math> is given by the inverse-logit:
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| :<math>\operatorname{logit}^{-1}(\alpha) = \frac{1}{1 + \operatorname{exp}(-\alpha)} = \frac{\operatorname{exp}(\alpha)}{ \operatorname{exp}(\alpha) + 1}</math>
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| If ''p'' is a [[probability]], then ''p''/(1 − ''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]]: | |
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| :<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>
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| [[Image:Logit.png|thumbnail|right|300px|Plot of logit(''p'') in the domain of 0 to 1, where the base of logarithm is ''e'']]
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| ==History==
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| 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}}
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| ==Uses and properties==
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| * 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]].
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| * The '''logit''' function is the negative of the [[derivative]] of the [[binary entropy function]].
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| * The '''logit''' is also central to the probabilistic [[Rasch model]] for [[measurement]], which has applications in psychological and educational assessment, among other areas.
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| * 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>
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| * 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.
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| == Comparison with probit ==
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| [[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.]]
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| 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:
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| :<math>\Phi(x) = \int_{-\infty}^{x} \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}} \operatorname{d}\!x</math>
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| 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.
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| == See also ==
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| * [[Discrete choice]] on binary logit, multinomial logit, conditional logit, nested logit, mixed logit, exploded logit, and ordered logit
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| * [[Limited dependent variable]]
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| * [[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/>
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| * [[Logit analysis (in marketing)|Logit analysis in marketing]]
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| * [[Multinomial logit]]
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| * [[Perceptron]]
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| * [[Probit]] another function with the same domain and range as the logit
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| * [[Ridit scoring]]
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| * [[Data transformation (statistics)]]
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| == References ==
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| {{More footnotes|date=November 2010}}
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| {{Reflist}}
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| ==Further reading==
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| *{{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}}
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| [[Category:Categorical data]]
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| [[Category:Functions and mappings]]
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If your computer is running slow, we have probably gone by the different stages of rage plus frustration. Having such a perfect tool like a computer can appear like a curse along with a blessing simultaneously when this arises. It is excellent when it is actually running quickly plus smooth, but then when it begins acting weird and slows technique down, frustration sets in. How can something as fabulous because a computer create a person so mad?
The PC registry begins to get errors plus fragmented the more you utilize the computer because we enter more information every time, also as make changes in our systems plus setup. When the registry starts to get overloaded plus full of mistakes, a computer might eventually crash. It can be done to fix it on your however, surprisingly dangerous, especially in the event you have no extensive experience inside doing so. Therefore, do NOT even attempt to do this oneself.
The error is basically a result of issue with Windows Installer package. The Windows Installer is a tool utilized to install, uninstall plus repair the most programs on your computer. Let you discuss a limited factors which helped a lot of people that facing the similar problem.
If that does not work you need to try and repair the issue with a 'registry cleaner'. What arises on numerous computers is that their registry database becomes damaged and unable to show the computer where the DLL files that it requirements are. Every Windows PC has a central 'registry' database that shops information about all of the DLL files on the computer.
After which, I also bought the Regtool registry reviver Software, plus it further secure my laptop having system crashes. All my registry problems are fixed, plus I will function peacefully.
S/w connected error handling - If the blue screen bodily memory dump occurs after the installation of s/w application or a driver it could be which there is system incompatibility. By booting into safe mode plus removing the software we can rapidly fix this error. We could furthermore try out a "system restore" to revert to an earlier state.
Reboot PC - Just reboot your PC to find when the error is gone. Frequently, rebooting the PC readjusts the internal settings plus software and hence fixes the problem. If it doesn't then move on to follow the instructions below.
All of these difficulties is conveniently solved by the clean registry. Installing the registry cleaner allows you to employ a PC without worries behind. You will capable to use you program without being afraid which it's going to crash in the center. Our registry cleaner usually fix a host of mistakes on a PC, identifying lost, invalid or corrupt settings in a registry.